Pelicans at risk in Salton Sea—an eco-epidemiological model-II

The Salton Sea which is located in the Southeast desert of California is becoming a dangerous habitat for birds. It is supposed that elevated salinity, accelerated eutrophication, blooms of Avian botulism and dramatic water quality fluctuation are the key factors for massive die-off of Tilapia (prey) and Pelican (predator) in the Salton sea. Chattopadhyay and Bairagi [Ecol. Model. 136 (2001) 103] proposed and analyzed a three-component eco-epidemiological model consisting of susceptible fish population, infected fish population and their predator, the Pelican population. We modify their model from more biologically realistic point of view and then analyze it. The main objective of the work is to find out conditions for which the modified system becomes disease free. Numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings. It is observed that if the initial value of the system is contained in the invariant set which contain the disease-free equilibrium, the solution will approach the disease-free equilibrium under suitable parametric conditions. If the initial value of the system is not in the invariant set, impulsive harvesting strategies can be used to change the initial state to the desired disease-free equilibrium state.