Infinite ODE Systems Modeling Size-Structured Metapopulations, Macroparasitic Diseases, and Prion Proliferation

Abstract

Infinite systems of ordinary differential equations can describe: •  Spatially implicit metapopulation models with discrete patch-size structure •  Host-macroparasite models that distinguish hosts by their parasite loads •  Prion proliferation models that distinguish protease-resistant protein aggregates by the number of prion units they contain It is the aim of this chapter to develop a theory for infinite ODE systems in sufficient generality (based on operator semigroups) and, besides well-posedness, to establish conditions for the solution semiflow to be dissipative and have a compact attractor for bounded sets. For metapopulations, we present conditions for uniform persistence on the one hand and prove on the other hand that a metapopulation dies out, if there is no emigration from birth patches or if empty patches are not colonized.