A baseline model for the co-evolution of hosts and pathogens

The basic reproduction ratio (R0) is the expected number of secondary cases per primary in a totally susceptible population. In a baseline model, faced with an individual host strain pathogen virulence evolves to maximise R0 which yields monomorphism. The basic depression ratio (D0) is the amount by which the total population is decreased, per infected individual, due to the presence of infection. Again, in a baseline model, faced with an individual pathogen strain host resistance evolves to minimise D0 which yields monomorphism. With this in mind we analyse the community dynamics of the interaction between R0 and D0 and show that multi-strain co-existence (polymorphism) is possible and we discuss the possibility of stable cycles occuring within the co-existence states. We show for co-existence, the number of host and pathogen strains present need to be identical in order to achieve stable equilibria. For polymorphic states we observe contingencies (outcome dependent on initial conditions) between both point equilibrium and sustained oscillations. Invasion criteria for host and pathogen strains are identified.