Speaker: Thanate Dhirasakdanon,
Department of Mathematics and Statistics,
Arizona State University

Title:Kolmogorovs differential equations and Markov population chains

Abstract:Spatially implicit metapopulation models with discrete patch-size structure and host-macroparasite models which distinguish hosts by their parasite loads lead to infinite systems of ordinary differential equations. In this talk, the linear foundations are laid. The linear foundations are of own interest as they apply to continuous-time population growth processes (Markov chains). Conditions are derived that the solutions of an infinite linear system of differential equations induce a $C_0$-semigroup on an appropriate sequence space. We derive estimates for the growth bound and the essential growth bound and study the asymptotic behavior. Our results will be illustrated for birth and death processes with immigration and catastrophes.