Modeling the behavior of a generalized Cholera epidemic model with asymptomatic measures for early detection

Abstract

To understand how a disease spreads through a society, mathematical formulations are a crucial tool for comprehending the complete dynamics of cholera. Model formulations are essential for thoroughly understanding the propagation of cholera throughout a population. For an assessment of the stable state of a newly established SEIRB system, both qualitative and quantitative evaluations are conducted. The reproductive number is derived to observe the infection spread rate among patients. Additionally, sensitivity analyses are performed to assess the impact of each parameter and to determine the rate of change in each. The existence of positive solutions with linear growth has been verified using global derivatives, and the level of effect in each subsection is determined through the application of Lipschitz criteria. By employing Lyapunov’s first derivative of the function, the framework is analyzed for global stability to evaluate the overall effect of both symptomatic and asymptomatic measures following early detection interventions. The Mittag-Leff1er kernel is utilized to obtain a robust solution via a fractal-fractional operator, enabling continuous monitoring for improved control measures. Simulations are performed to assess the global impact of both symptomatic and asymptomatic consequences of cholera and to observe the actual behavior of the disease. It has been confirmed that individuals with strong immune systems will recover efficiently if the infection is diagnosed early through timely detection measures. This analysis provides insight into the current state of cholera control, comparing outcomes for those receiving treatment and those whose robust immune systems negate the need for medication. Such investigations will enhance our understanding of disease transmission and support the development of effective control strategies based on our validated findings.