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Persistence and global stability analysis of an eco-epidemiological model of the Salton Sea

Md. Sabiar Rahman, Santabrata Chakravarty

Abstract


The Salton Sea is the biggest lake in the south-eastern California, which is being fed by different small rivers and agricultural drainage. We know that it has been facing severe problems due to its excessive fish and bird mortality. The present study deals with three component models consisting of susceptible fish population, infected fish population and their predator, specially pelican birds. The model under consideration is a modification of the previous model studied by Haque and Chattopadhyay (2007), from more biologically realistic point of view. Based upon thorough analysis of the problem under study, all the equilibria are adequately characterized and their nature of stability, namely local and global stability are properly discussed. The geometric approach has been used to establish the global stability analysis for the model under consideration, which is primarily based on the use of higher-order generalization of Bendixson’s criterion. An extensive quantitative analysis has been carried out through their graphical representation in order to validate the applicability of the model under consideration.

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