Mathematical model of eradication of tuberculosis through vaccination and treatment strategy with absence of immigration effect

Abstract

In this study, we proposed a mathematical model for the vaccination and treatment strategy to eradicate tuberculosis with absent of immigration effect, where we modified the existing model by incorporating the emigrants effect, efficacy of vaccination, treatment and new babies were considered 100% vaccinated. Existence and uniqueness of solution of the modified model was carried out and it shows that the solution exists and it is unique. The stability analysis of the disease free equilibrium shows that the disease-free equilibrium (DFE) is locally asymptotically stable. The effective reproductive number Re was computed under different conditions. In the case where there is treatment and vaccination we found Re to be 0.1530. The results show that mycobacterium tuberculosis can be eradicated if mass vaccination and treatment actions are properly initiated and enforced. Also, infected immigrants need to be restricted from entering the population to ensure fast eradication of mycobacterium tuberculosis.