A mathematical model on the transmission dynamics of typhoid fever with treatment and booster vaccination

Abstract

Typhoid fever is a potentially fatal illness that is caused by the bacteria Salmonella typhi. In this study, a deterministic mathematical model was formulated to look into transmission dynamics of typhoid fever with treatment and booster vaccination. The reproduction number R0 is calculated using the next-generation matrix approach. Then, a stability analysis on the equilibrium points was performed using Routh–Hurwitz criteria. It was revealed that the disease-free equilibrium point is locally asymptotically stable whenever R0 is less than 1 together with other conditions. We also showed that R0≤1 does not guarantee global stability of the typhoid-free equilibrium point and corroborated the result by showing the possible existence of backward bifurcation at R0=1. The model parameters in R0 were also subjected to sensitivity analysis, which revealed that the transmission rate, infection through an exposed person, and bacteria are the most influential parameters of the reproduction number R0. Numerical simulations were run to determine the impact of various parameters on the dynamics of typhoid.