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Some epidemiological models with nonlinear incidence. (English) Zbl 0722.92015
Summary: Epidemiological models with nonlinear incidence rates can have very different dynamic behaviors than those with the usual bilinear incidence rate. The first model considered here includes vital dynamics and a disease process where susceptibles become exposed, then infectious, then removed with temporary immunity and then susceptible again. When the equilibria and stability are investigated, it is found that multiple equilibria exist for some parameter values and periodic solutions can arise by Hopf bifurcation from the larger endemic equilibrium. Many results analogous to those in the first model are obtained for the second model which has a delay in the removed class but no exposed class.

MSC:
92D30 Epidemiology
34C23 Bifurcation theory for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34D08 Characteristic and Lyapunov exponents of ordinary differential equations
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