Mathematical Analysis of Typhoid Fever Dynamics with Age-Structured Control Measures

Abstract

This research develops a mathematical model to investigate the dynamics of typhoid fever by incorporating age structure, vaccination and treatment strategies. Recognizing that different age groups display varying susceptibility and contact rates, the model provides a detailed representation of transmission. The analysis is to emphasize how vaccination programs and treatment interventions, when tailored to age-specific characteristics, can significantly reduce transmission and control outbreaks. The system of nonlinear differential equations describing the disease dynamics is analyzed and solved using the homotopy perturbation method. This analytical approach allows for an approximation of solutions while capturing the nonlinear interactions within the system. Sensitivity analysis is carried out to determine the most influential parameters on disease spread, particularly those affecting the basic reproduction number. The simulations reveal that increasing vaccination coverage and treatment rates leads to a decline in typhoid fever cases across all age groups. Age-targeted interventions are shown to enhance the effectiveness of control strategies compared with uniform measures. Sensitivity analysis result further indicate that parameters such as vaccination rate, treatment efficacy and contact patterns play vital roles in disease progression and a potential for its eradication.