Potential effects of climate change on dengue transmission dynamics in Korea

Dengue fever is a major international public health concern, with more than 55% of the world population at risk of infection. Recent climate changes related to global warming have increased the potential risk of domestic outbreaks of dengue in Korea. In this study, we develop a two-strain dengue model associated with climate-dependent parameters based on Representative Concentration Pathway (RCP) scenarios provided by the Korea Meteorological Administration. We assess the potential risks of dengue outbreaks by means of the vector capacity and intensity under various RCP scenarios. A sensitivity analysis of the temperature-dependent parameters is performed to explore the effects of climate change on dengue transmission dynamics. Our results demonstrate that a higher temperature significantly enhances the potential threat of domestic dengue outbreaks in Korea. Furthermore, we investigate the effects of countermeasures on the cumulative incidence of humans and vectors. The current main control measures (comprising only travel restrictions) for infected humans in Korea are not as effective as combined control measures (travel restrictions and vector control), dramatically reducing the possibilities of dengue outbreaks.

Seasonal reproduction number R s for the single-strain model The system of ordinary differential equations for the single-strain model has the disease-free state x 0 = (S e , 0, S v , 0, 0, S h , 0, 0, 0) with η=0.
F and V are 5× 5 matrices are given by is the next generation matrix of the system for the single-strain model; Thus, the seasonal reproduction number of the system for the single-strain model at time t in the absence of the inflow rate of international travelers (i.e., η = 0) is given by the spectral radius of matrix F V −1 as follows;

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Seasonal reproduction number R s for the two-strain model When the inflow rate of dengue cases imported via international travel is absent, we consider the disease free state x 0 consisting of a 21 × 1 zero vector except for S e , S v , S h . (4) and (5) are rewritten as The net transition rates of the corresponding compartment are represented by V(x), where F and V are 14× 14 matrices at x 0 given by F V −1 is the next generation matrix of the system of ordinary differential equations for the two-strain model. Thus, the seasonal reproduction number of the system for the two-strain model in the absence of inflow of international travelers (i.e., η i = κ i = 0) is given by the spectral radius of matrix F V −1 as follows: , B. Data fitting for x 1 and x 2 by using least square method We compare the dengue incidence data in Taiwan with the results of numerical simulations (in the absence of imported dengue cases) to confirm the validity of parameter values in the model and determine x 1 and x 2 through the data fitting.
According to Centers for Disease Control of Taiwan, Taiwan experienced the large dengue fever outbreak in 2014 and a consecutive larger dengue fever outbreak in 2015, resulting in a total of 51579 cases. We focus on the 2014 dengue fever outbreak to fit our models to the data without control because the control strategies have not been implemented before the dengue major outbreak in 2015. The vertical infection rate (ν) is 0.028 [3] and population size in Taiwan in 2014 was 23,434,000 with the births and deaths 210383 and 163929, respectively, from which birth rate (µ hb ) and death rate (µ hd ) per day are computed as 0.000025 and 0.000019, respectively.
In order to obtain the transmission probabilities x 1 and x 2 from data fitting, we carry out numerical simulation for the period from week 1 (2013.12.29 − 2013.1.4) to week 52 (2014.12.21 − 2014.12.27). We set the initial infected human as 7 dengue cases on week 1 and the mosquito population size is two times larger than human population size initially.
Data fitting procedure Step 1. We generate the daily temperature and dengue incidence data. All weekly confirmed dengue cases are provided by Centers for Disease Control of Taiwan and there are 15,814 reported dengue cases during week 1 − week 52. Monthly temperature and precipitation are provided by Central Weather Bureau in Taiwan. Then, we generate the daily temperature and precipitation data and dengue incidence by using cubic spline interpolation.
Step 2. The daily incidence and weekly incidence are computed for single-strain model. The incidence at day t is defined by αE h (t). The weekly incidence during seven days from day t 1 to day t 2 is computed as Step 3. We carry out data fitting with least squares. We use LSQcurvefit function of Matlab which implements data fitting with nonlinear least squares methods during the period from week 0