The effect of heterogeneity on the evolution of parasite virulence

Microparasites generally evolve in response to the immune system of vertebrate hosts. Earlier models have examined parasite evolution by determining the growth rate of the parasite at which its transmission is maximized. These earlier studies considered this problem for acute infections of hosts with a single parasite strain (which cannot escape from the immune response), and assumed that there was no heterogeneity in the parameters describing the interaction of the parasite and the host. In this case transmission was maximized for the parasite with an intermediate rate of growth $r$ that corresponds to the parasite being just controlled by the immune response prior to its reaching a lethal density $D$. We extend the earlier work by examining the influence of heterogeneity in host parameters on the optimal growth rate of the parasite and its virulence. Our results suggest that: (i) an increase in heterogeneity initially leads to the decrease in the optimal growth rate of the parasite with subsequent increase as the variance is elevated to very high levels, (ii) the total transmission of the pathogen from an infected host decreases with an increase of the heterogeneity, and (iii) that the virulence as measured by the case mortality rate (a fraction of hosts who die when they are exposed to the pathogen) equals zero in homogeneous population and increases with increasing heterogeneity.