An eco-epidemiological system with infected prey and predator subject to the weak Allee effect

• Published in: Mathematical biosciences Vol. 246; no. 2; pp. 260 - 271
• Main Authors: Sasmal, Sourav Kumar, Chattopadhyay, Joydev
• Format: Journal Article
• Language: English
• Published: United States Elsevier Inc 01.12.2013
• Subjects: Animals; Communicable Diseases - epidemiology; Communicable Diseases - transmission; Computer Simulation; disease models; Eco-epidemiological system; Ecosystem; epidemiology; Functional response; Models, Theoretical; Population Dynamics; predator-prey relationships; predators; Predatory Behavior; Stability analysis; The Allee effect; Stability analysis; Functional response; Eco-epidemiological system; The Allee effect
• ISSN: 0025-5564; 1879-3134; 1879-3134
• DOI: 10.1016/j.mbs.2013.10.005

•We study dynamics of eco-epidemiological system with disease in prey and the weak Allee effects in predator.•Perform local and global dynamics of the model equations.•Model does not support the coexistence of susceptible-infected-predator. In this article, we propose a general prey–predator model with disease in prey and predator subject to the weak Allee effects. We make the following assumptions: (i) infected prey competes for resources but does not contribute to reproduction; and (ii) in comparison to the consumption of the susceptible prey, consumption of infected prey would contribute less or negatively to the growth of predator. Based on these assumptions, we provide basic dynamic properties for the full model and corresponding submodels with and without the Allee effects. By comparing the disease free submodels (susceptible prey–predator model) with and without the Allee effects, we conclude that the Allee effects can create or destroy the interior attractors. This enables us to obtain the complete dynamics of the full model and conclude that the model has only one attractor (only susceptible prey survives or susceptible-infected coexist), or two attractors (bi-stability with only susceptible prey and susceptible prey–predator coexist or susceptible prey-infected prey coexists and susceptible prey–predator coexist). This model does not support the coexistence of susceptible-infected-predator, which is caused by the assumption that infected population contributes less or are harmful to the growth of predator in comparison to the consumption of susceptible prey.