Pulse and constant control schemes for epidemic models with seasonality

Control schemes for infectious disease models with time-varying contact rate are analyzed. First, time-constant control schemes are introduced and studied. Specifically, a constant treatment scheme for the infected is applied to a SIR model with time-varying contact rate, which is modelled by a switching parameter. Two variations of this model are considered: one with waning immunity and one with progressive immunity. Easily verifiable conditions on the basic reproduction number of the infectious disease are established which ensure disease eradication under these constant control strategies. Pulse control schemes for epidemic models with time-varying contact rates are also studied in detail. Both pulse vaccination and pulse treatment models are applied to a SIR model with time-varying contact rate. Further, a vaccine failure model as well as a model with a reduced infective class are considered with pulse control schemes. Again, easily verifiable conditions on the basic reproduction number are developed which guarantee disease eradication. Some simulations are given to illustrate the threshold theorems developed.