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.
Biganda et al. (Sat,) studied this question.