A deterministic Tuberculosis epidemic infection model incorporating public interventions

Résumé

Tuberculosis (TB) is one of the devastating human ailments. To better understand the dynamics of TB disease, a deterministic compartmental model is designed to describe the dynamics of TB by incorporating public interventions such as vaccination, educational counselling, and treatment. The dynamics of the model are thoroughly investigated by utilizing the theory of the dynamical framework. The effective reproduction number R0 is derived using strict mathematical derivations. The theoretical outcome indicates that the disease-free equilibrium (DFE) is locally asymptotically stable if RC < 1 and the system is uniformly persistent when RC > 1. The qualitative analysis performed on the free model shows the existence of the occurrence of transcritical bifurcation at the threshold quantity of R0 = 1. The numerical simulations analysis of the model demonstrated that an extreme emphasis on tuberculosis public interventions appeared to essentially bring about a decrease in TB epidemic in the community.