Global dynamics of a vector-host epidemic model with age of infection - Yan-Xia Dang; Zhi-Peng Qiu; Xue-Zhi Li; Maia Martcheva (Mathematical Biosciences and Engineering)
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.