Some aspects of the coevolution of virulence and resistance in contact transmission disease processes with ecological constraints

Abstract

In this paper, the author constructs a general, continuous-time dynamical model of a coevolutionary host-microparasite interaction, which incorporates host resistance (degree of susceptibility to invasion by the parasite) and parasite virulence (pathogenicity and transmission efficiency). Discrete classes of resistance type and virulence type are allowed. It is assumed that high virulence parasite strains are able to take over hosts already occupied by lower virulence strains. Heritability of host resistance is assumed, but specific assumptions about the genetics of such inheritance are avoided. Instead, a ‘neutral’ view is adopted, which assumes that the disease process is the sole selective force acting on a disease-free resistance distribution. This allows the dimensionality of the model to be kept lower than corresponding explicitly population-genetic models. Ecological factors are taken into account via density dependence in host encounter rate (which also influences transmission properties of the disease via contact transmission), and by density dependence in host fecundity. Two distinct host types are considered, which we call ‘bunchers’ and ‘separators’, characterized by the form of reaction of the encounter rate to changes in host density. Detailed analyses are given for versions of the model having: (a) one resistance class and one virulence class; (b) two resistance classes and one virulence class; (c) two resistance classes and two virulence classes. Sufficient conditions are found in case (c) for the low resistance type to be eliminated by the coevolutionary process. Features which might tend to promote resistance polymorphism are also discussed.

coevolution, virulence class, resistance class, susceptibility, transmission probability, mutation rate, neutral reproduction, encounter rate, effective fecundity, ‘bunchers’, ‘separators’