An Epidemic Model with Pathogen Tolerance and Trade-Off

We develop an evolutionary epidemic model that accounts explicitly for the pathogen pool and incorporates population variations in host defense strategy, here measured in disease tolerance that is perfectly inherited by the offsprings. 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. While the set of disease free equilibria is a submanifold, and different tolerance classes can be represented at a disease free equilibrium,  the set of pandemic equilibria consists only of equilibria where only one tolerance class is present. The pandemic equilibrium corresponding to the highest tolerance, i.e., lowest disease-induced death rate is the only asymptotically stable pandemic equilibrium. We extend this model by incorporating the realistic feature of a trade-off between tolerance and reproduction. In this case, the set of disease free equilibria reduces to equilibria corresponding to individual tolerance classes but the set of pandemic equilibria increases in richness to contain equilibria where different tolerance classes are present. This is joint work with David Swigon, Mark Wilber, and Jason Walsman.