Modelling Vaccination Strategy Against Directly Transmitted Diseases Using a Series of Pulses

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Abstract
When a SIR model with a constant contact rate is used to describe the dynamics of directly transmitted infections, oscillations, which decay exponentially as time goes on, are obtained. By using this kind of model, we obtained the natural- and inter-epidemics periods of the disease. These two quantities are quasi-periods, since we are considering damped oscillations. The above two periods were estimated from rubella seroprevalence data from a small Brazilian community and, based on them, a vaccination strategy in a series of pulses was designed. The vaccination time lag between pulses is related to the natural-epidemics period, instead of the inter-epidemics period, multiplied by a fraction usually less than unity (the security factor). The results for different controlling scenarios showed that a series of pulses vaccination strategy can be a good option for developing countries.

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