A Well-Posed Fractional Order Cholera Model with Saturated Incidence Rate

Abstract

A fractional-order cholera model in the Caputo sense is constructed. The model is an extension of the Susceptible–Infected–Recovered (SIR) epidemic model. The transmission dynamics of the disease are studied by incorporating the saturated incidence rate into the model. This is particularly important since assuming that the increase in incidence for a large number of infected individualsis equivalent to a small number of infected individualsdoes not make much sense. The positivity, boundedness, existence, and uniqueness of the solution of the model are also studied. Equilibrium solutions are computed, and their stability analyses are shown to depend on a threshold quantity, the basic reproduction ratio (). It is clearly shown that if the disease-free equilibrium is locally asymptotically stable, whereas if , the endemic equilibrium exists and is locally asymptotically stable. Numerical simulations are carried out to support the analytic results and to show the significance of the fractional order from the biological point of view. Furthermore, the significance of awareness is studied in the numerical section.

Mathematical Modeling in Systems Biology

“…Two articles in this Special Issue focus on the modeling of infection transmission dynamics. The article by Isa Abdullahi Baba et al presents a fractional-order cholera model that is an extension of the Susceptible-Infected-Recovered epidemic model [8]. The model incorporates the saturated incidence rate to accurately represent the transmission dynamics of the disease.…”