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The dynamics of an eco-epidemiological model with distributed delay. (English) Zbl 1175.93022
Summary: The dynamical behavior of an eco-epidemiological model with distributed delay is studied. Sufficient conditions for the asymptotic stability of all the equilibria are obtained. We prove that there exists a threshold value of the conversion rate $$h$$ beyond which the positive equilibrium bifurcates towards a periodic solution. We further analyze the orbital stability of the periodic orbits arising from bifurcation by applying Poore’s condition. Numerical simulation with some hypothetical sets of data has been done to support the analytical findings.

##### MSC:
 93A30 Mathematical modelling of systems (MSC2010) 92D30 Epidemiology 93D20 Asymptotic stability in control theory 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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