Modelling density-dependent resistance in insect-pathogen interactions.

We consider a mathematical model for a host-pathogen interaction where the host population is split into two categories: those susceptible to disease and those resistant to disease. Since the model was motivated by studies on insect populations, we consider a discrete-time model to reflect the discrete generations which are common among insect species. Whether an individual is born susceptible or resistant to disease depends on the local population levels at the start of each generation. In particular, we are interested in the case where the fraction of resistant individuals in the population increases as the total population increases. This may be seen as a positive feedback mechanism since disease is the only population control imposed upon the system. Moreover, it reflects recent experimental observations from noctuid moth-baculovirus interactions that pathogen resistance may increase with larval density. We find that the inclusion of a resistant class can stabilise unstable host-pathogen interactions but there is greatest regulation when the fraction born resistant is density independent. Nonetheless, inclusion of density dependence can still allow intrinsically unstable host-pathogen dynamics to be stabilised provided that this effect is sufficiently small. Moreover, inclusion of density-dependent resistance to disease allows the system to give rise to bistable dynamics in which the final outcome is dictated by the initial conditions for the model system. This has implications for the management of agricultural pests using biocontrol agents-in particular, it is suggested that the propensity for density-dependent resistance be determined prior to such a biocontrol attempt in order to be sure that this will result in the prevention of pest outbreaks, rather than their facilitation. Finally we consider how the cost of resistance to disease affects model outcomes and discover that when there is no cost to resistance, the model predicts stable periodic outbreaks of the insect population. The results are interpreted ecologically and future avenues for research to address the shortfalls in the present model system are discussed.