On the modeling and stability analysis of fractional typhoid fever model with optimal control

Abstract

Typhoid fever remains a major public health hazard on a global scale. It is primarily transmitted by contaminated food and water, particularly in places with poor sanitation. This work presents a novel deterministic fractional model for the dynamics of typhoid fever transmission that considers memory and genetic influences using the Atangana–Baleanu derivative. This work uses fractional calculus to show the dynamics of typhoid transmission while accounting for factors such as environmental contamination and the emergence of drug-resistant variants. Requirements for the global asymptotic stability of both endemic and disease-free equilibria are developed by a thorough stability analysis, providing a theoretical basis for comprehending the thresholds required to reduce or eliminate typhoid fever. A comprehensive sensitivity investigation identifies key parameters influencing the basic reproduction number $R_0$. The application of optimal control theory, which demonstrates that the best outcomes in reducing the burden of disease are achieved when vaccination, treatment, and personal hygiene are integrated, also makes it possible to evaluate various intervention choices. The practical significance of the model for public health authorities is illustrated by numerical simulations that compare the model’s predictions with actual epidemiological data. The value of the model for public health professionals is highlighted by numerical statistics. The application of optimal control theory, which demonstrates that the best outcomes in reducing the burden of disease are achieved when vaccination, treatment, and personal hygiene are integrated, also makes it possible to evaluate various intervention choices.