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Backward bifurcation in epidemic control. (English) Zbl 0904.92031

Summary: For a class of epidemiological SIRS models that include public health policies, the stability at the uninfected state and the prevalence at the infected state are investigated. Backward bifurcation from the uninfected state and hysteresis effects are shown to occur for some range of parameters. In such cases, the reproduction number does not describe the necessary elimination effort; rather the effort is described by the value of the critical parameter at the turning point. An explicit expression is given for this quantity. The phenomenon of subcritical bifurcation in epidemic modeling is also discussed in terms of group models, pair formation, and macroparasite infection.

MSC:

92D30 Epidemiology
34C23 Bifurcation theory for ordinary differential equations
34D15 Singular perturbations of ordinary differential equations
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