an:06371878
Zbl 1300.92099
Gonz??lez-Parra, Gilberto; Arenas, Abraham J.; Chen-Charpentier, Benito M.
A fractional order epidemic model for the simulation of outbreaks of influenza A(H1N1)
EN
Math. Methods Appl. Sci. 37, No. 15, 2218-2226 (2014).
00336961
2014
j
92D30 34K37 65L05
epidemic models; fractional order model; influenza A(H1N1); Gr??nwald-Letnikov method
Summary: 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 Gr??nwald--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.