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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.
92C60Medical epidemiology
37N25Dynamical systems in biology
37G15Bifurcations of limit cycles and periodic orbits