Caputo-Fabrizio Fractional Order Epidemiological Model of Tuberculosis Transmission along with Imperfect Vaccination, Exogenous Reinfection and Endogenous Reactivation

Abstract

This study has been carried out on the dynamics of tuberculosis (TB) transmission considering vaccination, endogenous re-activation of the dormant infection, and exogenous re-infection. We can comprehend the behavior of TB under the influence of vaccination from this article. The theoretical analysis demonstrates that the disease-free equilibrium point is locally asymptotically stable and the fractional order system is Ulam-Hyers type stable. We compute the vaccination reproduction number (R_v) as well as the basic reproduction number (R_0) using the next-generation matrix (NGM) approach. Our findings indicate that vaccinating a limited segment of the population can effectively eradicate the disease. The Adams–Bashforth 3-step method has been used to obtain the numerical solution of our model. The numerical simulations presented at the end of this study show that vaccination can reduce the number of susceptible and infectious individuals in the population. Moreover, the graphical representations illustrate that the number of infected individuals rises due to both exogenous reinfection and endogenous reactivation.