Abstract
In this paper, a three-dimensional eco-epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcation and the permanence are investigated. It is found that Hopf bifurcation occurs when the delay ? passes though a sequence of critical values. The estimation of the length of delay to preserve stability has also been calculated. Numerical simulation with a hypothetical set of data has been done to support the analytical findings. The mathematical modelling of epidemics has become a very important sub- ject of research after the seminal model of Kermac-McKendric (1927) on SIRS (susceptible-infected-removed-susceptible) systems, in which the evolution of a disease which gets transmitted upon contact is described. Important studies in the following decades have been carried out, with the aim of controlling the
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