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Global dynamics of an SIRS model with demographics and transfer from infectious to susceptible on heterogeneous networks

1 School of Mathematics and Statistics, Changsha University of Science and Technology, Changsha, Hunan, 410114, P. R. China
2 College of Arts and Science, National University of Defense Technology, Changsha, Hunan, 410073, P.R. China
3 Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha, Hunan, 410114, P. R. China

Special Issues: Differential Equations in Mathematical Biology

In this paper, by taking full consideration of demographics, transfer from infectious to sus-ceptible and contact heterogeneity of the individuals, we construct an improved Susceptible-Infected-Removed-Susceptible (SIRS) epidemic model on complex heterogeneous networks. Using the next generation matrix method, we obtain the basic reproduction number $\mathcal{R}_0$ which is a critical value and used to measure the dynamics of epidemic diseases. More specifically, if $\mathcal{R}_0$ < 1, then the disease-free equilibrium is globally asymptotically stable; if $\mathcal{R}_0$ > 1, then there exists a unique endemic equilib-rium and the permanence of the disease is shown in detail. By constructing an appropriate Lyapunov function, the global stability of the endemic equilibrium is proved as well under some conditions. Moreover, the effects of three major immunization strategies are investigated. Finally, some numerical simulations are carried out to demonstrate the correctness and validness of the theoretical results.
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