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Dynamical behavior of a vector-host epidemic model with demographic structure. (English) Zbl 1165.34382
Summary: We propose a model that tracks the dynamics of many diseases spread by vectors, such as malaria, dengue, or West Nile virus (all spread by mosquitoes). Our model incorporates demographic structure with variable population size which is described by nonlinear birth rate and linear death rate. The stability of the system is analyzed for the existence of the disease-free and endemic equilibria points. We find the basic reproduction number ${R}_{0}$ in terms of measurable epidemiological and demographic parameters is the threshold condition that determines the dynamics of disease infection: if ${R}_{0}<1$ the disease fades out, and for ${R}_{0}>1$ the disease remains endemic. The threshold condition provides important guidelines for accessing control of the vector diseases, and implies that it is an efficient way to halt the spread of vector epidemic by reducing the carrying capacity of the environment for the vector and the host. Moreover, sufficient conditions are also obtained for the global stability of the unique endemic equilibrium ${E}^{*}$.
##### MSC:
 34D23 Global stability of ODE 92D30 Epidemiology