Modelling the impact of vaccination on transmission dynamics of Typhoid fever

Abstract

In this work, in order to evaluate the immediate and long-term impacts of vaccination on the transmission dynamics of TF, we develop a compartmental mathematical model which takes into account vaccination and medically hygienic compartments for the dynamics of TF transmission in a population. Based on the positivity and boundedness of the model solutions, the model is shown to be mathematically well posed. The next generation matrix method is used to determine the control reproduction number, R0π, of the model. It is shown that the model has a unique disease-free equilibrium, which is proved to be locally asymptotically stable when R0π is less than unity. Further analysis suggests that the model admits a unique endemic equilibrium when R0π is greater than unity. To investigate the effect of the model parameters on the transmission and spread of the disease in the population, sensitivity analysis is conducted. The dynamics of TF spread within the populations under the varying effects of some key sensitive parameters, such as the effective diseases transmission rate in human, bacteria shedding rate from symptomatic infectious humans, vaccine efficacy, decay rate of bacteria from the environment and recovery rate of symptomatic infectious humans, is further studied using numerical simulations. The study suggests some measures that can be put in place to guide against the menace of TF in the population.

Keywords

• Control reproduction number
• Typhoid fever
• Vaccination
• Medically hygienic
• Sensitivity analysis