Stability in cyclic epidemic models (Q1061654)

A general formulation for a family of cyclic epidemic models with density-dependent feedback mechanisms and removed classes is presented. A parameter, \(\lambda\), related to the basic reproductive rate determines the asymptotic behaviour of solutions of the model. It is shown that if \(\lambda <1\) the trivial solution is globally stable, and if \(\lambda >1\) it is conditionally stable. The results are applied to a set of differential equations that has been used to model the life cycle of a parasite that has two hosts.