Modeling the impact of limited treatment resources in the success of typhoid intervention

Despite recent progress in improvements to poor sanitation, typhoid disease is still endemic in many developing countries. Typhoid fever, more commonly called typhoid, is an infection caused by Salmonella typhoid. Symptoms include a lasting high fever, internal bleeding, and even death. Typhoid infection can occur through direct transmission (human-to-human) or indirect transmission, which occurs by ingesting contaminated food or water. In addition to poor sanitation, limited health resources can also contribute to the spread of typhus. This paper discusses modelling the transmission of typhoid with limited public health resources. The model was constructed to determine how limited public health resources affect the spread of typhoid. It was then analyzed analytically and numerically. The existence and stability of disease-free and endemic equilibrium points and the basic reproduction number ℛ0 were all determined analytically. Numerical simulations regarding the sensitivity of ℛ0 was conducted to support analytical result. Last but not least, an autonomous simulation was also undertaken to see the influence of the maximum treatment of uptake rate in the spread of typhoid. Our results suggest that since the backward bifurcation appear in the system, making ℛ0 < 1 but still close to one, is not enough to exterminate Typhoid from population. Since the success of hospitalization depend on the hospital capacity to threat infected individual, providing health interventions must be given in high intensity and pay attention to the capacity of the hospital when typhoid endemic occurs.