### Mathematical Biosciences and Engineering

2017, Issue 5&6: 1159-1186. doi: 10.3934/mbe.2017060

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

• Received: 01 July 2016 Accepted: 01 December 2016 Published: 01 October 2017
• MSC : Primary: 92D30

• 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 $\mathcal{R}_0 \gt 1$ . The results suggest that an effective strategy to contain vector-borne diseases is decreasing the basic reproduction number $\mathcal{R}_0$ below one.

Citation: Yan-Xia Dang, Zhi-Peng Qiu, Xue-Zhi Li, Maia Martcheva. Global dynamics of a vector-host epidemic model with age of infection[J]. Mathematical Biosciences and Engineering, 2017, 14(5&6): 1159-1186. doi: 10.3934/mbe.2017060

### Related Papers:

• 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 $\mathcal{R}_0 \gt 1$ . 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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