In the present work a mathematical model of the prey-predator system with disease in the prey is proposed. The basic model is then modified by the introduction of time delay. The stability of the boundary and endemic equilibria are discussed. The stability and bifurcation analysis of the resulting delay differential equation model is studied and ranges of the delay inducing stability as well as the instability for the system are found. Using the normal form theory and center manifold argument, we derive the methodical formulae for determining the bifurcation direction and the stability of the bifurcating periodic solution. Some numerical simulations are carried out to explain our theoretical analysis.
Kar, T. K. and Mondal, Prasanta K.
A Mathematical Study on the Dynamics of an Eco-Epidemiological Model in the Presence of Delay,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 7,
1, Article 20.
Available at: https://digitalcommons.pvamu.edu/aam/vol7/iss1/20