Mathematical modeling and analysis of mycobacterium tuberculosis transmission in humans with hospitalization and reinfection

• Autorzy: Mustapha Umar T. , Idris Buhari , Musa Salihu S. , Yusuf Abdullahi

Identyfikatory

DOI

10.17512/jamcm.2022.1.05

• Języki publikacji: EN

Abstrakty

EN

Tuberculosis (TB), a serious public health infection that mainly affects the lungs, is caused by bacteria (Mycobacterium tuberculosis, TB). This research is designed and analyzed using a compartmental modelling approach to study the transmission dynamics of TB with different stages of infection. Qualitative analysis of the proposed model reveals that the model exhibits two equilibrium points: the disease-free equilibrium point (DFE) and the endemic equilibrium (EE). The basic reproduction number (R₀ ) is determined using the next generation matrix technique, and stability analysis is carried out to show whether the disease can persist or die out in population. Further analysis of the model shows that the EE is globally asymptotically stable (GAS) when R₀ > 1. With the aid of the forward sensitivity index method, we determine the most sensitive parameters of the model to control the spread of TB infection effectively. Our analysis shows that treatment (medication) and campaign awareness coupled with other key control measures, could help maintain the spread of MTB infection in human geographical boundaries.

Słowa kluczowe

EN

Mycobacterium tuberculosis; mathematical modeling; reproduction number; stability analysis; sensitivity analysis

PL

prątek gruźlicy; modelowanie matematyczne; współczynnik reprodukcji; analiza stabilności; analiza wrażliwości

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2022
• Tom: Vol. 21, nr 1
• Strony: 55--66
• Opis fizyczny: Bibliogr. 21 poz., rys., tab.

Twórcy

autor

Mustapha Umar T.

• Department of Mathematics, Federal University Dutse, 7156 Jigawa, Nigeria

autor

Idris Buhari

• Department of Mathematics, Federal University Dutse, 7156 Jigawa, Nigeria

autor

Musa Salihu S.

• Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China
• Department of Mathematics, Kano University of Science and Technology, Wudil, Nigeria

autor

Yusuf Abdullahi

• Department of Mathematics, Federal University Dutse, 7156 Jigawa, Nigeria
• Department of Computer Engineering, Biruni University, 34010 Istanbul, Turkey

Bibliografia

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