Modeling directly transmitted infections in a routinely vaccinated population – the force of infection described by a Volterra integral equation

摘要

We present the time dependent analysis of a model taking into account a special immunization strategy, that is, susceptible individuals comprised on an age interval are vaccinated. Vaccination is the main protective mechanism against many directly transmitted infections. But, when a vaccination strategy is introduced, the pattern of the disease distribution in a community suffers alterations, which propagate along time until a new equilibrium scenario of the disease is attained. From the model, the time dependent force of infection, described by a non-linear Volterra integral equation, can be obtained by applying the characteristic method to solve a system of partial differential equations. Also the following correlated variables to the force of infection can be obtained: the average age of the acquisition of the first infection, the rate of new cases of infection and, in the case of rubella infection, the risk of infection. From the results, one of the main conclusions relates that the increasing in the average age of the acquisition of the first infection in not always true.