A data-driven deterministic model for typhoid transmission with stability analysis and neural based forecasting

Typhoid fever, caused by Salmonella typhi and transmitted through food or water contaminated with faecal matter, remains a major public health burden in developing regions, yet the role of treatment in its control has received limited modelling attention. In this study we developed and analysed a deterministic compartmental model that captures typhoid transmission dynamics and quantifies the impact of treatment and vaccination on disease elimination. The population is divided into susceptible, latent, infected, treatment, recovered, and vaccinated classes. Positivity and boundedness of solutions are established, and the basic reproduction number is obtained via the next-generation matrix method. The model is locally and globally asymptotically stable at the infection-free equilibrium when , and at the endemic equilibrium when . Real epidemiological data from Bahrain (1990–2010) are used to estimate the unknown contact rate by the least squares method, giving a close fit to reported cases . An Artificial Neural Network (ANN) is integrated to enhance numerical approximation, attaining a best validation mean squared error of 3.9 × 10⁻⁹ with regression coefficient R ≈ 1, confirming excellent agreement with the deterministic solutions. Sensitivity analysis identifies the contact and incidence rates as the strongest drivers of transmission, while the treatment, recovery, and progression parameters most effectively suppress it. Numerical simulations show that increasing the treatment parameter causes the disease to die out rapidly, underscoring treatment as an effective control strategy for typhoid fever.