(untitled) (Journal of Nonlinear Modeling and Analysis, 2026)
In this study, we examine a cholera epidemic model that incorporates educational transmission and delve into the long-term dynamics of the epidemic equilibrium point, particularly in relation to the spread of information about disease transmission. We find that if the basic reproduction number R_0 is less than or equal to 1, the disease is destined to be eradicated, and the unique disease-free equilibrium point becomes globally stable. It is noteworthy that the stability of this disease-free equilibrium is not influenced by the extent of disease education, the variety of infections, or the rate of education. On the other hand, if the basic reproduction number is greater than 1, we study the existence of the endemic equilibrium, and demonstrate that the disease will persist if β_0 > D_0. To assess the impact of educational campaigns on disease control, we further establish the asymptotic behavior of both infected and susceptible populations in response to educational interventions. Our findings indicate that well-executed educational campaigns can substantially contribute to the management and mitigation of the disease’s effects.