Abstract
Parasites are an acute threat to plant, animal and human populations. To effectively manage infectious diseases, we need to predict the evolution of critical parasite traits, such as transmission and virulence. Among the environmental factors that may affect pathogens evolution, the use of prophylactic treatments, which may exert strong selective pressures on pathogens, must be considered. In addition, spatio-temporal variations in treatment distribution, coupled with the increased mobility of parasites and hosts, are key factors affecting the evolutionary epidemiology of host-parasite interactions. The goal of this thesis was to develop theory to study the short- and long-term evolutionary epidemiology of structured host-parasite interactions in the presence of treatments, taking into account different types of treatments that fluctuate in both time and space. This theory can be applied to pathogens life-history traits evolution (such as virulence in the first two parts), or to resistance traits evolution (such as vaccine escape in the third part).In a first part, we have developed a theoretical model of a heterogeneous population of hosts, under a periodic treatment coverage. Using the adaptive dynamics framework and the concept of reproductive values, we have highlighted the impact of periodicity in treatment coverage on the short-term epidemiology and on the long-term evolution of pathogens life-history traits. Our results suggest that periodic treatment strategies can limit both disease spread and virulence evolution, depending on the type of treatment.In a second part, we have developed a spatial metapopulation model, with two subpopulations characterised by different treatment coverages and connected by pathogen migration. In this part we study the effects of migration and of the differences in coverage on the long-term virulence evolution. We have shown that the spatial structure of the host population and the selective pressure of treatments on pathogens may yield bistability or evolutionary branching points, which can lead to the coexistence of different pathogenic strains.Finally, the third part is an extension of the previous metapopulation model, broadly inspired by the Covid-19 pandemic. However, in contrast to the previous part, we focus on short-term pathogen evolution and study the speed of emergence of a vaccine escape mutant in a two-population model connected by pathogen migration. This model allows for the study of several scenarios inspired by the management of the pandemic. For instance, different vaccination strategies between connected countries, or the impact of border opening and closure on the speed of emergence of a vaccine escape mutant can be explored.Our models aim to remain general and conclusions could be adapted to specific host-pathogen interactions. Thus, our results have interesting implications for the management of infectious disease in animal and public health, and in agriculture.