Assessing the Impact of Vaccination Strategies and Re-infection Dynamics on Mycobacterium tuberculosis Transmission by Mathematical Modelling

In this work, we investigated the consequences of an inadequate vaccination along with other exogenous variables such as treatment-associated re-infection and re-infection among former patients. Our models represent six stages: Susceptible population, Vaccinated population, latently infected population, Rate of induced population, Quarantine population and Rate of recover population. In this model, we find out disease-free equilibrium points, reproduction number R_0 is used to control the re-infection rate in the population. Furthermore, the results suggest that even a subpar Mycobacterium tuberculosis vaccine is always successful at reducing the spread of infectious diseases among the population, even though its general effect improves with greater efficacy and penetration. It is demonstrated that a small percentage of the overall population receives immunization in a stable state and vaccine efficacy plays an equal part in decreasing the burden of disease. Based on the numerical simulation, the establishment of the TB disease is decrease and control by the vaccination coverage and efficacy of the treatment. Using an imperfect vaccine can control mycobacterium in the population. The next-generation matrix approach was utilized to determine the effective reproduction number of the proposed system. The utilization of the exponential theory which provided the disease-free equilibrium is stable and coexists endemic equilibrium point. The Lyapunov function were used to determine the disease is globally asymptotically stable. We find out the non-negative (in variant region). We used random data in MATLAB to figure out the result of the model.