Bifurcation and Sensitivity Analysis of a Dysentery Diarrhea Epidemic Model With Treatment and Environmental Pathways

Dysentery diarrhea remains a major public health challenge in low‐resource settings. This study develops a novel SITR‐B model that integrates treatment pathways, treatment failure, and environmental transmission. The model incorporates logistic bacterial growth and dual decay mechanisms, providing a realistic representation of pathogen dynamics. Analytical results show a forward bifurcation at , confirming an epidemic threshold. Sensitivity analysis identifies pathogen shedding ( ε 1 ) and human contact rate ( β h ) as dominant transmission drivers. Optimal control analysis reveals that a strategy combining initial intensive treatment with sustained sanitation significantly reduces both infections and environmental pathogens. Comparative simulations demonstrate that our model, through its explicit treatment structure, produces more realistic outcomes than previous frameworks. These findings provide mathematical evidence for combined intervention strategies, offering practical guidance for dysentery control in vulnerable populations.