A Novel Mathematical Model Evaluating the Impact of Saturated Treatment Response, Vaccination and Anti-Biotic Resistance on Transmission Dynamics of Typhoid Fever

Abstract

This research presents a novel mathematical model for evaluating typhoid fever transmission, incorporating treatment response, vaccination, and antibiotic resistance. By integrating these factors, the model provides insights into disease control. We analyze the impact of saturated treatment response, vaccine efficacy, and antibiotic resistance management. A qualitative
study confirms the model’s epidemiological soundness through uniqueness, positivity, stability, and boundedness analyses. Sensitivity analysis, based on the reproduction number, identifies key parameters influencing disease progression. Using next-generation matrices, we establish that ( 1) 0 R  ensures disease-free equilibrium stability, while ( 1) 0 R  leads to instability. Numerical simulations via the Homotopy Perturbation Method highlight the importance of high vaccination coverage for herd immunity. Findings stress the need for integrated strategies, including vaccination, improved treatment, and responsible antibiotic use. The study concludes that treatment saturation, vaccination, and antibiotic resistance are key considerations for effective typhoid fever control.