Evolution of pathogen tolerance and reproductive trade-off implications.

We develop an epidemic model that accounts explicitly for the pathogen pool and incorporates population variations in host defense strategy, measured in disease tolerance that is assumed to be perfectly inherited by offspring. Although the proposed model is more general, it is motivated by the devastating Batrachochytrium dendrobatidis (Bd) fungus that is responsible for severe declines in amphibians. We show that the model's basic reproduction number consists of a weighted average of individual basic reproduction numbers associated to each tolerance class. If the individual basic reproduction number associated to the highest tolerance level is less than one, then any solution converges to a (non-unique) disease-free equilibrium. We show that in the absence of a trade-off, different host defense strategies can coexist as long as the disease will go extinct eventually. In contrast, if the disease persists, the set of pandemic equilibria consists of isolated vertex equilibria, implying the survival of an individual host defense strategy. The pandemic equilibrium corresponding to the highest tolerance, i.e., lowest disease-induced death rate is the only asymptotically stable pandemic equilibrium. Additionally, to investigate the impact of a trade-off, we incorporate a tolerance cost in reproduction, whereby a higher tolerance comes at the expense of a lower reproductive rate. Now, the coexistence of host defense strategies in the absence of the disease is no longer supported. However, the set of pandemic equilibria increases in richness to contain equilibria where different tolerance classes are present.