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S0022-5193(16)30423-4 http://dx.doi.org/10.1016/j.jtbi.2016.12.014 YJTBI8897

To appear in: Journal of Theoretical Biology Received date: 25 August 2016 Revised date: 13 December 2016 Accepted date: 17 December 2016 Cite this article as: Yi Jing, Xia Wang, Sanyi Tang and Jianhong Wu, Data informed analysis of 2014 dengue fever outbreak in Guangzhou: impact of multiple environmental factors and vector control, Journal of Theoretical Biology, http://dx.doi.org/10.1016/j.jtbi.2016.12.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Data informed analysis of 2014 dengue fever outbreak in Guangzhou: impact of multiple environmental factors and vector control Yi Jinga , Xia Wanga,∗, Sanyi Tanga , Jianhong Wub a

School of Mathematics and Information Science, Shaanxi Normal University, Xi’an, 710062, P.R.China b Centre for Disease Modelling, York Institute for Health Research, York University, Toronto, Ontario, Canada

Abstract Epidemics of dengue fever in China were reported before 1940 and the outbreak of dengue fever in Guangdong province in 2014 is the most serious so far. The important question is what factors account for this serious outbreak, and how to evaluate the sensitivity of the multiple factors including weather variables and human actions on the dengue disease. Therefore, according to the relations among the temperature (daily mean temperature (DMT) and diurnal temperature range (DTR)), vector parameters and reproduction number we have proposed the analytical formula for the relative vector’s capacity and eﬀective reproduction number, and then we have the formula for the likelihood function by employing the generation interval-informed method. This allows us to estimate the unknown vector parameters by the maximum likelihood method and carry out the sensitivity analysis. The correlations between the density of mosquito vectors (the Breteau index (BI) , the adult mosquito density) and the daily newly reported cases of four diﬀerent districts of Guangzhou city have been studied by using the Pearson correlation and cross-correlation analyses. Our ﬁndings indicate that both the BI and the adult mosquito density are statistically signiﬁcantly correlated with the daily newly reported cases, and the vector parameters are closely related to the ∗

Corresponding author. Tel.: +86 (29)85310232. Email addresses: [email protected] (Xia Wang), [email protected], [email protected] (Sanyi Tang)

Preprint submitted to Journal of Theoretical Biology

December 20, 2016

DMT and DTR with relative complex relationships, which inﬂuence the eﬀective reproduction number comprehensively. Moreover, the trend of the eﬀective reproduction number is consistent with daily newly reported cases, which conﬁrms the eﬀectiveness of the government control measures. Sensitivity analysis results indicate that the temperature can be either an eﬀective barrier or a facilitator of vector-borne diseases, and consequently weather variable may result in complexity of dengue disease control. Keywords: Vector-borne disease; Temperature; Intervention; Breteau index; Reproduction number 1. Introduction Dengue fever is an acute infectious disease caused by one of four closely related while antigenically distinct virus serotypes (DEN-1, DEN-2, DEN-3 and DEN-4) of the genus Flavivirus (Gubler, 1998). The virus is transmitted to humans by Aedes 5

aegypti and Ae.albopictus primarily, and dengue fever is regarded as one of the world’s most widespread vector-borne diseases (Brady et al., 2012; Bhatt et al., 2013). This disease is spreading mainly in tropical and subtropical regions (Liu-Helmersson et al., 2014). Epidemics of dengue fever in China were reported before 1940. There has been a

10

long period, 1940-1977, when the epidemic was unreported until 1978 when a sudden outbreak (DEN-4) took place in the city of Foshan of the Guangdong Province (Qiu et al., 1993) and spread to seven adjacent counties and cities with a total of 22,122 cases, including 16 fatalities (Guan et al., 2000). Since then, outbreaks or epidemics of dengue fever occurred frequently in southern mainland

15

China, including the provinces Guangdong, Guangxi, Hainan, Fujian and Zhejiang provinces. The outbreak in the Guangdong province in 2014 was the most serious in China, with 41,155 dengue fever cases conﬁrmed by clinical and laboratory diagnoses as of October 27th, 2014, according to the Guangdong provincial Health and Family Planning Commission (Ramzy, 2014).

20

Weather and climate conditions have been reported to be important factors in 2

determining mosquito behavior and the eﬀectiveness of dengue virus transmission (Liu-Helmersson et al., 2014). Several studies have examined the relationship between the meteorological factors and dengue spread. These studies have been conducted in multiple settings and using several qualitative techniques including 25

mathematical modelling and simulations, cross correlation and time-series analysis (Burattini et al., 2008; Chadee et al., 2007; Chowell et al., 2006; Depradine et al., 2004; Wu et al., 2007). Results of these studies indicate that dengue spread is climate sensitive, and in particular the mosquito density and average temperature play a critical role in dengue fever transmission in Guangzhou (Shen et al., 2015;

30

Lu et al., 2009). Other studies found that global trade, increasing population mobility/travel, crowded urban living conditions, global warming, virus evolution and ineﬀective vector-control strategies increase the risk of dengue spread globally (Guzman et al., 2002; Simmons et al., 2012). Moreover, imported dengue fever cases and mosquito density play a critical role in local dengue fever transmission,

35

together with weather variables (Sang et al., 2014, 2015; Cheng et al., 2016). Global warming, widespread vectors, frequent population migration, and population growth have contributed to the spread of the dengue fever, making it a serious threat to public health in China (Fan et al., 1989). Geographically, Guangzhou is the major epidemic city in China, and more than

40

80% of dengue cases were reported. Importantly, what we want to know is that which factors were accounted for the most serious outbreak in 2014. Based on the data sets including the Breteau index (BI), the adult mosquito density, the daily newly reported cases, daily mean temperature (DMT) and diurnal temperature range (DTR), we have employed multiple statistical methods such as the

45

correlation analysis and likelihood based estimation to investigate the relations among the BI, adult mosquito density and daily newly reported cases, and to determine the unknown parameters related to the vector population, which allow us to address the eﬀects of DMT and DTR on the interesting parameters and consequently help us to understand how the temperature changes inﬂuence the

50

outbreak of dengue fever. 3

Moreover, during the 2014 dengue outbreak in Guangdong province, a series of measures were implemented to control the outbreak of dengue disease, of which killing mosquito was a main component. In particular, every Friday afternoon from 5 to 6 o’clock was chosen as the ﬁxed time to carry out the synchronized 55

action of killing mosquito. October 1st is a national holiday and there was huge human population mobility, so the governments enhanced control strategies and the campaign of killing mosquito started on October 3rd (Friday), and subsequently in the afternoon of every Friday until October 24th. Therefore, based on the relations between the relative vectorial capacity and basic reproduction

60

number, we estimate the eﬀective reproduction number which is a function of time rather than the basic reproduction number (Diekmann et al., 1990). In fact, when an epidemic starts in a partially susceptible population or control measures of the disease have been implemented, it is more convenient to work with the eﬀective reproductive number, R0 (t), deﬁned as the actual average number of

65

secondary cases per primary case at time t (t > 0). The value of R0 (t) is an indication of the severity of the epidemic as time development, and gives information about the measures needed to control the disease (Pinho et al., 2010; Chowell et al., 2007). Therefore, precise estimation of R0 (t) is of importance for outbreak evaluation and management, and R0 (t) shows time-dependent variation

70

with the decline in susceptible individuals (intrinsic factors) and with the implementation of control measures (extrinsic factors). It follows that the estimation and sensitivity analysis for R0 with respect to the key parameters can help us to reveal the important roles of temperature variations and human actions. Thus, in order to investigate the development of the epidemic and the impact of

75

temperature variation on the transmission of the disease, we estimated R0 (t) of each district in Guangzhou city from time period September 22nd to October 30th, 2014. The organization of this paper is as follows. We initially introduced the relative data sets, which consist the outbreak data of Guangzhou, the mosquito densities

80

and the weather data during the period of the outbreak. Next, Pearson correlation 4

and cross-correlation analyses were employed to show how strong the correlation is between the mosquito density and the daily newly reported cases, and how they aﬀect each other. Thirdly, we proposed a likelihood function and then estimated the vector parameters with the method of maximum likelihood estimators (MLEs). 85

Further, the unknown vector parameters and the eﬀective reproduction number R0 (t) during the period of the outbreak have been estimated. Finally, the eﬀects of control measures on the dengue disease have been discussed by analysing the variation tendency of the R0 (t), which could help us to propose more eﬀective programmes for the epidemic prevention and control.

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2. Materials and methods 2.1. Study area Guangzhou, the capital city of Guangdong province, is situated in the southcentral of the Guangdong Province and has a humid subtropical climate inﬂuenced by the Asian monsoon. It has an average annual temperature of 21.9◦ C,

95

with the highest DMT (33.0 − 34.9◦ C) observed between July and August and the lowest DMT (6.5 − 12.1◦ C) observed between January and February. The annual average rainfall ranges from 1370-2353 mm. Summers in Guangzhou are wet with relatively high temperature and a relatively high humidity index, both being ideal for the dissemination and growth of the vector of dengue fever-Aedes.

100

Guangzhou consists of 10 districts and 2 satellite cities. For comparison reason, four districts named Haizhu district, Tianhe district, Huangpu district, Zengcheng district are chosen as the study areas. Note that the scale of the epidemic for those four districts had great diﬀerences, and we are interested in what accounted for the diﬀerent scale of the outbreak of these four districts. Therefore, unless otherwise

105

stated, as an example the Haizhu district has been chosen to show the main results in the main text due to Haizhu district is the most serious district among the four districts, and results of other three districts are shown in the Appendix.

5

2.2. Data collection 2.2.1. Mosquito density 110

Conventional surveillance methods for Aedes larval indices, used to describe the mosquito density, have been used systematically in Guangzhou since 2002(Shen et al., 2015). The BI surveillance data, the common index for Aedes density surveillance, was collected in all 12 districts in Guangzhou during the study period. From each district, one to three streets were selected as the BI

115

monitoring points and containers in each of the more than 50 selected houses were checked daily. BI was calculated according to the number of positive containers containing mosquito egg or mosquito larvae per 100 houses inspected. Adult mosquitos were caught using the artiﬁcial mosquito methods, and the adult mosquito density means the number of adult mosquitos at each monitoring point

120

every artiﬁcial hour. The accumulated cases exceeded 6000 by September 21, 2014, after which the Guangzhou CDC began to report the density of mosquito vectors for each district (ﬁrst reporting day was September 22, 2014). Therefore, the data sets we use for the density of mosquito vectors in each of the 12 districts cover the period of

125

09.22 − 10.30, 2014 and these include the BI and adult mosquito density. The density of mosquito vectors in the Haizhu district is shown in Fig.1(A) and (B), and similar data sets for other three districts are listed in the Appendix. 2.2.2. Dengue fever case data Dengue fever has been declared as a legally notiﬁable communicable disease in

130

China since 1989. Therefore, the data sets about the dengue cases can be obtained from the surveillance system of Guangzhou CDC. Therefore, the daily newly reported cases and accumulated number of cases for the 12 districts during the period of 9.22 − 10.30, 2014 can be obtained. Thus, the prevalence (daily newly reported cases per 100,000 person) of each district could be calculated. The daily

135

newly reported cases and the prevalence (/100,000 person) in the Haizhu district during this period are shown in Fig.1(C) and (D), and those in other three districts are listed in the Appendix. 6

2.2.3. Weather data To study the inﬂuence of DMT and DTR on the transmission of dengue fever, 140

we obtained daily historical maximum and minimum temperatures for the 12 districts from China Weather Network, and calculate the respective DMT and the DTR. We also calculate the temperature at any time point within a day by assuming that there is a sinusoidal hourly temperature variation between the two extremes. The daily maximum (red line) and minimum (blue line) temperatures in

145

the Haizhu district are shown in Fig.2, and those in the other three districts are listed in the Appendix. 2.3. Methods for data analysis Let A denote the adult mosquito density, B the BI, and N the daily newly reported cases. We use Pearson correlation (Huang et al., 2011; Taylor, 1990) and

150

cross-correlation analyses (Huang et al., 2011; Sampei et al., 2009; William, 2006; Zhao et al., 2011) to examine the statistical relationships among B, A and N for each district during the period of 9.22-10.30, 2014. Pearson correlation analysis is conducted using SPSS software (version 19.0, SPSS Inc.) to reveal a statistically signiﬁcant correlation between the density of mosquito vectors and the daily newly

155

reported cases. As time lags between the density of mosquito vectors and the daily newly reported cases might exist and these delays might have played a key role in their correlation, we also carry out a spectral analysis technique for cross-correlation analysis to investigate casual interactions over time between two processes, to detect statistical signiﬁcance and causal interactions in the

160

relationship between the density of mosquito vectors and the daily newly reported cases in each district. Then the association between the density of mosquito vectors and the daily newly reported cases becomes evident. 2.4. Likelihood-based method for parameter estimation Vectorial capacity, a key index for epidemic potential, describes a vector’s ability to spread disease among humans and takes the host, virus, and vector interactions into account (Garrett-Jones, 1964; Liu-Helmersson, 2012). In Ross-McDonald 7

(Anderson et al., 1991), the relative vectorial capacity (Rvc ) is deﬁned as the vectorial capacity relative to the vector-to-human population ratio. Therefore, a higher Rvc indicates higher potential for a dengue epidemic. It is known that Rvc can be aﬀected directly by the weather conditions as each parameter involved in calculating the Rvc depends on DMT (Lambrechts et al., 2011; Scott et al., 2000; Yang et al., 2009; Focks et al., 1995) and DTR. The relative vectorial capacity (Rvc ), according to (Liu-Helmersson et al., 2014), can be expressed as Rvc = a2 bh bm exp(−μm n)/μm , where the parameter a is the average daily vector biting rate (the average number 165

of mosquito bites per person per mosquito per day); bh represents the probability of vector to human transmission per bite; bm is the probability of human to vector infection per bite; n is the duration of the extrinsic incubation period (EIP); and μm is the vector mortality rate. Here, we estimated relevant vector parameters to estimate Rvc and the eﬀective reproduction number. Let x be the DMT and y the DTR, and assume that there is a sinusoidal hourly temperature variation between the two extremes (x ± y/2) within a period of 24 hours. Further, we divide one day into 48 equal intervals and denote the temperature on each time point ti by Tti . The relationship between the temperature and aforementioned parameters in the above calculation of Rvc are based on development results from laboratory studies which can be derived from the peer-reviewed literatures(Liu-Helmersson et al., 2014; Brady et al., 2014; Lambrechts et al., 2011; Scott et al., 2000; Yang et al., 2009; Focks et al., 1995). In particular, the vector biting rate, the probability of vector to human transmission per bite, the probability of human to vector infection per bite, the duration of the EIP and the vector mortality rate at each time point, denoted as

8

a , bh , bm , n and μm respectively, can be calculated as follows: a (Tti )

= a1 Tti + a2 , 12.4 ≤ Tti ≤ 32, bh (Tti ) = a3 (Tti )(Tti − a4 ) a5 − Tti , 12.286 ≤ Tti ≤ 32.461, ⎧ ⎪ ⎨ a11 (Tti ) − a12 , 12.4 ≤ Tti ≤ 26.1, bm (Tti ) = ⎪ ⎩ 1, 26.1 < Tti ≤ 32.5, n (Tti )

= a13 + exp(a14 − a15 Tti ),

μm (Tti ) = a6 + a7 Tti + a8 Tt2i + a9 Tt3i + a10 Tt4i , where Tti

=

y 2

−6 sin( ti12 π) + x, ti = 0.5, 1, 1.5, . . . , 24, i = 1, 2, . . . , 48.

Taking the averages of a , bh , bm , n and μm over the 48 time points, the vector biting rate, the probability of vector to human transmission per bite, the probability of human to vector infection per bite, the duration of the EIP and the vector mortality rate per day (i.e. a, bh , bm , n and μm ) = a1 x + a2 , 12.4 ≤ x ≤ 32, bh (x, y) = ( 48 i=1 a3 (Tti )((Tti ) − a4 ) a5 − (Tti ))/48, 12.286 ≤ (Tti ) ≤ 32.461, bm (x, y) = ( 48 i=1 bm (Tti ))/48, n(x, y) = ( 48 i=1 (a13 + exp(a14 − a15 Tti )))/48, 48 μm (x, y) = ( i=1 (a6 + a7 Tti + a8 Tt2i + a9 Tt3i + a10 Tt4i ))/48, a(x, y)

can be obtained. Substituting these expressions of parameters into the expression of Rvc , we obtain Rvc (x, y) = a2 (x, y)bh (x, y)bm (x, y) exp(−μm (x, y)n(x, y))/μm (x, y). Since the basic reproduction number R0 represents the number of new cases generated by one typical infectious person during his/her infectious period (Th ) when introduced into a totally susceptible population, and since the vectorial capacity (Vc ) represents the daily reproduction number (Garrett-Jones, 1964; 9

Liu-Helmersson, 2012; Anderson et al., 1991), we have that V c and Rvc are related to R0 as follows V c = R0 /Th and Rvc = V c/m = R0 /(Th m), from which it follows R0 = Rvc Th m. Consequently, R0 is a function of the six vector parameters a, bh , bm , μm , n, m. These parameters can be estimated using the data sets described above. To estimate these parameters, we use the likelihood-based method and the generation interval-informed method (White et al., 2008). The likelihood function is given by likf unction =

39 exp(−φt )φNt t

t=1

where φt = R0 (t)

min(t,k) j=1

Γ(Nt + 1)

,

pj Nt−j ,

R0 (t) = Rvc (t)Th m(t), Rvc (t) = a2 (t)bh (t)bm (t) exp(−μm (t)n(t))/μm (t), m(t) = a16 A(t)/Nh . 170

In the above formulation, the parameter k is the maximum value of the serial interval (the sum of the mosquito’s EIP and the incubation period, both being 4 − 10 days(WHO, 2015)); Γ(x) is the gamma function; N = {N1 , N2 , . . . , N39 }, and Nt the daily newly reported cases on day t, 1 ≤ t ≤ 39; pj is the probability function for the generation interval on day j which is assumed to follow a gamma

175

distribution with mean 14 and variance 2. More discussions are summarized in Table 1. We also calculate the Wald conﬁdence intervals (Azzalini, 1996; Pawitan, 2001) of these estimated parameters using the maximum likelihood estimates (MLEs) method. Other parameters in Table 2 are based on published studies cited. For example, 10

180

a4 , a5 in bh can be ﬁxed as 12.286 and 32.461 respectively ﬁrst and then we can ﬁx a3 as 0.001044. More detailed discussions on the choice of those parameters can be found in (Liu-Helmersson et al., 2014) and references therein. In our simulations and estimations, we also ﬁx μm = a6 and a7 = a8 = a9 = a10 = 0. The infectious period of dengue (Th ) is between 4 and 12

185

days (WHO, 2015) and is thus ﬁxed to 5 days, following (Nishiura et al., 2007). Further, we base on the reference (WHO, 2015) to assume the maximum value of the serial interval k is k = 20 here. On the other hand, Nh for each district can be obtained from the statistic information network of Guangzhou, shown in Table 3. Since there was very few death cases reported, we ignore the dengue induced

190

mortality rate and consider the total population of each district ﬁxed during the 2014 outbreak. 3. Results 3.1. Correlation analysis To overcome irregular reporting of BI and adult mosquito density, we generate

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these values on each day by using the cubic spline interpolation method. The resulted BI and density of adult mosquito and daily newly reported cases in the Haizhu district are shown in Fig.1, data for other districts are shown in the Appendix. The Pearson correlation analysis results about the association between the

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density of mosquito vectors (the BI, the adult mosquito density) and the daily newly reported cases in the Haizhu district are summarized in Table 4. These results show that both BI and adult mosquito density are statistically signiﬁcantly correlated with the daily newly reported cases in the Haizhu district (r = 0.619, p < 0.01, and r = 0.537, p < 0.01, respectively). Note that the data of

205

BI and adult mosquito density are collected from diﬀerent monitoring points and the adult mosquito control eﬀects were diﬀerent in each region. Consequently, we observe naturally a relatively weak correlation (r = 0.38, p < 0.05) between BI and adult mosquito density in Table 4. 11

We further calculate the cross-correlation function (CCF) between the density of 210

mosquito vectors and the daily newly reported cases and this function is shown in Fig.3. This reveals that there are statistically signiﬁcant cross-correlation between BI versus daily newly reported cases and between adult mosquito density versus daily newly reported cases with lags ranging from -4 to 7 days, and -1 to 6 days, respectively. The result also indicates that there exists closely signiﬁcant

215

cross-correlation between BI and adult mosquito density at lags ranging from -7 to 2 days. Therefore, there exist a feedback relationship and contemporaneous relationships between mosquito density and daily newly reported cases, and between BI and the adult mosquito density. We also observe that the local maximal cross correlation coeﬃcient exceeds 0.5 (moderately or highly correlated)

220

at the time lags of 0, 5, 1 days, respectively. The correlation analyses between the density of mosquito vectors and the daily newly reported cases for other three districts are shown in the Appendix. 3.2. Parameter estimations Based on the above discussions, the unknown parameters need to be estimated

225

from data are a1 , a2 , a6 , a11 , a12 , a13 , a14 and a15 . Using the aforementioned likelihood function, MLE and Wald conﬁdence interval methods, we estimate these eight unknown parameters and their 95% Wald conﬁdence intervals and report the estimations for the four districts in Table 5. We then utilize the relations between the ﬁve vector parameters (a, bh , bm , μm , n) and the estimated parameters listed in

230

Table 5 to estimate the values of the ﬁve vector parameters. These establish useful relationships among the vector parameters, the DMT and DTR. 3.3. Eﬀects of temperature on the four vector parameters To understand how DMT and DTR aﬀected dengue epidemic potential, we create contour plots and the trends of the vector parameters with the estimated

235

parameters for the Haizhu districts, shown in Fig.4 and Fig.5 respectively. The contour plots and trends of the vector parameters with the estimated parameters of other three districts are listed in the Appendix. 12

According to the annual temperature variation in Guangzhou, DMT ranges from 12◦ C to 34◦ C (x-axis) and the DTR ranges from 0◦ C to 22◦ C (y-axis), as shown in 240

Fig.4. These two ranges have also been used in other literatures (Liu-Helmersson et al., 2014; Lambrechts et al., 2011). All parameters except the biting rate (a) show nonlinear dependence on both DMT and DTR, indicating the quite complex eﬀects of DMT and DTR on the unknown parameters. This is conﬁrmed by the contour plots for the Haizhu district. Also, we create the trends

245

of the vector parameters during the period of the epidemic outbreak from Sep. 22nd to Oct. 29th in the Haizhu district (Fig.5). It follows from this ﬁgure that we can see how the vector parameters vary as the temperature parameters change, which have similar eﬀects on the parameters n, a, bm , and bh . From Fig.4.(A), we see that the EIP of the vector (n) is decreasing as DMT

250

increases, and increases as DTR increases. From Fig.5.(A), we can see that the EIP (n) was about 5 − 9 days during the dengue outbreak. Moreover, the EIP of the Haizhu district was less than 6 days until October 2nd, which had a relatively small value. Note that, during this period, the DMT was about 28◦ C and the DTR was about 9◦ C. After October 2nd, the vector parameter n had an upward trend

255

and reached a small peak on October 7th, while DMT had a downtrend with the DTR keeping 10◦ C. In mid October, the DMT was lower and the DTR was larger relatively, which resulted in a relatively longer EIP for the mosquito correspondingly (EIP reached 8.5 days on October 14th). Since DMT was generally unchanged and DTR had a downtrend from October 14th, EIP of the vector had a

260

downtrend and was stabilized around 6 days in the end of the October. Fig.4.(B) shows that the biting rate (a) increased linearly with DMT and was independent of DTR, and Fig.5.(B) shows that the biting rate of the mosquito in the Haizhu district lies between 0.45 and 0.55, clearly a strong ﬂuctuation with respect to the DMT.

265

It follows from Fig.4.(C) that when DTR was 0◦ C, similarly to the biting rate a, the probability of human to vector infection per bite (bm ) increased linearly with respect to DMT until 26.1◦ C and then became almost constant (one). While bm 13

increased as DTR increased if the DMT < 19◦ C; bm was almost a constant and independent of the DTR when the DMT was around 20◦ C; For a relatively high 270

DMT (> 21◦ C), bm decreases as DTR increases. From Fig.5.(C), bm of the Haizhu district keeps at about 0.95 until October 2nd, from which the DMT is about 28◦ C and the DTR is about 9◦ C. bm has a downtrend and reaches 0.78 on October 7th after October 3rd, and during this period the DMT has a downtrend while the DTR keeps at 10◦ C. In mid October, the DMT is about 23◦ C and the DTR is

275

relative large, which result in the smallest bm , i.e. 0.71 on October 14th. After that bm begins to increase with a complex pattern, here the DMT is about 25◦ C and the DTR decreases. Fig.4.(D) indicates that the relationship between the temperature and bh (the probability of vector to human transmission per bite) is complex. When DTR is

280

0◦ C, as DMT increases, bh increases almost linearly at low temperature, reaches a peak value at middle DMT, and then decreases when DMT is relative high. When the DMT takes the extremes (DMT < 18◦ C and DMT > 32◦ C), bh increases as DTR increases, while bh decreases as DTR increases when the DMT ranges from 18◦ C to 32◦ C. It follows from Fig.5.(D) that the bh in the Haizhu district was

285

about 0.6 − 0.9. It decreased from October 22nd since the DMT and DTR had some small ﬂuctuations, and then bh kept at about 0.85 at the end of October. 3.4. Eﬀects of control measure on the eﬀective reproduction number The eﬀective reproduction number R0 (t) of these four districts during the outbreak can be obtained with the estimated parameters. The eﬀective

290

reproductive number R0 (t) for the Haizhu district (red line) and Zengcheng district (blue line) are shown in Fig.6. The R0 (t) for the Tianhe districts and Huangpu district are shown in the Appendix. It follows from Fig.6 that the eﬀective reproduction number for the Zengcheng district ﬂuctuated between 0.26 and 3.68, and the eﬀective reproduction number for the Haizhu district ﬂuctuated

295

between 0.15 and 10.25. Therefore, the eﬀective reproduction numbers for the two districts exhibited a great diﬀerence, which can be used to address what factors could account for the diﬀerent scales of the epidemic. However, we must emphasize 14

here that we do not consider any delay factors of control measures on the eﬀective reproduction number in the present study. 300

Guangzhou CDC started to announce the density of mosquito vectors for each district from September 22, 2014. By the end of October, the outbreak was controlled broadly. So, Guangzhou CDC reported the daily new cases once a week on every Monday since November and did not report it any more. And further based on the weather data we have, the eﬀective reproductive number R0 (t) can be

305

obtained from the time intervals 9.22 to 10.29, 9.23 to 10.30 for Haizhu and Zengcheng districts, respectively, as shown in Fig.6. It was reported that aﬀected by the 15th typhoon Kalmaegi on September 15th, 2014, Guangzhou appeared rainy weather during 9.15-9.18, which is conducive for the breeding of Aedes and makes the clean work more diﬃcult. So, the BIs from

310

September 22nd to September 24th were signiﬁcantly large in almost all districts of Guangzhou, and consequently resulted in a rapid increasing of adult mosquito density. Thus, the eﬀective reproduction numbers for the Haizhu and Zengcheng districts show an upward trend and reached a small peak in the initial stage, as shown in Fig.6. From September 22nd the Emergency Management Oﬃce of

315

Guangdong Province, Guangdong CDC started to remind the public to pay attention to the dengue fever via mobile phone short messages, and a universal anti-mosquito operation was conducted in Guangzhou on the September 24th. All those integrated measures had greatly reduced the eﬀective reproduction numbers for both regions, as shown in Fig.6.

320

More speciﬁcally, Fig.6 indicates that R0 (t) of the Haizhu district had a downward trend during the period of 9.26-9.28, and then raised rapidly and reached the highest peak on the September 30th with R0 (t) = 10.25. Guangzhou Municipal People’s Government Oﬃce notiﬁed about the in-depth development of the reuniﬁcation of the city’s anti-mosquito measures for the prevention and

325

control of dengue fever epidemic on September 17th. Guangzhou Patriotic Health Campaign Committee decided to carry out three times the city’s mosquito enhanced control actions before and after the National Day holiday, namely, on the 15

afternoon of September 24th, 28th and October 8th, respectively. The mosquito-culling task was assigned to each department and each person to remove 330

all standing water and eliminate mosquito breeding grounds. Thus, reported cases decreased gradually during this period. However, during the seven days of National holiday, the increasing ﬂow of people to the area facilitated the spread, imposing great challenges for mitigation. This resulted in a rapidly increasing of the reported cases in the Haizhu district. Besides, there were heavy rains on

335

October 2nd and October 3rd, it was diﬃcult to clean the water, contributing to another small peak of the R0 (t) of Haizhu district. R0 (t) for the Zengcheng district reached a small peak on October 1st, followed by a transient decrease and then sharp increase to reach the peak value 3.68 on October 4th (in Fig.6). As mentioned earlier, Guangzhou carried out a city wise enhanced mosquito control

340

program on October 3rd. This seems to have contributed to the reduction of the number of adult mosquitoes in the Zengcheng district. From Fig.6, we note that R0 (t) < 1 in the Haizhu district on October 7th. According to the news report, Guangzhou carried out the enhanced mosquito culling measure within the whole city in this day, and the people living in the

345

epidemic-key areas including schools and construction sites had a vacation. In addition, the government set some stations where citizens could receive the mosquito killing tablet for free. Therefore, it is not surprised to see the monitored adult mosquito density decreased rapidly On October 7th, followed by the decrease in the number of reported cases. Fig.6 shows that R0 (t) for the Zengcheng district

350

began to decline after October 3rd, and kept less than 1 due to enhanced mosquito-culling program on October 8th. Overall, out study conﬁrms that the city’s large-scale campaign on October 7th and October 8th had indeed a signiﬁcant impact on reducing the eﬀective reproduction number to below the unity on October 7th.

355

The city’s water management authority also put mosquito-eating ﬁsh to the rivers in some districts around October 13th, so the number of adult mosquito in these districts decreased gradually. After October 18th, the basic actions to kill 16

the mosquito was going on, while the R0 (t) was larger than 1 until October 26th in Haizhu district due to the relative serious epidemic at initial stage, and then it was 360

less than 1 on the end of October, as shown in Fig.6. All those conﬁrm that the dengue disease in Haizhu district was eﬀectively controlled by the integrated mitigating measures. R0 (t) of Zengcheng district declined after reaching another small peak on October 11th, and then kept less than 1. The daily new cases increased and the R0 (t) failed to stabilize below 1 due to two days shower on

365

October 21st and October 22nd, and R0 (t) began to decline and stabilize at below 1 after October 23rd, which means that the epidemic in Zengcheng district was controlled eﬀectively and successfully. 3.5. Uncertainty and sensitivity analyses Based on the above discussion, we can see that the trends of R0 (t) and daily new

370

cases are consistent which could be greatly aﬀected by the weather conditions and human actions. Therefore, in this subsection, we explored the parameter space by performing an uncertainty analysis using a Latin hypercube sampling (LHS) method, an extension of Latin sampling. Note that, in order to carry out the sensitive analyses, we directly provide the ranges of key parameters including

375

a, bh , bm , μm , n, m, as shown in Table 6, which could implicitly address the eﬀects of temperature parameters (DMT, DTR) on the vector parameters. Because the daily variation of temperature causes the vector parameters changes accordingly, and choosing the wide ranges of key parameters could allow us to determine the key parameters easily. Based on the above facts, in the following we investigate the

380

sensitivity of parameters with respect to the basic reproduction number R0 rather than the eﬀective reproduction number R0 (t). In particular, we focus on the eﬀects of the daily variation of parameters on the eﬀective reproduction number R0 (t) on a special day. Sensitivity analysis was done by evaluating the partial rank correlation coeﬃcients (PRCCs) (see detail in (Blower et al., 1994; Marino et al.,

385

2008; Mckay et al., 1979)) for various input parameters (such as a, bh , bm , μm , n and m) against the output variables (here, the basic reproduction number R0 ) with the LHS method over time, which can help us to determine the most signiﬁcant 17

parameters on the eﬀects of disease outbreak. The ranges of the six input parameters (a, bh , bm , μm , n and m) can be obtained from the peer literatures, as 390

shown in Table 6. The results of PRCC, and p-values are shown in Table 6. Fig.7 represents the sensitivity of the six parameters a, bh , bm , μm , n, m for the basic reproduction number R0 . From Fig.7, we can see that the mortality rate μm of the vector is the most sensitive parameter in determining the basic reproduction number R0 , which is negatively correlated with strong PRCC value (-0.96). The

395

next sensitive parameter is the EIP (n) of the dengue fever virus, which is negatively correlated with relative strong PRCC value (-0.91614). The biting rate a of the mosquito, the probability of vector to human transmission per bite bh , the probability of human to vector infection per bite bm , and the ratio of the number of mosquitoes to the human population m are positive correlated with relative

400

weak PRCC values. According to the results of the sensitivity analyses above, we ﬁnd that the management of mosquito control is the most eﬀective and critical way to control the epidemic as the vector mortality rate μm is the most sensitive parameter in determining the basic reproduction number R0 . They are negatively correlated,

405

which means that the higher the vector mortality rate, the smaller the basic reproduction number. It is essential to remark the inﬂuence of the DMT and the DTR because the EIP (n) is the second sensitive parameter for the basic reproduction number R0 , where n is closely related to the DMT and DTR. From Fig.5.(A), we see the trend of n of Haizhu district for the period of the epidemic

410

outbreak clearly. EIP of the dengue fever virus ﬂuctuated with diﬀerent temperatures of every day. In general, EIP of the dengue virus has a uptrend and is stable with 6 days in the end of the October. And Fig.7 indicates that the longer EIP may result in the smaller eﬀective reproduction number in the middle of October. The eﬀective reproduction number decreases and is less than 1 with

415

the higher vector mortality rate and the longer EIP, which clariﬁes that DMT and the DTR play a critical role in the transmission of the dengue fever virus and they are also key factors related to the dengue fever. 18

Moreover, we explored the sensitivity of the vector parameters for the basic reproduction number in another way, which takes the eﬀects of variations of DMT 420

and DTR on parameters into consideration. Since the parameters a, bh , bm , n are related to DMT and DTR, the input parameters are DMT, DTR, μm , and m, and then a, bh , bm , n can be calculated by using the formula. Similarly, the output parameter is also the basic reproduction number R0 . Then the PRCCs for the six parameters a, bh , bm , n, μm, m against R0 are evaluated to investigate the

425

comprehensive sensitivity of vector parameters caused by variations of DMT and DTR. We consider the ranges of DMT and DTR as (12.4, 32.5), (0, 20) respectively for these ranges meet the regular temperature variation of Guangzhou. The ranges of μm and m are also obtained from the peer literatures and are the same as those in Table 6. The ranges of the input parameters, results of PRCC,

430

and p-values are shown in Table 7. Fig.8 represents the sensitivity of the six parameters a, bh , bm , μm , n, m for the basic reproduction number R0 and this result is a litter bit diﬀerent from Fig.7. From Fig.8, we can see that the mortality rate μm of the vector is the most sensitive parameter in determining the basic reproduction number R0 , which is

435

negatively correlated with strong PRCC value (-0.95128). The next sensitive parameter is the ratio of the number of mosquitoes to the human population (m) and the probability of vector to human transmission per bite (bh ), which are positively correlated with relative strong PRCC value (0.5586, 0.53168, respectively). The least sensitive parameter is the probability of human to vector

440

infection per bite bm , which is positive correlated with very weak PRCC value (0.014385). The EIP (n) of the dengue fever virus is negatively correlated with relative weak PRCC value (-0.404), and the biting rate (a) is positive correlated with relative weak PRCC (0.1735). This result also indicates that the management of mosquito control is the most

445

eﬀective and critical way to control the dengue fever. The vector mortality rate μm is the most sensitive parameter and the ratio of the number of mosquitoes to the human population m is the next sensitive parameter in determining the basic 19

reproduction number R0 . These two parameters are negative and positive correlated to R0 , respectively. The higher the vector mortality rate and the less 450

the ratio of the number of mosquitoes to the human population, the smaller the basic reproduction number. Therefore, our main results conﬁrm that the integrated measures for killing mosquito and eliminating breeding grounds for mosquito during this epidemic by the Guangdong government are eﬀective, which greatly mitigated the outbreak of dengue fever.

455

It follows from Fig.4 that the vector parameters a, bh , bm , n are closely related to the DMT and DTR. The biting rate (a) shows a linear dependence on DMT and an independence on DTR, and the other three parameters (bh , bm , n) show a nonlinear dependence on both DMT and DTR. Therefore, varying the temperature (i.e. parameters DMT and DTR) can result in a relative complex eﬀect on the

460

vector parameters, and then aﬀects the value of the basic reproduction number. Moreover, all the six vector parameters (a, bh , bm , μm , n, m) are correlated and aﬀect the basic reproduction number in a complex way, which could yield a slightly diﬀerent result of sensitivity analysis compared with result shown in Fig.7. In particular, the result indicates that the DMT and DTR are closely correlated to

465

the transmission of the dengue virus, and consequently the DMT and DTR would greatly aﬀect the severity of the outbreak of the dengue fever in Guangdong in 2014. 4. Discussion Our focus in this paper is to quantify the impact of vector parameters and

470

weather conditions on the dengue fever outbreak patterns in the Guangdong province in 2014, and to determine key factors aﬀecting the outbreak evolution and outcomes. We have chosen for our study area, four districts of the Guangzhou city: Haizhu, Tianhe, Huangpu and Zengcheng. We have discussed the data sets available for our study, and used these sets to inform association between the

475

density of mosquito vectors and the daily newly reported cases. Our results conﬁrmed that both BI and adult mosquito density were statistically signiﬁcantly 20

correlated with the daily newly reported cases. We also used the CCF to conclude that there existed a feedback and a contemporaneous relationship, and observed that there were statistically signiﬁcant cross-correlation between the mosquito 480

density and the daily newly reported cases at lags ranging from -4 to 7 days, and -1 to 6 days, respectively. We also used the MLE method to estimate important unknown parameters in each involved district and created contour plots and the trend of the vector parameters with the estimated parameters of the four districts. Using these

485

contour plots, we illustrated how DMT and DTR aﬀected the four vector parameters, and the epidemic potential (Rvc ). We obtained the estimations of the four vector parameters (a, bh , bm , n) with the daily diﬀerent temperatures for the period under study, and this facilitated our analysis about how the vector parameters and weather conditions aﬀected the Rvc and R0 (t) as time varied. We

490

did obtain the eﬀective reproduction number R0 (t). By analyzing the trend of this eﬀective reproduction number, we examined the eﬀectiveness of implemented control measures. In particular, we examined the impact of the enhanced mosquito-culling program implemented by the Guangzhou Patriotic Health Campaign Committee (three times before and after the National Day holidays)

495

and observed large decrease of the eﬀective reproduction number resulted form this campaign. Finally, almost all vector parameters are temperature-relevant, and our results showed that the DMT and DTR could signiﬁcantly aﬀect the values of these parameters. We suggest that control programs must take into account of the ﬂuctuation of temperatures to optimize mitigation eﬀect. Compared with the

500

estimated parameter values shown in Table 5, the diﬀerences of the μm and the number of mosquito per person m of each district, we examined how eﬀective the mosquito killing measures were in each district. For example, μm in the Tianhe district was the largest one (0.4926), and in the Zengcheng district had the smallest (0.3894). This indicates that the intensity of the mosquito-killing

505

measures in these districts were not be the same. This might be one of the main factors for the diﬀerent scales of epidemics in four districts. 21

To further describe how the temperature inﬂuenced the diﬀerent scaled of epidemic, we created the trends of the vector parameters a, n, bm , bh with the estimated parameters, and these trends revealed the diﬀerences of ﬂuctuations and 510

ranges of parameters. The EIP (n) of the mosquito in the Huangpu district varied with a wide range (here 6-10 days), while n in the Zengcheng district varied with a narrow range (here 4.6-6.5 days), which could facilitate the transmission of the dengue fever virus. The biting rate a of these four districts during the period was consistent generally, i.e. about 0.45-0.55 for the Haizhu and the Zengcheng district,

515

about 0.45-0.65 for Tianhe, and 0.35-0.45 for Huangpu. At the same time, the estimated values for bm , bh did not show too much diﬀerence, but they were closely related to DMT and DTR. Our results clariﬁed that slight changes of DMT and DTR can signiﬁcantly aﬀect the parameters a, n, bm , bh , and consequently impact the eﬀective reproduction number. We have conducted some sensitivity analyses

520

using two diﬀerent approaches, as shown in Fig.7 and Fig.8. Liu and Helmersson (Liu-Helmersson, 2012) have investigated the eﬀects of the six vector parameters (a, bh , bm , μm , n, m) on the basic reproduction number R0 , but the eﬀects of daily temperature variations was not considered there, which we believe may yield incorrect estimations and predictions. As shown in Fig.4, the vector parameters

525

a, bh , bm , n were closely related to the DMT and DTR with complex relationships (linear and nonlinear relationships). Thus, all the six parameters had interactions with each other and then inﬂuenced the eﬀective reproduction number comprehensively. Our results indicate that DMT and DTR are closely correlated to the transmission of the dengue virus, and DMT and DTR could have played a

530

complex role on the outbreak considered. In conclusion, our results show that the temperature can be either an eﬀective barrier or a facilitator of vector-borne diseases (Descloux et al., 2012). The DMT and the DTR are intrinsically related to the dengue epidemic potential, and here, are shown to have played a critical role on the transmission of the dengue virus and the development of the epidemic in

535

Guangzhou, China, 2014. We emphasize here again that we did not take the lags and BI into consideration 22

in our study. This will require a further study. Acknowledgements This work is supported by the National Natural Science Foundation of China 540

(NSFC 11471201, 11631012, 11601301), by the Fundamental Research Funds for the Central Universities (GK201401004, GK201603003), and by General Financial Grant from the China Postdoctoral Science Foundation (2016M602758).

23

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parameter x y a bh bm n µm Th a16 Nh m m·a pj k

Table 1: Parameter deﬁnitions deﬁnition the daily mean temperature (DMT) the diurnal temperature range (DTR) the average daily vector biting rate (/person/mosquito/day) the probability of vector to human transmission per bite the probability of human to vector infection per bite the duration of the EIP (day) the vector mortality rate infectious period (day) a given constant, and a16 A(t) means the total female mosquito population on day t the total human host population in the district the ratio of the number of mosquitoes to the human population average number of mosquito bites per person per day (/person/day) the probability for the generation interval on day j the maximum value of the serial interval

Table 2: Fixed parameter values from the references

parameter a3 a4 a5 a7 a8 a9 a10 k Th

value 0.001044 12.286 32.461 0 0 0 0 20 5

reference (Liu-Helmersson et al., 2014; Lambrechts et al., 2011) (Liu-Helmersson et al., 2014; Lambrechts et al., 2011) (Liu-Helmersson et al., 2014; Lambrechts et al., 2011)

(WHO, 2015) (WHO, 2015; Nishiura et al., 2007)

Table 3: Number of population for each interested district

district Haizhu Tianhe Huangpu Zengcheng

Nh 1599800 1506100 434700 1069700

Table 4: Pearson correlation analysis between the BI, the adult mosquito density and the daily newly reported cases in Haizhu district from September 22nd to October 30th 2014.

B A N

B A N 1 0.380* 0.619** 0.380* 1 0.537** 0.619** 0.537** 1

Signiﬁcance of correlation coeﬃcient diﬀerent from zero: ** represents p < 0.01, * represents p < 0.05.

29

Table 5: Estimation of unknown parameter values and their conﬁdence intervals parameter Haizhu Tianhe Huangpu Zengcheng a1 0.0176 0.0190 0.0135 0.0155 (0.0109, 0.0242) (0.0112, 0.0269) (0.0085, 0.0183) (0.0109, 0.0201) a1 95%CI a2 0.0637 0.0512 0.0544 0.0839 a2 95%CI (0.0479, 0.0795) (0.0365, 0.0657) (0.0413, 0.0676) (0.0796, 0.0883) 0.3945 0.4926 0.4128 0.3894 a6 (µm ) a6 (µm ) 95%CI (0.2914, 0.4975) (0.4221, 0.5632) (0.3360, 0.4896) (0.3025, 0.4765) 0.0640 0.0526 0.0630 0.0591 a11 a11 95%CI (0.0497, 0.0784) (0.0365, 0.0688) (0.0464, 0.0795) (0.0456, 0.0726) a12 0.6709 0.5893 0.5916 0.7078 (0.6057, 0.7362) (0.5549, 0.6237) (0.5587, 0.6246) (0.6691, 0.7465) a12 95%CI a13 3.6430 3.4621 3.8933 3.8135 a13 95%CI (3.3835, 3.9026) (3.1379, 3.7862) (3.6613, 4.1254) (3.4261, 4.2008) 4.5180 5.4621 5.4105 4.3417 a14 a14 95%CI (4.2034, 4.8326) (5.0299, 5.8943) (5.0243, 5.7968) (3.8679, 4.8156) 0.1439 0.1831 0.1681 0.1566 a15 a15 95%CI (0.1320, 0.1556) (0.1672, 0.1989) (0.1576,0.1785) (0.1529, 0.1602) a16 1581500 3013600 384600 523850 (1521300, 1641700) (2917400, 3109800) (359330, 409870) (516720, 530980) a16 95%CI

Parameter a bh bm µm n m

Range (0.15, 0.55) (0.3, 0.8) (0.3, 0.8) (0.1, 0.5) (7, 12) (3, 15)

Parameter DMT DTR µm m a bh bm n

Range (12.4, 32.5) (0, 20) (0.1, 0.5) (3, 15)

Table 6: Result of sensitive analysis PRCC p-value reference 0.68565 0 (Liu-Helmersson et al., 2014; Chitnis, 2005) 0.53695 0 (Liu-Helmersson et al., 2014; Chitnis, 2005) 0.4681 0 (Liu-Helmersson et al., 2014; Chitnis, 2005) -0.96 0 (Garba et al., 2010; Liu-Helmersson et al., 2014) -0.91614 0 (Focks et al., 1995; Shen, 2014) 0.31895 0 (Chitnis, 2005)

Table 7: Results of sensitive analysis PRCC p-value -0.95128 0.5586 0.1735 0.53168 0.014358 -0.404

0 0 5.5511e-15 0 0.52104 0

30

reference

(Garba et al., 2010; Liu-Helmersson et al., 2014) (Chitnis, 2005)

(A)

(B) 100 Adult mosquito density

30

BI

20

10

0

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

80 60 40 20 0

10.30

9.22

9.27

10.2

10.7

(C)

10.22

10.30

10.17

10.22

10.30

25 Prevalence (/100,000 person)

Daily newly reported cases

10.17

(D)

350 300 250 200 150 100 50 0

10.12 Time

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

20 15 10 5 0

10.30

9.22

9.27

10.2

10.7

10.12 Time

Fig. 1: The reported BI, the adult mosquito density, the daily newly reported cases and the prevalence (/100,000 person) of the Haizhu district from September 22nd to October 30th 2014 have been shown in (A), (B), (C) and (D), respectively.

34 daily maxmum temperature daily minimum temperature

32

30

Temperature(oC)

28

26

24

22

20

18

16

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.29

Fig. 2: The temperature variation for daily maximum and minimum temperatures of the Haizhu district from September 22nd to October 29th 2014 has been shown.

31

(B)

(C) 0.8

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0

CCF(A with N)

0.8

CCF(B with N)

CCF(B with A)

(A) 0.8

0.2

0

0.2

0

−0.2

−0.2

−0.2

−0.4

−0.4

−0.4

−0.6 −20

−10

0 Lag

10

−0.6 −20

20

−10

0 Lag

10

−0.6 −20

20

−10

0 Lag

10

20

Fig. 3: Cross-correlation coeﬃcients between the BI, the adult mosquito density and the daily newly reported cases in Haizhu district from September 22nd to October 30th 2014. The two dotted lines in the graphs represent the upper and lower conﬁdence bounds of 95% conﬁdence intervals.

(A)n

(B)a 0.6

30 20

20 0.55

25 20 10

15

5 0

0.5

15 DTR(oC)

DTR(oC)

15

15

20

25

0.45 10 0.4

10

5

5

0

30

0.35 0.3 15

20

DMT(oC)

25

30

DMT(oC)

(C)b

(D)b

m

h

1 20

20

0.8

15

0.6

10

0.4

5

0.2

0.8 DTR(oC)

DTR(oC)

15 0.6 10 0.4 5 0.2 0

15

20

25

0

30

o

15

20

25

30

o

DMT( C)

DMT( C)

Fig. 4: The eﬀects of DMT and DTR on the vector parameters of Haizhu district with the estimated parameters.

32

(B) 0.65

8

0.6

7

0.55

a

n

(A) 9

6 5

0.5

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

0.45

10.29

9.22

9.27

10.2

10.7

(C)

10.12 Time

10.17

10.22

10.29

10.17

10.22

10.29

(D)

1 0.95

0.95

0.9 0.85 bh

bm

0.9 0.85

0.8 0.75

0.8

0.7 0.75 0.7

0.65 9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.29

9.22

9.27

10.2

10.7

10.12 Time

Fig. 5: The parameters of Haizhu district for the period of September 22nd to October 29th, 2014.

12 11

Haizhu district Zengcheng district

10 9 8

0

R (t)

7 6 5 4 3 2 1 0

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.27

10.30

Fig. 6: The eﬀective reproduction number R0 (t) of Haizhu district (red line) and Zengcheng district (blue line) for the period of September 22nd to October 29th 2014, September 23rd to October 30th 2014 respectively.

33

0.5

PRCCs

0

−0.5

n

m

2000

2000

1000

1000

1000

0

−2000 −1000

R0

2000

0

0 a

−2000 −1000

1000

0 −1000

−1000

−1000

0 bh

1000

−2000 −1000

2000

2000

1000

1000

1000

0

0

0 μm

2000

0 bm

1000

0 m

1000

0 −1000

−1000

−1000 −2000 −2000

R0

2000

R0

R0

μm

bm

bh

a

R0

R0

−1

−2000 −1000

0 n

1000

−2000 −1000

Fig. 7: Sensitive analysis. The sensitivity of the six parameters a, bh , bm , µm , n, m for the basic reproduction number R0

34

1

PRCCs

0.5

0

−0.5

bh

a

200

1000

100

500

n

m

200

−200 −500

R0

0

0

m

400

0

−100

−500

0

−1000 0 a

−1500 −500

500

0 bh

−200 −500

500

300

2000

1000

200

1000

100

0

0

R

0

2000

R

R0

μ

bm

R

R0

−1

0 bm

500

0 m

500

0

0 −1000 −2000 −1000

−1000

−100 0 μ

1000

−200 −500

0 n

m

500

−2000 −500

Fig. 8: Sensitive analysis considering variations of DMT and DTR. The sensitivity of the six parameters a, bh , bm , µm , n, m for the basic reproduction number R0

35

Appendix 4.1. Zengcheng district 34 daily maxmum temperature daily minimum temperature

32 30

Temperature(oC)

28 26 24 22 20 18 16

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.27 10.30

Fig. 9: The temperature variation of the Zengcheng district from September 22nd to October 30th 2014.

(A)

(B)

50

35 30 Adult mosquito density

40

BI

30 20 10 0

25 20 15 10 5

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

0

10.30

9.22

9.27

10.2

10.7

(C)

10.22

10.30

10.17

10.22

10.30

1.5 Prevalence (/100,000 person)

Daily newly reported cases

10.17

(D)

20

15

10

5

0

10.12 Time

1

0.5

0 9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.30

9.22

9.27

10.2

10.7

10.12 Time

Fig. 10: The reported BI, the adult mosquito density, the daily newly reported cases and the prevalence (/100,000 person) of the Zengcheng district from September 22nd to October 30th 2014 have been shown in (A), (B), (C) and (D), respectively.

4.2. Tianhe district

36

(B)

(C) 0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

CCF(A with N)

0.6

CCF(B with N)

CCF(B with A)

(A) 0.8

0

−0.2

0

−0.2

−0.2

−0.4

−0.4

−0.4

−0.6

−0.6

−0.6 −20

−10

0 Lag

10

20

−0.8 −20

−10

0 Lag

10

−0.8 −20

20

−10

0 Lag

10

20

Fig. 11: Cross-correlation coeﬃcients between the BI, the adult mosquito density(the density of mosquito vectors) and the daily newly reported cases in Zengcheng district from September 22nd to October 30th 2014.The two dotted lines in the graphs represent the upper and lower conﬁdence bounds of 95% conﬁdence intervals.

(A)n

(B)a

20

20

0.5

15

10

10

5 0

DTR(oC)

15

o

DTR( C)

20 10

0.4

5

5 20

15

0

30

DMT(oC)

0.3 20

30

DMT(oC)

(C)bm

(D)bh 1

20

20

0.8

15

0.6

10

0.4

5

0.2

0.6

10

0.4

5 0

DTR(oC)

15

o

DTR( C)

0.8

0.2 20

0

30 o

20

30 o

DMT( C)

DMT( C)

Fig. 12: The eﬀect of DMT and DTR on the vector parameters of the Zengcheng district with the estimated parameters.

37

(B)

(A) 0.6

7

n

a

6 0.5

5 0.4 9.23 9.28 10.3 10.8 10.13 10.18 10.23 10.30 Time (D) 1

4 9.23 9.28 10.3 10.8 10.13 10.18 10.23 10.30 Time (C) 1

0.9 bh

b

m

0.9 0.8 0.7

0.8 0.7

9.23 9.28 10.3 10.8 10.13 10.18 10.23 10.30 Time

9.23 9.28 10.3 10.8 10.13 10.18 10.23 10.30 Time

Fig. 13: The parameters of Zengcheng district for the period of September 23rd to October 30th 2014.

36 daily maxmum temperature daily minimum temperature

34 32

Temperature(oC)

30 28 26 24 22 20 18

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.27 10.30

Fig. 14: The temperature variation of the Tianhe district from September 22nd to October 30th 2014.

38

(A)

(B) 15 Adult mosquito density

20

BI

15

10

5

0

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10

5

0

10.30

9.22

9.27

10.2

10.7

(C)

10.22

10.30

10.17

10.22

10.30

14 Prevalence (/100,000 person)

Daily newly reported cases

10.17

(D)

200

150

100

50

0

10.12 Time

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

12 10 8 6 4 2 0

10.30

9.22

9.27

10.2

10.7

10.12 Time

Fig. 15: The reported BI, the adult mosquito density, the daily newly reported cases and the prevalence (/100,000 person) of the Tianhe district from September 22nd to October 30th 2014 have been shown in (A), (B), (C) and (D), respectively.

(B)

(C) 0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

−0.2

CCF(A with N)

0.6

CCF(B with N)

CCF(B with A)

(A) 0.6

0

−0.2

0

−0.2

−0.4

−0.4

−0.4

−0.6

−0.6

−0.6

−0.8 −20

−10

0 Lag

10

20

−0.8 −20

−10

0 Lag

10

20

−0.8 −20

−10

0 Lag

10

20

Fig. 16: Cross-correlation coeﬃcients between the BI, the adult mosquito density(the density of mosquito vectors) and the daily newly reported cases in Tianhe district from September 22nd to October 30th 2014.The two dotted lines in the graphs represent the upper and lower conﬁdence bounds of 95% conﬁdence intervals.

39

(B)a 50

15

40

10

30

20

DTR(oC)

20 o

DTR( C)

(A)n

20

5 20

0

30

(C)bm

30

(D)bh 0.8

15

o

0.6

10

0.4

5

DTR(oC)

1

20

DTR( C)

0.3 20 DMT(oC)

o

20

0.8

15

0.6

10

0.4

5

0.2

0.2 20

0.4

5

DMT( C)

0

0.5

10

10 0

0.6

15

0

30 o

20

30 o

DMT( C)

DMT( C)

Fig. 17: The eﬀect of DMT and DTR on the vector parameters of the Tianhe district with the estimated parameters.

(A)

(B)

10

0.8

a

n

8 0.6

6 4 9.22 9.27 10.2 10.7 10.12 10.17 10.23 Time (C) 1

0.4 9.22 9.27 10.2 10.7 10.12 10.17 10.23 10.30 Time (D) 1

10.30

0.8

b

bh

m

0.8 0.6

0.6

0.4 9.22 9.27 10.2 10.7 10.12 10.17 10.23 10.30 Time

0.4 9.22 9.27 10.2 10.7 10.12 10.17 10.23 10.30 Time

Fig. 18: The parameters of Tianhe district for the period of September 22nd to October 30th 2014.

40

6

5

0

R (t)

4

3

2

1

0

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.27 10.30

Fig. 19: The eﬀective reproductive number R0 (t) of Tianhe district for the period of September 22nd to October 30th 2014.

4.3. Huangpu district 34 daily maxmum temperature daily minimum temperature

32 30 28

Temperature(oC)

670

26 24 22 20 18 16

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.28

Fig. 20: The temperature variation of the Huangpu district from September 22nd to October 28th, 2014.

41

(A)

(B) 60

25

50

Adult mosquito density

30

BI

20 15 10 5 0

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

40 30 20 10 0

10.30

9.22

9.27

10.2

10.7

(C)

10.22

10.30

10.17

10.22

10.30

25 Prevalence (/100,000 person)

Daily newly reported cases

10.17

(D)

100 80 60 40 20 0

10.12 Time

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

20 15 10 5 0

10.30

9.22

9.27

10.2

10.7

10.12 Time

Fig. 21: The reported BI, the adult mosquito density, the daily newly reported cases and the prevalence (/100,000 person) of the Huangpu district from September 22nd to October 30th 2014 have been shown in (A), (B), (C) and (D), respectively.

(B)

(C) 0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0 −0.1

CCF(A with N)

0.5

CCF(B with N)

CCF(B with A)

(A) 0.5

0 −0.1

0 −0.1

−0.2

−0.2

−0.2

−0.3

−0.3

−0.3

−0.4

−0.4

−0.4

−0.5 −20

−0.5 −20

−10

0 Lag

10

20

−10

0 Lag

10

20

−0.5 −20

−10

0 Lag

10

20

Fig. 22: Cross-correlation coeﬃcients between the BI, the adult mosquito density(the density of mosquito vectors) and the daily newly reported cases in Huangpu district from September 22nd to October 30th 2014.The two dotted lines in the graphs represent the upper and lower conﬁdence bounds of 95% conﬁdence intervals.

42

(A)n

(B)a 60

15

40

10

30

5

20 20

0.4

15

0.35

10

0.3 5

10

0

0.45

20

50

DTR(oC)

DTR(oC)

20

0.25

0

20

30

DMT( C) (C)bm

(D)bh 0.8

15

0.6

10

0.4

5

DTR(oC)

1

20

DTR(oC)

30

DMT(oC)

o

20

0.8

15

0.6

10

0.4

5

0.2

0.2 0

20

0

30

20

o

30 o

DMT( C)

DMT( C)

Fig. 23: The eﬀects of DMT and DTR on the vector parameters of the Huangpu district with the estimated parameters.

(A)

(B)

9

0.44

8

0.42 a

0.46

n

10

7

0.4

6

0.38

5

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

0.36

10.28

9.22

9.27

10.2

10.7

(C)

10.12 Time

10.17

10.22

10.28

10.17

10.22

10.28

(D)

1.05 0.95 1

0.9 0.85 bh

bm

0.95 0.9

0.8 0.75 0.7

0.85

0.65 0.8

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.28

9.22

9.27

10.2

10.7

10.12 Time

Fig. 24: The parameters of Huangpu district for the period of September 22nd to October 28th, 2014.

43

7

6

5

0

R (t)

4

3

2

1

0

9.22

9.27

10.2

10.7

10.12 Time

10.17

10.22

10.28

Fig. 25: The basic reproduction number R0 (t) of Huangpu district for the period of September 22nd to October 28th, 2014.

44

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