An SEI model with density-dependent demographics and epidemiology

Abstract

Two compartmental models for the dynamics of an infectious disease in a wild-animal population are analysed. The models feature density-dependent birth, death, and contact rates, and pseudovertical disease transmission. For the SI model it is shown that up to four steady states may exist, depending on the parameter values, and that one of these states is globally stable. For the SEI model four equivalent steady states exist, but periodic solutions are now possible for some parameter values.