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

Graduation date: 2012Modeling and analyzing the combined effects of disease and population dynamics\ud is important in understanding the effects of mechanisms such as pathogen transmission\ud and direct competition between host species on the distribution and abundance of different\ud species in an ecological community. Mathematical analysis of such models in a\ud spatially explicit environment gives additional important insight into these systems. Motivated\ud by our participation in the IGERT Ecosystem Informatics program, we explore\ud the interactions between and among disease, competition, and spatial heterogeneity from\ud a mathematical modeling perspective. In particular, we formulate a model in which two\ud species compete directly via Lotka-Volterra competition and share a directly transmitted\ud pathogen via both mass action (density-dependent) and frequency-dependent incidence.\ud We determine conditions under which the pathogen is endemic as well as conditions for\ud long-term coexistence of the two species and the pathogen. As the interior equilibria are\ud intractable, we examine a special case for which full stability analysis is possible. We show\ud that in this case, mass action and frequency incidence behave qualitatively the same. We\ud prove existence, uniqueness, and stability for the full model with frequency incidence under\ud the assumption of no death due to disease using theory of asymptotically autonomous\ud equations. Using persistence theory, we show that for the full model with mass action, if\ud all boundary equilibria are unstable, then both species and the pathogen persist uniformly\ud strongly. We extend the multi-host competition-disease model to include multiple patches\ud in order to model Barley Yellow Dwarf Virus in native grasslands. Our results suggest\ud that connectivity can interact with arrival time and host infection tolerance to determine\ud the success or failure of an invasion. Lastly, we simulate the spread of the multi-host virus\ud rinderpest in livestock across the United States, finding that the outcome varies greatly\ud with the starting location of the epidemic