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Zbl 1225.37108
Pang, Jianhua; Cui, Jing-An; Hui, Jing
Rich dynamics of epidemic model with sub-optimal immunity and nonlinear recovery rate. (English)
[J] Math. Comput. Modelling 54, No. 1-2, 440-448 (2011). ISSN 0895-7177

Summary: We propose a simple epidemic model with sub-optimal immunity and an arbitrary recovery rate function to understand the impact of different forms of recovery rate. It shows that a nonlinear recovery rate leads to rich dynamic behaviors, such as multiple endemic equilibria, bistability, periodicity and bifurcations. Furthermore, we are pleasantly surprised to find that between the SIS and SIR models there are very similar dynamics with a special recovery rate function. Therefore, in order to simulate the disease trends more accurately, we need to construct a reasonable recovery rate, which is as important as the reasonable incidence rate.

MSC 2000:: *37N25 Dynamical systems in biology
92D30 Epidemiology
34C23 Bifurcation (periodic solutions)
34C25 Periodic solutions of ODE
34D20 Lyapunov stability of ODE

Keywords: sub-optimal immunity; nonlinear recovery rate; periodicity; bistability; bifurcation

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