The effect of delayed host self-regulation on host-pathogen population cycles in forest insects

Delayed host self-regulation using a Beverton-Holt function and delayed logistic self-regulation are included in a host-pathogen model with free-living infective stages (Anderson and May's model G) with the purpose of investigating whether adding the relatively complex self-regulations decrease the likelihood of population cycles. The main results indicate that adding delayed self-regulation to the baseline model increases the likelihood of population cycles. The dynamics display some of the key features seen in the field, such as cycle peak density exceeding the carrying capacity and a locally stable equilibrium coexisting with a stable cycle (bistability). Numerical studies show that the model with more complex forms of self-regulation can generate cycles which match most aspects of the cycles observed in nature.