Existence of solutions and stability analysis for a fractional helminth transmission model within the framework of Mittag-Leffler kernel

Abstract

In recent years, the many tools from fractional calculus have been extensively used in the mathematical modeling of infectious diseases. In this paper, an integer order helminth transmission model proposed by Lambura et al. is extended to a fractional model by incorporating the fractional Atangana-BaleanuCaputo derivative. Certain basic features such as non-negativity of solutions, invariant region within which the model equations are epidemiologically meaningful as well as equilibrium points and basic reproduction number are explored. Furthermore, the existence, uniqueness and Ulam-Hyers of the associated fractional model are explored via a fixed point technique and generalized Gronwall inequality