Non-spatial and spatial models for multi-host pathogen spread in competing species : applications to barley yellow dwarf virus and rinderpest

Abstract

Modeling and analyzing the combined effects of disease and population dynamics is important in understanding the effects of mechanisms such as pathogen transmission and direct competition between host species on the distribution and abundance of different species in an ecological community. Mathematical analysis of such models in a spatially explicit environment gives additional important insight into these systems. Motivated by our participation in the IGERT Ecosystem Informatics program, we explore the interactions between and among disease, competition, and spatial heterogeneity from a mathematical modeling perspective. In particular, we formulate a model in which two species compete directly via Lotka-Volterra competition and share a directly transmitted pathogen via both mass action (density-dependent) and frequency-dependent incidence. We determine conditions under which the pathogen is endemic as well as conditions for long-term coexistence of the two species and the pathogen. As the interior equilibria are intractable, we examine a special case for which full stability analysis is possible. We show that in this case, mass action and frequency incidence behave qualitatively the same. We prove existence, uniqueness, and stability for the full model with frequency incidence under the assumption of no death due to disease using theory of asymptotically autonomous equations. Using persistence theory, we show that for the full model with mass action, if all boundary equilibria are unstable, then both species and the pathogen persist uniformly strongly. We extend the multi-host competition-disease model to include multiple patches in order to model Barley Yellow Dwarf Virus in native grasslands. Our results suggest that connectivity can interact with arrival time and host infection tolerance to determine the success or failure of an invasion. Lastly, we simulate the spread of the multi-host virus rinderpest in livestock across the United States, finding that the outcome varies greatly with the starting location of the epidemic.