Volume 19, Number 3, Fall 2011
DENSITY DEPENDENCE IN DISEASE
INCIDENCE AND ITS IMPACTS ON
REBECCA DE BOER AND MICHAEL Y. LI
Abstract. Incidence describes the rate at which new cases of infectious diseases occur. An accurate description of disease incidence is vital to infectious disease modelling. Incidence in epidemic models commonly depends on the size of the infectious and suceptible sub-populations, and may also depend on the size or density of the total population. We show that, even in the simplest SIR models, population dependent incidence can lead to complicated dynamics, including backward bifurcations that result in bistability and Hopf bifurcations that result in periodic oscillations. The types of density dependent incidence we consider can be interpreted as capturing changes in social behaviours as population size changes. Our results demonstrate that density-dependent incidence can be a new mechanism for complex disease dynamics.