Role of Allee in controlling chaos in an eco-epidemiological model with disease in predator

Abstract

There has been a sharp decline in the population of the world's largest living carnivorous marsupial, Tasmanian tiger, or Thylacine. This has led to the species nearing its extinction although several efforts for its survival plans. This article addressee the issues to understand the dynamics behind the extinction of many endangered species such as the above mentioned species. In this article, we study the spread of Tasmanian devil virus in the Tasmanian tiger population and analysing the survival of population through this infection. Hence, we propose here an eco-epidemiological model with Allee effect with interaction assumed to be of Holling type II functional response between prey and predator. The resulting mathematical model is analysed for long term dynamics using linear stability analysis. The global stability of endemic equilibrium is established. Through rigorous mathematical analysis and numerical simulations, it has been established that the presence of Allee effect and Holling type interaction have much impact on extinction of the species. Exhaustive numerical simulations revels very rich dynamics of the model and also justify the analytical results. We have discussed the way to eradicate and control the disease in the system which can lead to increase in the population of Tasmanian tiger.