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Analysis of a delay prey-predator model with disease in the prey species only. (English) Zbl 1168.92328
Summary: A three-dimensional eco-epidemiological model with delay is considered. The stability of the two equilibria, the existence of Hopf bifurcations and permanence are investigated. It is found that Hopf bifurcations occur when the delay $$\tau$$ passes through a sequence of critical values. The estimation of the length of delay to preserve stability has also been calculated. Numerical simulations with a hypothetical set of data have been done to support the analytical findings.

##### MSC:
 92D30 Epidemiology 92D40 Ecology 34K18 Bifurcation theory of functional-differential equations 34K20 Stability theory of functional-differential equations
##### Keywords:
predator-prey model; eco-epidemiology; delay; Hopf bifurcation
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