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2 2022

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

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

Journal of Applied Mathematics and Computational Mechanics

2022

Vol. 21, nr 1

55--66

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.

Mathematical analysis of a MERS-Cov coronavirus model

DarAssi Mahmoud H., Shatnawi Taqi A. M., Safi Mohammad A.

Demonstratio Mathematica

2022

Vol. 55, nr 1

265--276

In this study, we have proposed a mathematical model to describe the dynamics of the spread of Middle East Respiratory Syndrome disease. The model consists of six-coupled ordinary differential equations. The existence of the corona-free equilibrium and endemic equilibrium points has been proved. The threshold condition for which the disease will die out or becomes permanent has been computed. That is the corona-free equilibrium point is locally asymptotically stable whenever the reproduction number is less than unity, and it is globally asymptotically stable (GAS) whenever the reproduction number is greater than unity. Moreover, we have proved that the endemic equilibrium point is GAS whenever the reproduction number is greater than unity. The results of the model analysis have been illustrated by numerical simulations.