# zbMATH — the first resource for mathematics

Stability and Hopf bifurcation of an eco-epidemiological model with delays. (Chinese. English summary) Zbl 1071.34078
Summary: A system of retarded functional-differential equations is proposed as a predator-prey model with disease in the prey. Invariance properties, boundary equilibria and global stability are analyzed. The authors show that a positive equilibrium is locally asymptotically stable when time delay $$\tau= \tau_1+ \tau_2$$ is suitable small, while a loss of stability by a Hopf bifurcation can occur as the delays increase.

##### MSC:
 34K20 Stability theory of functional-differential equations 92D25 Population dynamics (general) 34K18 Bifurcation theory of functional-differential equations 34K60 Qualitative investigation and simulation of models involving functional-differential equations 92D30 Epidemiology
##### Keywords:
predator-prey model; global stability; Hopf bifurcation