A deterministic model for highly contagious diseases: The case of varicella

The classic nonlinear Kermack-McKendrick model based upon a system of differential equations has been widely applied to model the rise and fall of global pandemic and also seasonal epidemic by introducing a forced harmonic infectivity which would change throughout the year. These methods work well in their respective domains of applicability, and for certain diseases, but they fail when both seasonality and high infectivity are combined. In this paper we consider a Susceptible-Infected-Recovered, or SIR, model with two latent states to model the propagation and evolutionary history of varicella in humans. We show that infectivity can be calculated from real data and we find a nonstandard seasonal variation that cannot be fitted with a single harmonic. Moreover, we show that infectivity for the present strains of the virus has raised following a sigmoid function in a period of several centuries. This could allow the design of vaccination strategies and the study of the epidemiology of varicella and herpes zoster.