A Fractional SIRC Model For The Spread Of Diseases In Two Interacting Populations

Abstract

In this contribution we address the following question: what is the behavior of a disease spreading between two distinct populations that interact, under the premise that both populations have only partial immunity to circulating stains of the disease? Our approach consists of proposing and analyzing a multi-fractional Susceptible (S), Infected (I), Recovered (R) and Cross-immune (C) compartmental model, assuming that the dynamics between the compartments of the same population is governed by a fractional derivative, while the interaction between distinct populations is characterized by the proportion of interaction between susceptible and infected individuals of both populations. We prove the well-posedness of the proposed dynamics, which is complemented with simulated scenarios showing the effects of fractional order derivatives (memory) on the dynamics.

Keywords

• mathematical modeling
• diseases spreading
• immunological memory
• population interaction.