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Viral infection model with periodic lytic immune response. (English) Zbl 1079.92048

Summary: The dynamical behavior and bifurcation structure of a viral infection model are studied under the assumption that the lytic immune response is periodic in time. The infection-free equilibrium is globally asymptotically stable when the basic reproductive ratio of virus is less than or equal to one. There is a non-constant periodic solution if the basic reproductive ratio of the virus is greater than one. It is found that period doubling bifurcations occur as the amplitude of the lytic component is increased. For intermediate birth rates, the period triplication occurs and then period doubling cascades proceed gradually toward chaotic cycles. For large birth rate, the period doubling cascade proceeds gradually toward chaotic cycles without the period triplication, and inverse period doubling can be observed. These results can be used to explain the oscillation behavior of virus populations, which was observed in chronic HBV or HCV carriers.

MSC:

92C50 Medical applications (general)
34D23 Global stability of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
92C60 Medical epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
37N25 Dynamical systems in biology
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