A Generalist Predator Regulating Spread of a Wildlife Disease: Exploring Two Infection Transmission Scenarios

M. Sen¹ ; M. Banerjee² ; A. Morozov^3, 4

¹ Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore
² Department of Mathematics and Statistics, I. I. T. Kanpur, India
³ Department of Mathematics, University of Leicester, UK
⁴ Shirshov Institute of Oceanology, Moscow, Russia

Mathematical modelling of natural phenomena, Tome 10 (2015) no. 2, pp. 74-95

Résumé

Ecoepidemiology is a well-developed branch of theoretical ecology, which explores interplay between the trophic interactions and the disease spread. In most ecoepidemiological models, however, the authors assume the predator to be a specialist, which consumes only a single prey species. In few existing papers, in which the predator was suggested to be a generalist, the alternative food supply was always considered to be constant. This is obviously a simplification of reality, since predators can often choose between a number of different prey. Consumption of these alternative prey can dramatically change their densities and strongly influence the model predictions. In this paper, we try to bridge the gap and explore a generic eco-epidemiological system with a generalist predator, where the densities of all prey are dynamical variables. The model consists of two prey species, one of which is subject to an infectious disease, and a predator, which consumes both prey species. We investigate two main scenarios of infection transmission mode: (i) the disease transmission rate is predator independent and (ii) the transmission rate is a function of predator density. For both scenarios we fulfil an extensive bifurcation analysis. We show that including a second dynamical prey in the system can drastically change the dynamics of the single prey case. In particular, the presence of a second prey impedes disease spread by decreasing the basic reproduction number and can result in a substantial drop of the disease prevalence. We demonstrate that with efficient consumption of the second prey species by the predator, the predator-dependent disease transmission can not destabilize interactions, as in the case with a specialist predator. Interestingly, even if the population of the second prey eventually vanishes and only one prey species finally remains, the system with two prey species may exhibit different properties to those of the single prey system.

Détail

DOI : 10.1051/mmnp/201510206

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