Interplay of Functional Responses and Weak Allee Effect on Pest Control via Viral Infection or Natural Predator: An Eco-epidemiological Study

Abstract

We propose and analyze a deterministic eco-epidemiological system where the susceptible pest exhibits a weak Allee effect due to mating limitation. We make the following assumptions: (i) Allee effect is built in the reproduction process of susceptible pest where infected pest has no contribution; and (ii) growth rate of natural predator is negative for consuming infected pest. We also assume that the functional response of predator for susceptible pest is linear, hyperbolic, or sigmoidal, whereas for infected pest is linear, as infected pest are weakened and easy to catch. We study the dynamics of the system around each of the ecological feasible equilibrium and observe some interesting features of the system dynamics. The reduction of disease eradication, and predator–pest coexistence are observed around the predator free and disease free equilibrium respectively. It is also observed that the interior equilibrium is always unstable and the result is true for any choice of functional responses. Our results suggest that introduction of predator or natural enemies with sigmoidal functional response is a good candidate to represent disease eradication.