When does pathogen evolution maximize the basic reproductive number in well-mixed host-pathogen systems?

Pathogen evolution towards the largest basic reproductive number, R0, has been observed in many theoretical models, but this conclusion does not hold universally. Previous studies of host-pathogen systems have defined general conditions under which R0 maximization occurs in terms of R0 itself. However, it is unclear what constraints these conditions impose on the functional forms of pathogen related processes (e.g. transmission, recover, or mortality) and how those constraints relate to the characteristics of natural systems. Here we focus on well-mixed SIR-type host-pathogen systems and, via a synthesis of results from the literature, we present a set of sufficient mathematical conditions under which evolution maximizes R0. Our conditions are in terms of the functional responses of the system and yield three general biological constraints on when R0 maximization will occur. First, there are no genotype-by-environment interactions. Second, the pathogen utilizes a single transmission pathway (i.e. either horizontal, vertical, or vector transmission). Third, when mortality is density dependent: (i) there is a single infectious class that individuals cannot recover from, (ii) mortality in the infectious class is entirely density dependent, and (iii) the rates of recovery, infection progression, and mortality in the exposed classes are independent of the pathogen trait. We discuss how this approach identifies the biological mechanisms that increase the dimension of the environmental feedback and prevent R0 maximization.