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Impact of spatially heterogeneous temperature on the dynamics of dengue epidemics

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  • In recent years, the growing spatial spread of dengue, a mosquito-borne disease, has been a major international public health concern. In this paper, we propose a mathematical model to describe an impact of spatially heterogeneous temperature on the dynamics of dengue epidemics. We first consider homogeneous temperature profiles across space and study sensitivity of the basic reproduction number to the environmental temperature. We then introduce spatially heterogeneous temperature into the model and establish some important properties of dengue dynamics. In particular, we formulate two indices, mosquito reproduction number and infection invasion threshold, which completely determine the global threshold dynamics of the model. We also perform numerical simulations to explore the impact of spatially heterogeneous temperature on the disease dynamics. Our analytical and numerical results reveal that spatial heterogeneity of temperature can have significant impact on expansion of dengue epidemics. Our results, including threshold indices, may provide useful information for effective deployment of spatially targeted interventions.

    Mathematics Subject Classification: 35K57, 37N25, 92D30.


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  • Figure 2.1.  Functional curves $\delta (T)$, oviposition rate, $\mu_a(T)$, aquatic phase mortality rate, $\theta (T)$, mosquito emergence rate from acuatic phase, and $\mu_m(T)$, mosquito mortality rate, fitted to the experimental data [44]

    Figure 2.2.  Functional curve $\beta_m (T)$, the transmission probability from human to mosquito, fitted to the data generated from the previous estimates [17]

    Figure 3.1.  The basic reproduction number, $\bar{\mathcal{R}}_0$, vs. environmental temperature, $T$, for different values of carrying capacity, $C$.

    Figure 4.1.  Spatio-temporal distribution of prevalence (left) and new infection (right) during an epidemic. Here, $T_m = 22.5$℃ and $\Delta T = 25$℃, and $D_M = D_H = 0.0001$.

    Figure 4.2.  Distribution of prevalence (left) and new infection (middle) at different times and the total infection during an epidemic (right). Here, $T_m = 22.5$℃ and $\Delta T = 25$℃, and $D_M = D_H = 0.0001$.

    Figure 4.3.  Distribution of prevalence (left) and new infection (middle) at different times and the total infection during an epidemic (right) for the end point temperature difference $\Delta T = 15$℃ (upper panel) and $\Delta T = 35$℃ (lower panel). Here $T_m = 22.5$℃ and $D_M = D_H = 0.0001$.

    Figure 4.4.  Distribution of prevalence (left) and new infection (middle) at different times and the total infection during an epidemic (right) for the mean temperature $T_m = 15$℃ (upper panel) and $T_m = 30$℃ (lower panel). Here $\Delta T = 25$℃ and $D_M = D_H = 0.0001$.

    Figure 4.5.  Distribution of prevalence (left) and new infection (middle) at different times and the total infection during an epidemic (right) for $D_M/D_H = 0.1$ (upper panel) and $D_M/D_H = 10$ (lower panel). Here $T_m = 22.5$℃ and $\Delta T = 25$℃.

    Table 2.1.  Model parameters

    Parameter Description Value Reference
    $k$ fraction of female larvae from eggs 0.5 (0-1) [18,27]
    $b$ per capita biting rate 0.1 [4,27]
    $\mu_h$ Natural death rate of humans 4.22$\times 10^{-5}$ d$^{-1}$ Calculated, [16]
    $1/\gamma_h$ Intrinsic period 10 days [4,16,18,27]
    $\alpha_h$ Human recovery rate 0.1 d$^{-1}$ [18,27]
    $D_M, D_H$ Diffusion coefficients - varied
    $\delta_m$ In $\delta(x)$ 9.531 Data fitting
    $\delta_h$ In $\delta(x)$ 22.55 Data fitting
    $N_{\delta}$ In $\delta(x)$ 7.084 Data fitting
    $a_{0\mu_a}$ In $\mu_a(x)$ 2.914 Data fitting
    $a_{1\mu_a}$ In $\mu_a(x)$ -0.4986 Data fitting
    $a_{2\mu_a}$ In $\mu_a(x)$ 0.03099 Data fitting
    $a_{3\mu_a}$ In $\mu_a(x)$ -0.0008236 Data fitting
    $a_{4\mu_a}$ In $\mu_a(x)$ 7.975$\times 10^{-6}$ Data fitting
    $a_{0\theta}$ In $\theta(x)$ 8.044$\times 10^{-5}$ Data fitting
    $a_{1\theta}$ In $\theta(x)$ 11.386 Data fitting
    $a_{2\theta}$ In $\theta(x)$ 40.1461 Data fitting
    $a_{0\mu_m}$ In $\mu_m(x)$ 0.1901 Data fitting
    $a_{1\mu_m}$ In $\mu_m(x)$ -0.0134 Data fitting
    $a_{2\mu_m}$ In $\mu_m(x)$ 2.739$\times 10^{-4}$ Data fitting
    $a_{0\gamma_m}$ In $\gamma_m(x)$ 5$\times 10^{4/3}$ Data fitting
    $a_{1\gamma_m}$ In $\gamma_m(x)$ 0.0768 Data fitting
    $\beta_{mh}$ In $\beta_m(x)$ 18.9871 Data fitting
    $N_{\beta_m}$ In $\beta_m(x)$ 7 Data fitting
    $a_{0\beta_h}$ In $\beta_h(x)$ 1.044$\times 10^{-3}$ Data fitting
    $a_{1\beta_h}$ In $\beta_h(x)$ 12.286 Data fitting
    $a_{2\beta_h}$ In $\beta_h(x)$ 32.461 Data fitting
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