Transmission dynamics of typhoid fever with nonlinear incidence rate and saturated treatment
摘要
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 nonlinear 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. We calibrated the model parameters using clinical data from Mbandjock, located in Cameroon’s Center Region. Sensitivity analysis reveals that higher transmission rates can accelerate the spread of the epidemic; however, interventions influenced by nonlinear 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. A reduction of about 89.3% in the population of infected individuals, when the combined control measures are insured for continuous 25 months. Overall, numerical simulation support the actual reported data of Mbandjock, which ensures the relevance of the model and simulated outcomes.