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Volume 8, Issue 3, June 2020, Page: 123-144
Spread and Control of Multi-drug Resistance Tuberculosis and Drug-sensitive Tuberculosis in Ethiopia: A Mathematical Model Analysis
Shimelis Bekele Zerefe, Department of Mathematics, Addis Ababa Science and Technology University, Addis Ababa, Ethiopia
Temesgen Tibebu Mekonnen, Department of Mathematics, Debre Berhan University, Debre Berhan, Ethiopia
Received: Apr. 22, 2020;       Accepted: May 15, 2020;       Published: May 29, 2020
Abstract
In this work we considered nonlinear dynamical system to study the dynamics of two-strain Tuberculosis epidemic in Ethiopia. We proved that the solution of the considered dynamical system is positive and bounded. We found that the considered dynamical system has disease free and endemic equilibrium points. We proved that the local and global stability of disease free equilibrium point and endemic equilibrium point. We found the effective reproduction number of the dynamical system. Also, the effective reproduction number of the dynamical system which experience drug sensitive strain and the effective reproduction number of the dynamical system which experience multi drug resistance strain. Using real data collected from different health sectors from Ethiopia we found that the numerical value of the effective reproduction number of the drug sensitive tuberculosis is 1.03 and the effective reproduction number of the drug resistance tuberculosis is 4.78 and the effective reproduction number of the dynamical system max{1.03, 4.78}=4.78. So that MDR strain is spreads strongly than DS strain. Numerical simulation is also done to illustrate the influence of different parameters on the effective reproduction number. Using sensitive analysis we identify the most influential parameter to change the behavior of the solution of the considered dynamical system is the number of effective contacts of susceptible or vaccinated individuals make with an infectious individual.
Keywords
Drug-sensitive Tuberculosis, Drug Resistance Tuberculosis, Effective Reproduction Number, Sensitivity Analysis, Numerical Analysis
Shimelis Bekele Zerefe, Temesgen Tibebu Mekonnen, Spread and Control of Multi-drug Resistance Tuberculosis and Drug-sensitive Tuberculosis in Ethiopia: A Mathematical Model Analysis, American Journal of Applied Mathematics. Vol. 8, No. 3, 2020, pp. 123-144. doi: 10.11648/j.ajam.20200803.15
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