Modeling dysentery spread and the impact of public awareness on control dynamics

Dysentery remains a leading cause of morbidity and mortality in developing regions, exacerbated by poor sanitation and limited access to healthcare. This study develops a novel mathematical model to analyze the transmission dynamics of dysentery and evaluate the effectiveness of control strategies, with a specific focus on the impact of public awareness. The model uniquely stratifies the population into compartments based on health education status and disease severity, allowing for a nuanced analysis of intervention impacts. We derived a key epidemiological threshold, the basic reproduction number, to determine the conditions for disease elimination or persistence. Our analysis demonstrates that a disease-free equilibrium is locally and globally stable when this threshold is below one. Furthermore, we employed optimal control theory to simulate and compare three intervention strategies: public awareness campaigns, hygiene and sanitation improvements, and treatment of infected individuals. Numerical simulations reveal that while each intervention alone reduces disease burden, a combined strategy is the most effective and cost-efficient approach to curtailing outbreaks. These findings underscore the critical importance of integrated public health policies that synergize education, prevention, and treatment for effective and sustainable dysentery control.