A Data‐Driven Caputo Fractional‐Order Model for Typhoid Fever Transmission With Imperfect Vaccination and Environmental Contamination

Typhoid fever remains a major public health problem in settings with inadequate vaccination, unsafe water, poor sanitation, and environmental contamination. This study developed a data‐driven Caputo fractional‐order model incorporating imperfect vaccination, direct and environmental transmission, waning immunity, and pathogen contamination. Positivity, boundedness, existence, uniqueness, Hyers–Ulam stability, and local stability of the disease‐free equilibrium were established. The effective reproduction number, , was derived, with the disease‐free equilibrium stable when . The model was fitted to 90 monthly laboratory‐confirmed Typhi and Paratyphi cases recorded from October 2016 to March 2024, yielding an estimated fractional order of α = 0.75. Numerical results showed that fractional memory significantly altered disease progression, with smaller α reducing exposed, infectious, and environmental pathogen burdens. Treatment produced the fastest reduction in human infection, whereas sanitation and pathogen removal were most effective in controlling environmental contamination. The findings supported integrated typhoid control combining vaccination, treatment, safe water, sanitation, and environmental decontamination.