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Dynamics of influenza A drift: The linear three-strain model. (English) Zbl 0947.92017
Summary: We analyze an epidemiological model consisting of a linear chain of three cocirculating influenza A strains that provide hosts exposed to a given strain with partial immune cross-protection against other strains. In the extreme case where infection with the middle strain prevents further infections from the other two strains, we reduce the model to a six-dimensional kernel capable of showing self-sustaining oscillations at relatively high levels of cross-protection. Dimensional reduction has been accomplished by a transformation of variables that preserves the eigenvalue responsible for the transition from damped oscillations to limit cycle solutions.
MSC:
92C60Medical epidemiology
37N25Dynamical systems in biology
92D30Epidemiology
37G15Bifurcations of limit cycles and periodic orbits