Dispersal and Disease Dynamics in Populations with and without Demography
An integrodifference equation model is introduced to study the spatial spread of epidemics through populations with overlapping and non-overlapping epidemiological generations. Monotone and non-monotone epidemic growth functions are considered. The focus is on the application of a recent theory of existence of travelling wave solutions for integrodifference equations. Numerical studies with emphasis on the minimum asymptotic speed of propagation (c*) are conducted. The results presented are contrasted with similar works carried out in the context of ecological invasions. The theoretical results are illustrated numerically in the context of SI (susceptible-infected) and SIS (susceptible-infected-susceptible) epidemic models. The simulations are carried out in one and two spatial dimensions using various dispersal kernels. In order to explore future possibilities, an alternative framework for dispersal model is introduced via the use of a metapopulation approach. That is, a system of nonlinear ordinary differential equations is used to model the impact of transient populations on disease dynamics. A preliminary study of a simple two group model is conducted in the context of the interactions between migratory and local bird populations. The motivation comes from the recent avian influenza epidemic.
This research was partially supported by the Sloan Foundation, Cornell University, the Mathematical and Theoretical Biology Institute, Los Alamos National Laboratory, the University of Puerto Rico at Mayaguez, Arizona State University, the National Science Foundation and the National Security Agency.
Dispersal; Integrodifference Equations; Epidemiology; Discrete-time models; Travelling wave solutions; Metapopulation
dissertation or thesis