Three Population Models Applied to Competition, Disease and Invasion

In this work, we present three diffrent types of population models. The first two models are examined in the context of optimal control problems. The third involves the construction of an invasion model using a significant amount of data.

The first model describes the interaction of three populations, motivated by a combat scenario. One of the three populations can switch the mode of alliance with the other two populations between cooperation and competition. The other two populations always compete with each other. In this system of parabolic partial differential equations, the control is the function which measures the strength of alliance.

The second model is a metapopulation SIR model for the spread of rabies among raccoons. This system of ordinary differential equations considers subpopulations connected via movement of individuals between subpopulations. The strength of the connectivity between two subpopulations is inversely proportional to the geographical distance between them. We apply control theory to find the best strategy (timing and location) for vaccination to control the disease.

The third problem involves construction of a model of the spread of Eurasian collared doves in the U.S. using an integrodifference equation. We investigate the effect of spatial variation of the length of the growing season on the growth rate of the collared dove. Since the growing season length affects the breeding season length, we take into account the difference in the number of clutches in estimating the number of offspring produced each breeding season.