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Transmission dynamics of a general temporal-spatial vector-host epidemic model with an application to the dengue fever in Guangdong, China

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  • Due to the nature of the spread of vector-host epidemic disease, there are many factors affecting its dynamic behaviors. In this paper, a vector-host epidemic model with two seasonal development periods and awareness control of host is proposed to investigate the multi-effects of the spatial heterogeneity, seasonal development periods, temporal periodicity and awareness control. We first address the well-posedness of the model and then derive the basic reproduction number $ R_0 $. In the case where $ R_0<1 $, we establish the global attractivity of the disease-free periodic solution, and in the case where $ R_0>1 $, we show that the disease is uniformly persistent and the system admits at least one positive periodic endemic steady state, and further obtain the global attractivity of the positive endemic constant steady state for the model with constant coefficients. As a case study, we conduct numerical simulations for the dengue fever transmission in Guangdong, China, 2014. We find that the greater heterogeneity of the mosquito distribution and human population may increase the risk of disease transmission, and the stronger awareness control may lower the risk of disease transmission.

    Mathematics Subject Classification: Primary: 92D30, 35K57; Secondary: 35Q92, 37N25.


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  • Figure 1.  The diagram of the vector-host disease transmission

    Figure 2.  The temporal-spatial periodic evolution solution of system (12) with with initial value (44) and the Nuemann boundary condition when $ \mathcal{R}_0 = 3.0391>1 $

    Figure 3.  The temporal-spatial periodic evolution solution of system (12) with with initial value (44) and the Nuemann boundary condition when $ \mathcal{R}_0 = 0.9701<1 $

    Figure 4.  (a) The basic reproduction number $ R_0 $ decreases with $ m $. (b): The basic reproduction number $ R_0 $ increases with $ \eta $;

    Figure 5.  The basic reproduction number $ R_0 $ increases with $ \xi $

    Table 1.  Parameter values

    Value Definition Reference
    $ N_h $ 603(km$ ^2 $)$ ^{-1} $ Total human see text
    population density
    $ A_{h} $ $ 8.96\times10^{-4} $(km$ ^2 $ month)$ ^{-1} $ Human birth rate see text
    $ \sigma $ $ 3.90\times 10^{-4} $(km$ ^2 $ month)$ ^{-1} $ Human death rate see text
    $ m $ [0–1] conscious control rate [46]
    of the susceptible human
    $ u $ $ 6.18\times10^{-10} $(km$ ^2 $ month)$ ^{-1} $ Disease-related mortality [26]
    $ \alpha $ $ 30.4/6 $ month $ ^{-1} $ Human constant recovery rate [50]
    $ \tau_p $ $ [3 / 30.4,14 / 30.4] $ month $ ^{-1} $ Development time of [44]
    dengue virus in human
    $ A_w $ to be estimated Recruitment rate see text
    of mosquitoes
    $ \tau_w $ to be evaluated Development time see text
    of dengue virus
    in mosquitoes
    $ l $ 0.1-0.75 Transmission probability from [11]
    mosquitoes to hosts per bite
    $ p $ 0.3-0.75 Transmission probability from [11]
    hosts to mosquitoes per bite
    $ \delta $ to be evaluated Death rate see text
    of mosquitoes
     | Show Table
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    Table 2.  Monthly mean temperature Guangdong Province (in $ \left.^{\circ} \mathrm{C}\right) $

    Month Jul Aug Sep Oct Nov Dec
    Temperature 32.7 32.5 30.4 27.6 23.6 18.4
    Month Jan Feb Mar Apr May June
    Temperature 16.7 17.2 20.7 25.6 29.4 30.7
     | Show Table
    DownLoad: CSV
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