Numerical investigation of fractional-order cholera epidemic model with transmission dynamics via fractal–fractional operator technique

The goal of this research is to determine if it is conceptually sufficient to eliminate infection in a community by utilizing mathematical modelling and simulation techniques when appropriate protective controls are adopted. In this research, we investigate the straightforward interaction transmission method to create a deterministic mathematical formulation of cholera infectious dynamics via the fractal–fractional (F–F) derivative operator. Furthermore, the qualitative characteristics of the framework are investigated, including the invariant region, the existence of a positive invariant solution, the equilibria conditions and their stabilities. In addition, the fundamental reproductive number R0<1 is calculated, indicating that the strategy is more plausible. The Atangana–Baleanu, Caputo–Fabrizio, and Caputo F–F differential operators are recently described F–F differential operators that are used to describe the computational formula of the cholera epidemic model. We examined the numerical dynamics of the cholera epidemic, considering three assumptions: (i) altering fractal order while fixing fractional order; (ii) changing fractional order while fixing fractal order; and (iii) fluctuating fractal and fractional orders simultaneously. For the numerical modelling of the aforesaid model, our analysed graphical representations and numerical simulations via MATLAB indicate that the newly proposed Atangana–Baleanu, Caputo–Fabrizio, and Caputo F–F differential operators yield notable outcomes when compared to the classical framework. According to the simulated data, reduced contact rate, successful recovery rate, and appropriate hygiene are the most essential aspects for eliminating cholera disease from the community.