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

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Sulayman Fatima 1 Amit Mishra 2

1. Department of Mathematical Sciences, Ibrahim Badamasi Babangida University Lapai +234, Nigeria

2. Department of Computer Sciences, Baze University, Abuja +234, Nigeria

* Corresponding author.

DOI: https://doi.org/10.5815/ijmsc.2020.03.05

Received: 1 Nov. 2019 / Revised: 21 Nov. 2019 / Accepted: 15 Dec. 2019 / Published: 8 Jun. 2020

Index Terms

Tuberculosis Transmission, Control Strategy, Disease Free Equilibrium, Effective Reproduction Number, Stability.


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.

Cite This Paper

Sulayman Fatima, Amit Mishra," A SEIRS Model of Tuberculosis Infection Model with Vital Dynamics, Early Treatment for Latent Patients and Treatment of Infective", International Journal of Mathematical Sciences and Computing(IJMSC), Vol.6, No.3, pp.42-52, 2020. DOI: 10.5815/ijmsc.2020.03.05


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