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Stability and Hopf bifurcation in a viral infection model with nonlinear incidence rate and delayed immune response. (English) Zbl 1239.92071

Summary: A viral infection model with nonlinear incidence rate and delayed immune response is investigated. It is shown that if the basic reproduction ratio of the virus is less than unity, and the infection-free equilibrium is globally asymptotically stable. By analyzing the characteristic equation, the local stability of the chronic infection equilibrium of the system is discussed. Furthermore, the existence of Hopf bifurcations at the chronic infection equilibrium is also studied. By means of an iteration technique, sufficient conditions are obtained for the global attractiveness of the chronic infection equilibrium. Numerical simulations are carried out to illustrate the main results.

MSC:

92C60 Medical epidemiology
34K20 Stability theory of functional-differential equations
34K18 Bifurcation theory of functional-differential equations
65C20 Probabilistic models, generic numerical methods in probability and statistics
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