In this paper, we propose a nonlinear fractional order model in order to explain and understand the outbreaks of influenza A(H1N1). In the fractional model, the next state depends not only upon its current state but also upon all of its historical states. Thus, the fractional model is more general than the classical epidemic models. In order to deal with the fractional derivatives of the model, we rely on the Caputo operator and on the Grünwald–Letnikov method to numerically approximate the fractional derivatives. We conclude that the nonlinear fractional order epidemic model is well suited to provide numerical results that agree very well with real data of influenza A(H1N1) at the level population. In addition, the proposed model can provide useful information for the understanding, prediction, and control of the transmission of different epidemics worldwide. Copyright © 2013 John Wiley & Sons, Ltd.

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In this paper we study the existence of a positive periodic solutions for nested models of respiratory syncytial virus RSV, by using a continuation theorem based on coincidence degree theory. Conditions for the existence of periodic solutions in the model are given. Numerical simulations related to the transmission of respiratory syncytial virus in Madrid and Rio Janeiro are included.

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