Fractional dynamics of a two-strain dengue model with co-infections and saturated incidences

Abstract

In this work, we formulate a two-strain model of dengue infection, incorporating the possibility of co-infection through integer and Caputo-type fractional derivatives. We present the foundational theory and results related to fractional operators for the analysis of the proposed dengue model. We establish the positivity and boundedness of the solution to validate the model. It is demonstrated that the solution to the proposed model exists and is unique. The basic reproduction number, denoted by [Formula: see text], is determined, and the local asymptotic stability of the dengue-free equilibrium point is established when [Formula: see text]. We also prove the existence of an endemic equilibrium and establish the global stability of solutions to the fractional model in the Ulam–Hyers sense. Additionally, we construct a numerical scheme and prove its stability under certain conditions. Several numerical simulations are performed to validate our analytical results, and we examine the impact of various input factors on the solution pathways of the system through these simulations.