A new fractional model for vector-host disease with saturated treatment function via singular and non-singular operators

Abstract

In this paper, we consider a vector-host epidemic model with saturated incidence and treatment functions. This type of function is biologically more suitable in situations where the number of infected individuals is getting larger and the medical facilities are limited. Further, as most of the biological phenomena possess the fading memory and show crossover behavior. Therefore, in the present study, initially we develop the proposed model using integer-order derivative and then two different fractional operators namely Caputo and Atangana-Baleanu in Caputo sense (ABC) are used to formulate the fractional model. Some of the basic properties including positivity, existence, uniqueness and stability results at the disease free equilibrium of the Caputo model are shown. The existence and uniqueness of the ABC model are explored via fixed point theorem. Furthermore, the fractional models are solved numerically using an efficient iterative scheme. Finally, detailed simulation results are depicted in order to demonstrate the significance of the order of fractional operators and model parameters on the disease dynamics.