Disease induced dynamics in host-parasitoid systems: chaos and coexistence
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All animals and plants are, to some extent, susceptible to disease caused by varying combinations of parasites, viruses and bacteria. In this paper, we present a mathematical model of interactions between a host, two parasitoids and a pathogen which shows that the presence of an infection can preserve and promote diversity in such multi-species systems. Initially, we use a system of ordinary differential equations to investigate interactions between two species of parasitoids, a host and a host infection. We show that the presence of all four species is necessary for the system as a whole to persist, and that in particular, the presence of the pathogen is necessary for the coexistence of the two parasitoid species. The inclusion of infection induces a wide range of dynamics, including chaos, and these dynamics are robust for a wide range of parameter values. We then extend the model to include spatial effects by introducing random motility (diffusion) of all three species and examine the subsequent spatio-temporal dynamics, including travelling waves and other more complicated heterogeneous behaviour. The computational simulation results of the model suggest that infection in the hosts can blunt the effects of competition between parasitoids, allowing the weaker competitor to survive. Regardless of the nature of the stability of the coexistent steady state of the system, there is an initial period of transient dynamics, the length of which can be extended by an appropriate choice of initial conditions. The existence of these transient dynamics suggests that systems subject to regular restoration to a starting state, such as agro-ecosystems, may be kept in a continual state of dynamic transience, and this has implications for the use of natural enemies to control insect pests, the preservation of biodiversity in farmland habitats and the more general dynamics of disease processes.