The tikhonov theorem in some models of mathematical biosciences

Abstract

In this chapter we discuss some applications of the Tikhonov theorem to models presented in Chap. 1. We provide a rigorous derivation of the Allee model from a system of mass-action type population equations and discuss an SIS epidemiological model with vital processes in which the latter act on a much slower timescale than the disease. This chapter is concluded with an analysis of a predator– prey model with prey being able to move between geographical patches at a fast rate.