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A discrete-time deterministic epidemic model is proposed with the aim of reproducing the behaviour observed in the incidence of real infectious diseases, such as oscillations and irregularities. For this purpose we introduce, in a naive discrete-time SIRS model, seasonal variability in the loss of immunity and in the infection probability, modelled by sequences of kicks. Restrictive assumptions are made on the parameters of the models, in order to guarantee that the transitions are determined by true probabilities, so that comparisons with stochastic discrete-time previsions can be also provided. Numerical simulations show that the characteristics of real infectious diseases can be adequately modeled.

A DiscreteSIRSModel with Kicked Loss of Immunity and Infection Probability