
Mathematical Biosciences and Engineering, 2017, 14(5&6): 11591186. doi: 10.3934/mbe.2017060
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Global dynamics of a vectorhost 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 326118105, USA
Received: , Accepted: , Published:
In this paper, a partial differential equation (PDE) model is proposed to explore the transmission dynamics of vectorborne diseases. The model includes both incubation age of the exposed hosts and infection age of the infectious hosts which describe incubationage 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 vectorborne diseases: the diseasefree 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 vectorborne diseases is decreasing the basic reproduction number $\mathcal{R}_0$ below one.
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