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Homoclinic orbits in a disease transmission model with nonlinear incidence and nonconstant population. (English) Zbl 1126.34337

Summary: Periodic oscillations are proved for an SIRS disease transmission model in which the size of the population varies and the incidence rate is a nonlinear function. For this particular incidence function, analytical techniques are used to show that, for some parameter values, periodic solutions can arise through a Hopf bifurcation and disappear through a homoclinic loop bifurcation. The existence of periodicity is important as it may indicate different strategies for controlling disease.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
92D30 Epidemiology
37N25 Dynamical systems in biology
34C25 Periodic solutions to ordinary differential equations
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