On a multi-order fractional SIRC model for Influenza

Abstract

Since influenza is a seasonal mutating disease, in this paper, we propose and analyze a multi-fractional version of the SIRC model (which relates the S-susceptible, I-Infected, R-recovered, and C-cross-immune individuals in the population N) to capture the immunological memory gained by individuals that have previous contact Influenza strains. We show the well-posedness and consistency of the proposed multi-fractional dynamics and analyze the stability of stationary points with an analytical/numerical strategy. The simulated scenarios show that the proposed model describes more precisely reported Influenza H1N1 data, from the State of Rio Grande do Sul, in the year 2010. Moreover, it shows that the memory enhanced by the fractional dynamics (that model the immunological memory) implies a substantial decrease of susceptibility of re-infection by strain mutations in long-running diseases, but is larger in the beginning.