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Dynamics of infection with nonlinear incidence in a simple vaccination model. (English) Zbl 1205.34059
Summary: We develop and analyze a simple SIV epidemic model including susceptible, infected and imperfectly vaccinated classes, with a nonlinear incidence rate. We investigate the interaction of the nonlinear incidence and partial immunity. Our main results show that a nonlinear incidence rate could induce a forward bifurcation with hysteresis except for the backward bifurcation. The plausible effects of a vaccination program are demonstrated by two models with nonlinear incidence rate. A vaccination program may contribute to disease spreading, depending on which transmission term involves the nonlinear incidence rate.

34C60Qualitative investigation and simulation of models (ODE)
34D20Stability of ODE
92C60Medical epidemiology
34C23Bifurcation (ODE)
Full Text: DOI
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