R: Host Longevity Matters.

The basic reproduction ratio, R, is a fundamental concept in epidemiology. It is defined as the total number of secondary infections brought on by a single primary infection, in a totally susceptible population. The value of R indicates whether a starting epidemic reaches a considerable part of the population and causes a lot of damage, or whether it remains restricted to a relatively small number of individuals. To calculate R one has to evaluate an integral that ranges over the duration of the infection of the host. This duration is, of course, limited by remaining host longevity. So, R depends on remaining host longevity and in this paper we show that for long-lived hosts this aspect may not be ignored for long-lasting infections. We investigate in particular how this epidemiological measure of pathogen fitness depends on host longevity. For our analyses we adopt and combine a generic within- and between-host model from the literature. To find the optimal strategy for a pathogen from an evolutionary point of view, we focus on the indicator [Formula: see text], i.e., the optimum of R as a function of its replication and mutation rates. These are the within-host parameters that the pathogen has at its disposal to optimize its strategy. We show that [Formula: see text] is highly influenced by remaining host longevity in combination with the contact rate between hosts in a susceptible population. In addition, these two parameters determine whether a killer-like or a milker-like strategy is optimal for a given pathogen. In the killer-like strategy the pathogen has a high rate of reproduction within the host in a short time span causing a relatively short disease, whereas in the milker-like strategy the pathogen multiplies relatively slowly, producing a continuous small amount of offspring over time with a small effect on host health. The present research allows for the determination of a bifurcation line in the plane of host longevity versus contact rate that forms the boundary between the milker-like and killer-like regions. This plot shows that for short remaining host longevities the killer-like strategy is optimal, whereas for very long remaining host longevities the milker-like strategy is advantageous. For in-between values of host longevity, the contact rate determines which of both strategies is optimal.