A Study of Chaotic Dynamics and Its Possible Control in a Predator-Prey Model with Disease in the Predator
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The effect of parasites and pathogens in the prey population received a lot of attention, but disease in the predator population has been studied comparatively little in literature. In this study, we have considered a predator-prey model with disease in the predator population. Here, we have analyzed the local stability of the model system around the equilibria. We have derived the ecological as well as the disease basic reproduction numbers and analyzed the community structure of the model system by these numbers. Our numerical results reveal that disease introduction in the predator population produces chaotic dynamics. We have observed stable focus, limit cycles, period doubling, and chaos for variation of the force of infection in the predator population. It is also observed that half-saturation constants are responsible for occurrence and control of chaos. It is found that chaos may be prevented by increasing the predation efficiency of the infected predator.
KeywordsDisease in predator Chaos Stable Hopf bifurcation Reproduction number Half-saturation constant
Mathematics Subject Classification (2010)37N25
The authors are grateful to the reviewers for their helpful comments and suggestions. The authors are also grateful to the editor for his suggestions.
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