Continuous Population Models

In this chapter we look at a population in which all individuals develop independently of one another. For this situation to occur these individuals must live in an unrestricted environment where no form of competition is possible. If the population is small then a stochastic model is more appropriate, as the likelihood that the population becomes extinct due to chance must be considered. However, a deterministic model may provide a useful way of gaining sufficient understanding about the dynamics of a population whenever the population is large enough. Furthermore, perturbations to populations at equilibrium often generate on short time scales independent individual responses, which are appropriately modeled by deterministic models. For example, the propagation of a disease in a large population via the introduction of a single infected individual leads to the generation of secondary cases. The environment is free of “intraspecific” competition, at least at the beginning of the outbreak, when a large population of susceptibles provides a virtually unlimited supply of hosts. In short, the spread of disease in a large population of susceptibles may be thought of as an invasion process via independent contacts with a few infectious individuals.