Fractional-order modeling of typhoid fever dynamics with screening, sanitation, and treatment interventions

Typhoid fever remains a persistent public health burden in low- and middle-income countries due to inadequate sanitation, antimicrobial resistance, and asymptomatic carriage. This study develops a Caputo fractional-order compartmental model to capture the memory-dependent dynamics of typhoid transmission, incorporating three core interventions: screening, sanitation, and treatment. The model stratifies the human population into susceptible, exposed, infectious, screened-infectious, and recovered compartments, coupled with an environmental reservoir of Salmonella Typhi. Using fractional calculus, we derive the effective reproduction number Rₑ and demonstrate that the disease-free equilibrium is locally asymptotically stable when Rₑ < 1 . Positivity, boundedness, existence, uniqueness, and Hyers–Ulam stability of solutions are rigorously established. Numerical simulations reveal that higher fractional orders accelerate convergence to equilibrium, while increasing screening, sanitation effectiveness, and treatment rates substantially reduce Rₑ . Contour plots further quantify synergistic intervention effects. The proposed fractional-order framework offers a more realistic representation of disease progression and control than integer-order models, providing actionable insights for typhoid elimination strategies.