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Analysis of a delay nonautonomous predator-prey system with disease in the prey. (English) Zbl 1217.93073
Summary: We have considered a nonautonomous predator-prey model with time delay due to gestation, in which a disease that can be transmitted by contact spreads among the prey only. Here, we have established some sufficient conditions on the permanence of the system by using inequality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-makers in targeting prevention and treatment resources for maximum effectiveness.
MSC:
93C15Control systems governed by ODE
93D30Scalar and vector Lyapunov functions
49N75Pursuit and evasion games in calculus of variations
92D30Epidemiology