Physical Sciences and Mathematics Commons^™

Viruses and bacteria responsible for infectious diseases often mutate and are carried between geographical regions. We consider a mathematical model which begins to account for these factors. We assume two disjoint populations that only occasionally co-mingle and two strains of a disease present in these populations. Of interest are the equations describing the dynamics of this system, the conditions under which epidemics will occur, and the long term behavior of the system under various initial conditions. We fi#12;nd general conditions

under which a state of disease-free equilibrium is stable. Additionally, we #12;find existence of a biologically relevant equilibrium where two …

One extinction hypothesis of the Columbian mammoth (Mammuthus columbi), called overkill, theorizes that early humans overhunted the animal. We employ two different approaches to test this hypothesis mathematically: analyze the stability of the equilibria of a 2D ordinary differential equations (ODE) system and develop a metapopulation differential equations model. The 2D ODE system is a modified predator-prey model that also includes migration. The metapopulation model is a spatial expansion of the first model on a rectangular grid. Using this metapopulation system, we model the migration of humans into North America and the response in the mammoth population. These approaches show …