Dynamics and optimal intervention strategies in a Shigellosis transmission model

This research explores how water treatment contributes to limiting the transmission of Shigellosis, an infection caused by bacteria from the Shigella genus. A mathematical framework is formulated to evaluate the influence of protective strategies and water purification on the spread of the disease. To confirm the model's biological relevance, its well-posedness is investigated. The basic reproduction number $(\mathfrak{R}_0)$, a critical indicator of disease behavior, is derived using the matrix operator method. Findings indicate that if $\mathfrak{R}_0<1$, the Shigellosis-free state has local and global stability, implying that effective control mechanisms could lead to elimination of Shigellosis. Conversely, if $\mathfrak{R}_0>1$, the infection persists, with the endemic equilibrium exhibiting local asymptotic stability. A comprehensive cost-effectiveness analysis reveals that combining environmental protection with water treatment represents the most economically efficient intervention strategy. Numerical simulations conducted in MATLAB confirm that water treatment significantly reduces Shigellosis transmission, reinforcing its effectiveness as a public health strategy.