Backward/Hopf bifurcations in SIS models with delayed nonlinear incidence rates

Abstract

The classical SIS model with a constant transmission rate exhibits simple dynamic behaviors fully determined by the basic reproduction number. Behavioral changes and intervention measures influenced by the level of infection, likely with a time lag, require the transmission rate to be a nonlinear function of the total infectives. This nonlinear transmission, as shown in this paper via a combination of qualitative and numerical analysis, can generate interesting dynamical behaviors at the population level including backward and Hopf bifurcations. We conclude that sustained infections and periodic outbreaks can be consequences of delayed changes in behaviors or human intervention.

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