On the interaction between several species of hosts and parasites

Abstract

The fundamental equations, which serve to determine the population densities and the age-distribution occurring in the interaction between several species of hosts and parasites, are derived. The equations determining the steady state, when such si, state is possible, are then deduced, and it is shown that a steady state is impossible when the number of parasite-species is less than the number of host-species. The problem is much simplified when the individuals of the host-species have probabilities of interaction which are independent of their ages; in particular the behavior near the steady state is found to be described by a system of simultaneous linear integro-differential equations. These show that when only 2 species interact the steady state, to a first approximation, is unstable, and that oscillations of increasing amplitude occur. It is shown how the theory may be extended to include hyperparasites.