Transmission dynamics of typhoid fever with non-linear incidence rate and saturated treatment

Typhoid fever has always remained a highly endemic disease and posed a significant public health challenge, particularly in tropical developing nations. This paper presents a comprehensive model for typhoid fever which incorporates non-linear incidence and saturated treatment. We focus on the three control measures: prevention, vaccination, and treatment. We derive the basic reproduction number and analyze the local and global stability of the disease-free equilibrium using Lyapunov stability theory. Bifurcation analysis reveals that forward bifurcation can occur depending on the specific model parameters. Sensitivity analysis reveals that higher transmission rates can accelerate the spread of the epidemic; however, interventions influenced by non-linear rate such as increased awareness and behavioral changes along with saturated treatment strategies, are effective in lowering the basic reproduction number below one, thereby playing a key role in controlling the disease. Additionally, Pontryagin’s maximum principle is utilized to identify the most effective control strategies for minimizing the spread of typhoid fever. Numerical simulations support the analytical findings and illustrate the influence of various parameters on the dynamics of typhoid fever.