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Global dynamics of a vector-host epidemic model with age of infection

1. Department of Public Education, Zhumadian Vocational and Technical College, Zhumadian 463000, China
2. School of Science, Nanjing University of Science and Technology, Nanjing 210094, China
3. Department of Mathematics and Physics, Anyang Institute of Technology, Anyang 455000, China
4. Department of Mathematics, University of Florida, 358 Little Hall, PO Box 118105, Gainesville, FL 32611-8105, USA

In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vector-borne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubation-age dependent removal rates in the latent period and the variable infectiousness in the infectious period, respectively. The reproductive number $\mathcal R_0$ is derived. By using the method of Lyapunov function, the global dynamics of the PDE model is further established, and the results show that the basic reproduction number $\mathcal R_0$ determines the transmission dynamics of vector-borne diseases: the disease-free equilibrium is globally asymptotically stable if $\mathcal R_0≤ 1$, and the endemic equilibrium is globally asymptotically stable if $\mathcal{R}_0>1$. The results suggest that an effective strategy to contain vector-borne diseases is decreasing the basic reproduction number $\mathcal{R}_0$ below one.

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