Multistability bifurcation analysis and transmission pathways for the dynamics of the infectious disease-cholera model with microbial expansion inducing the Allee effect in terms of Guassian noise and crossover effects.

Cholera is a life-threatening form of diarrhoea resulting from a bacterial infection of the gastrointestinal system caused by Vibrio cholerae. The aim of this article is to explore the dynamic characteristics of cholera disease transmission and the equilibrium level of recovery in a stochastic cholera framework by adopting piecewise fractional differential operator approaches. Firstly, we provide a detailed fractional-order form of the cholera model, showing the system's positivity and boundedness. Meanwhile, equilibrium analysis is performed to comprehend the model's behaviour and stability for disease-free as well as endemic-free equilibrium. Bacterial development rates have been reported to correlate with the Allee phenomenon. The resulting system exhibits multi-stability for forward and saddle-node bifurcations based on various settings. Global sensitivity is calculated employing the partial rank correlation coefficient approach. Furthermore, the model analyzes a stochastic fractional cholera system. Through a rigorous analysis, we demonstrate that the stochastic model offers a unique global positive solution. Lyapunov function theory is used to create criteria that ensure the model's unique erogodic stationary distribution at [Formula: see text]. Afterwards, the phenomenon that excessive noises can result in the elimination of cholera is discovered. Moreover, this model enables us to study a range of behaviors, from bridging to unpredictability, helping us to understand and predict the process from the beginning to the end of the virus. Moreover, the piecewise differential operators have chosen to extend novel pathways for researchers across several fields, enabling them to convey unique features in various time periods. These operators can be gathered with classical, Caputo, Atangana-Baleanu-Caputo fractional derivative, and random perturbation. As a result, the analytical insights are validated using computational modeling, providing a novel viewpoint on spreading diseases in a societal environment.