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Dynamical analysis of a diffusive SIRS model with general incidence rate. (English) Zbl 1443.37064
Summary: In this paper, we propose a diffusive SIRS model with general incidence rate and spatial heterogeneity. The formula of the basic reproduction number \(\mathcal R_0\) is given. Then the threshold dynamics, including globally attractive of the disease-free equilibrium and uniform persistence, are established in terms of \(\mathcal{R}_0\). Special cases and numerical simulations are presented to support our main results.
MSC:
37N25 Dynamical systems in biology
92D30 Epidemiology
92B05 General biology and biomathematics
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