Modeling the effects of SEIR-type typhoid epidemic model using computational approaches

Abstract

This study presents a comprehensive mathematical analysis of a typhoid transmission model to investigate the influence of key epidemiological parameters on disease dynamics. The proposed model incorporates essential compartments representing the susceptible, exposed, infected, and recovered populations, along with the re-infection mechanism to capture realistic typhoid transmission behavior. Numerical simulations were performed using the Chebyshev Polynomial-Exponential Method (CPEM) and Classical Euler Method (CEM) to obtain approximate solutions. The comparative results confirm that both numerical schemes provide stable and consistent outcomes. Parameter sensitivity analysis revealed that increasing the transmission rate $(\varphi)$ accelerates the infection spread by decreasing the susceptible population and increasing the exposed and infected classes. Similarly, a higher infection rate $(\xi)$ enlarges the infectious pool, whereas an increase in the recovery rate $(\nu)$ promotes disease reduction. Conversely, a higher re-infection rate $(\zeta)$ contributes to recurring outbreaks. Surface and contour plots further illustrate the nonlinear interactions and sensitivities between the parameters. These findings highlight the importance of controlling transmission, enhancing recovery strategies, and sustaining immunity to effectively reduce the spread and recurrence of typhoid fever.