Thresholds for macroparasite infections.

Abstract

We analyse here the equilibria of an infinite system of partial differential equations modelling the dynamics of a population infected by macroparasites. We find that it is possible to define a reproduction number R(0) that satisfies the intuitive definition, and yields a sharp threshold in the behaviour of the system: if R(0) < 1, the parasite-free equilibrium (PFE) is asymptotically stable and there are no endemic equilibria; if R(0) > 1, the PFE is unstable and there exists a unique endemic equilibrium. The results mainly confirm what had been obtained in simplified models, except for the fact that no backward bifurcation occurs in this model. The stability of equilibria is established by extending an abstract linearization principle and by analysing the spectra of appropriate operators.