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A discrete epidemic model with stage structure. (English) Zbl 1066.92045
Summary: A discrete SIS epidemic model with stage structure is proposed where a disease spreads among mature individuals. A basic reproduction number R 0 of the model is formulated, which is more complicated to calculate than that of differential equation models because the attractor of the model in the disease free space may be composed of equilibria, period cycles, and even strange attractors. If the recruitment rate is of Beverton-Holt type, when R 0 <1 and the recovery rate is equal to 0, the disease free equilibrium is globally stable, and R 0 is monotone for any parameter of the system. When the recruitment rate is of Ricker’s type, it is shown that the existence and extinction of the disease can emerge alternately with the change of the intrinsic growth rate. The method for finding basic reproduction numbers can be applied to other discrete epidemic models.
39A11Stability of difference equations (MSC2000)
39A10Additive difference equations