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 $\mathcal{R}_{0}$ 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 $\mathcal{R}_{0}$ is less than 1 together with other conditions. We also showed that $\mathcal{R}_{0}≤ 1$ does not guarantee global stability of the typhoid-free equilibrium point and corroborated the result by showing the possible existence of backward bifurcation at $\mathcal{R}_{0}=1$. The model parameters in $\mathcal{R}_{0}$ 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 $\mathcal{R}_{0}$. Numerical simulations were run to determine the impact of various parameters on the dynamics of Typhoid.