Semi-analytical approach to a fractional-order model for the dynamics and control of Typhoid fever

Abstract

The persistent threat of typhoid fever to global public health is most severe in regions where sanitation is poor and safe drinking water is scarce. The illness, which is caused by Salmonella Typhi, can result in systemic infection and serious complications if not treated promptly. Populations at greater risk, particularly in low-resource environments, are especially affected due to inadequate healthcare facilities. This research presents a novel fractional-order mathematical model to assess the transmission dynamics of typhoid fever, incorporating memory effects and intricate transmission patterns that traditional integer-order models fail to capture. The study uniquely applied the Adams-Bashforth method alongside fractional-order derivatives to obtain the model's solution, offering a more accurate representation of disease progression. Sensitivity analysis showed the critical roles of treatment intervention , reducing contact rate and improved sanitation in lowering the prevalence of the disease. Furthermore, the study assesses how public health initiatives, such as enhanced water quality, hygiene education, and advancements in rapid diagnostics, influence the management of typhoid fever. Simulation results suggest that a comprehensive strategy such as effective management of contaminated agents, efficient treatment, and strengthened public health systems can greatly mitigate  transmission and enhance disease management outcomes.