A mathematical model on the transmission dynamics of typhoid fever with treatment and booster vaccination - Kailan Suhuyini, Abdulai; Seidu, Baba (Frontiers in Applied Mathematics and Statistics, 2023)
Typhoid fever is a potentially fatal illness caused by the bacterium Salmonella Typhi. In this study, a deterministic mathematical model was formulated to look into typhoid fever transmission dynamics with treatment and boosted vaccination. The reproduction number R_0 is calculated using the next generation matrix approach. Then stability analysis on the equilibrium points were established using Routh-Hurwitz criteria. It was revealed that the disease-free equilibrium point is locally asymptotically stable whenever R_0 is less than 1 together with other conditions. We also showed that R_0≤ 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 R_0=1. The model parameters in R_0 were also subjected to sensitivity analysis, which revealed that transmission rate, infection through exposed and bacteria are the most influential parameters of the reproduction number R_0. Numerical simulations were run to determine the impact of various parameters on the dynamics of Typhoid.