Diarrheal diseases remain a leading cause of morbidity and mortality among children under five in developing countries, with asymptomatic carriers playing a crucial role in disease transmission. This study presents a mathematical model for diarrheal disease transmission that explicitly distinguishes between asymptomatic and symptomatic infected individuals. The model, denoted as SVEI\(_A\)I\(_S\), incorporates vaccination, disease progression, and treatment interventions. We analyze the mathematical properties of the model including positivity and boundedness of solutions. Numerical solutions are obtained using the fourth-order Runge–Kutta method (RK4). A comprehensive sensitivity analysis is performed to identify the most influential parameters affecting disease transmission and prevalence. The numerical results demonstrate that the RK4 method provides accurate solutions with global truncation error O(\(h^4\)). Sensitivity analysis identifies the transmission rate (\(\beta \)) and the proportion of asymptomatic infections (\(\nu \)) as the most critical parameters influencing disease dynamics. This work provides a foundation for understanding the role of asymptomatic transmission in diarrheal disease persistence and evaluating intervention strategies.
