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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.

MSC:
34C60Qualitative investigation and simulation of models (ODE)
34D20Stability of ODE
92C60Medical epidemiology
34C23Bifurcation (ODE)
Software:
XPPAUT
WorldCat.org
Full Text: DOI
References:
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