The Importance of Aggregation in the Dynamics of Host-Parasite Interaction in Wildlife: A Mathematical Approach

Abstract

This study examines, from a modelling point of view, the dynamics of infectious diseases in wildlife caused by macroparasites and by tick-borne infections. The overall aim was to investigate the important role played by parasite aggregation in the dynamics of both systems. For macroparasites we first developed some deterministic models that incorporate explicit mechanisms for generating aggregation in parasite distribution, specifically multiple infections and host heterogeneity. We explored the role of aggregation in host regulation and in determining a threshold value for parasite establishment. A large aggregation makes it more difficult for parasites both to regulate hosts, and to get established in a population at carrying capacity. Furthermore, the stabilization yielded by aggregation strongly depends on the mechanism that produces the aggregation. We then introduced some uncertainties into the host-macroparasite system, presenting an individual-based stochastic model that incorporated the same assumptions as the deterministic model. Stochastic simulations, using parameter values based on some real case studies, preserved many features of the deterministic model, like the average value of the variables and the approximate length of the cycles. An important difference is that, even when deterministic models yield damped oscillations, stochastic simulations yield apparently sustained oscillations. The amplitude of such oscillations may be so large as to threaten the parasites’ persistence. With respect to tick-borne diseases we presented a general model framework that incorporated both viraemic and non-viraemic routes of infections. We compute the threshold for disease persistence and study its dependence on the parameters and on host densities. The effects of tick aggregation and correlation between different tick stages on the host have both an important effect on infection persistence, if non-viraemic transmission occurred. In the case of Lyme Disease and Tick-borne Encephalitis (TBE) in Trentino (northern Italy) we showed some numerical results, using parameter estimates based on a detailed field study, and explored the effects of uncertainty on the endemic equilibrium of both diseases assuming only viraemic transmission for Lyme Disease while for TBE we permitted only non-viraemic transmission through co-feeding ticks. In conclusion we have examined the patterns and changes of aggregation in a number of contrasting systems and believe that these studies highlight both the importance of considering heterogeneities in modelling host-parasite interactions and, more specifically, modelling the biological mechanisms that produce aggregation in parasite distributions.