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Tuberculosis is one of the most destructive bacteria in human being and the second cause of mortality after HIV/AIDS in the whole world. In this research work, a SEIRS of mathematical model for the transmission of tuberculosis incorporating vital dynamics, early therapy of patient with tuberculosis were studied and a model for treatment of infective as controls was developed. The effective reproduction number and the disease-free equilibrium was also analysed for the stability. The results revealed that the two controls reduce effective number below unity. Furthermore, it shows that early therapy of patient with tuberculosis is more effective in mitigating the spread of tuberculosis burden.

A SEIRS Model of Tuberculosis Infection Model with Vital Dynamics, Early Treatment for Latent Patients and Treatment of Infective