Dynamics of a prey-predator system with infection in prey




Kant, Shashi
Kumar, Vivek

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Texas State University, Department of Mathematics


This article concerns a prey-predator model with linear functional response. The mathematical model has a system of three nonlinear coupled ordinary differential equations to describe the interaction among the healthy prey, infected prey and predator populations. Model is analyzed in terms of stability. By considering the delay as a bifurcation parameter, the stability of the interior equilibrium point and occurrence of Hopf-bifurcation is studied. By using normal form method, Riesz representation theorem and center manifold theorem, direction of Hopf bifurcation and stability of bifurcated periodic solutions are also obtained. As the real parameters are not available (because it is not a case study). To validate the theoretical formulation, a numerical example is also considered and few simulations are also given.



Predator-prey model, Linear Functional Response, Hopf-bifurcation, Stability analysis, Time delay


Kant, S., & Kumar, V. (2017). Dynamics of a prey-predator system with infection in prey. <i>Electronic Journal of Differential Equations, 2017</i>(209), pp. 1-27.


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