On considering the influence of recovered individuals in disease propagations

• Immune adults can catalyze the interaction among susceptible and sick children.
• However, adults take care of sick children, shortening the convalescence period.
• These features are considered in an epidemic SIR model.
• The proposed model allows the existence of multiple stable steady-states.
• Its predictions are evaluated from data related to varicella incidence in Europe.

Consider diseases transmitted through personal contacts, for which recovery usually confers complete and long-lasting immunity, like some of the common viral infections of childhood. Here, an epidemic model based on differential equations is proposed to evaluate the influence of the recovered (immune) individuals on the spread of such diseases. Indeed, immune individuals can affect the infection rate of susceptible individuals and the recovery rate of sick individuals. The predictive ability of the proposed model is assessed from records concerning the incidence of varicella in three European countries, in a pre-vaccination era.