Analysis And Dynamics Of Cholera Epidemic System In Society Via Fractal-Fractional Operator

To comprehend the dynamics of disease propagation within a society, mathematical formulation is a crucial tool to understand the complex dynamics. In order to transform the mathematical model with the objective of bolstering the immune system into a fractional-order model, we use the definition of Fractal-Fractional with Mittag-Leffler kernel. For an assessment of the stable position of a recently modified system, qualitative as well as quantitative assessments are carried out. We validate the property positivity and reliability of the developed system by evaluating its boundedness and uniqueness, which are important features of an epidemic model. The positive solutions with linear growth have been verified by the global derivative, and the level of effects of different parameters in each sub-section is determined through employing Lipschitz criteria. By employing Lyapunov’s first and second derivatives of the function, the framework is examined on a global scale to evaluate the overall effect with symptomatic and asymptomatic measures. Bifurcation analysis was performed to check the behavior of each sub-compartment under different parameters effects. The Mittag-Leffler kernel is used to obtain a robust solution via Fractal-Fractional operator for continuous monitoring of spread and control of cholera disease under different dimensions. Simulations are carried out to observe both the symptomatic and asymptomatic consequences of cholera globally, also to observe the actual behavior of cholera disease for control measures, and it has been confirmed that those with strong immune systems individuals recover early due to early detection measures. The actual state of cholera disease can be controlled by taking the following measures: early detection of disease for both individuals receiving medication and those who do not require medication because of their robust immune systems. This kind of research will be beneficial in determining how diseases spread and in developing effective control plans based on our validated findings.