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 (Formula presented.) 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 (Formula presented.) is less than 1 together with other conditions. We also showed that (Formula presented.) does not guarantee global stability of the typhoid-free equilibrium point and corroborated the result by showing the possible existence of backward bifurcation at (Formula presented.). The model parameters in (Formula presented.) 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 (Formula presented.). Numerical simulations were run to determine the impact of various parameters on the dynamics of typhoid.