Qualitative analysis of an eco-epidemiological model with a role of prey and predator harvesting

The present study deals with the dynamical response of an eco-epidemiological model consisting of prey and predator species having infection in prey population. The inclusion of prey refugia is taken into account to avoid predator attack. The entire prey population is divided into two parts: healthy prey which are capable of reproducing following the logistic law and infected prey which is removed by predation or death before having the possibility of reproducing. Also we have considered the role of harvesting of the susceptible prey and the predator. For biological validity of the model, positivity and boundedness of the system are studied. The dynamical behaviour of the model has been analyzed elaborately. The stability aspects of the basic model around the infection free state, predator free state and the infected steady state from a local as well as a global perspective are studied. The main aim is to study the role of harvesting on the dynamics of disease propagation and/or eradication. By considering harvesting in susceptible prey and predator population, our study gives a new direction to eco-epidemiological model. Changes in local and global dynamical behaviour in terms of important system parameters are obtained. By the numerical simulation Hopf-bifurcation and the stable and unstable behaviour of the system due to harvesting and rate of infection have been observed.