A novel numerical dynamics of fractional derivatives involving singular and nonsingular kernels: designing a stochastic cholera epidemic model

Abstract

<abstract><p>In this research, we investigate the direct interaction acquisition method to create a stochastic computational formula of cholera infection evolution via the fractional calculus theory. Susceptible people, infected individuals, medicated individuals, and restored individuals are all included in the framework. Besides that, we transformed the mathematical approach into a stochastic model since it neglected the randomization mechanism and external influences. The descriptive behaviours of systems are then investigated, including the global positivity of the solution, ergodicity and stationary distribution are carried out. Furthermore, the stochastic reproductive number for the system is determined while for the case $ \mathbb{R}_{0}^{s} > 1, $ some sufficient condition for the existence of stationary distribution is obtained. To test the complexity of the proposed scheme, various fractional derivative operators such as power law, exponential decay law and the generalized Mittag-Leffler kernel were used. We included a stochastic factor in every case and employed linear growth and Lipschitz criteria to illustrate the existence and uniqueness of solutions. So every case was numerically investigated, utilizing the newest numerical technique. According to simulation data, the main significant aspects of eradicating cholera infection from society are reduced interaction incidence, improved therapeutic rate, and hygiene facilities.</p></abstract>

A Caputo-Fabrizio fractional-order cholera model and its sensitivity analysis

“…Additionally, they can effectively capture the behavior of systems with long-range interactions, making them a valuable tool for modeling complex systems [26][27][28][29][30][31][32][33][34][35][36]. In [37], a stochastic computational model of cholera infection was proposed in the context of a direct contact transmission pathway using fractional calculus theory. The research results suggest that policymakers should consider measures such as reducing interactions, improving treatment rates, and enhancing hygiene facilities to eradicate cholera.…”