Research Article
Mathematical Modelling and Optimal Control of Tuberculosis Transmission Dynamics in Werder District, Somali Regional State, Ethiopia
Tasew Ayele Taddese*,
Tsega Mhretab Gebre Silase,
Tsegaw Muche Tessema,
Sadam Dawud Adem
Issue:
Volume 7, Issue 1, March 2026
Pages:
1-22
Received:
18 January 2025
Accepted:
13 June 2025
Published:
16 January 2026
DOI:
10.11648/j.scidev.20260701.11
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Views:
Abstract: Tuberculosis (TB) is an infectious disease caused by mycobacterium tuberculosis bacteria (tubercle bacilli) and spreads through the air from an infectious person to a susceptible person. This research aims to investigate the transmission dynamics of tuberculosis (TB) using a mathematical model with optimal control and to estimate the reproduction number in the Werder district of the Somali regional state. To achieve the objective of the study, we employed different mathematical tools and available cumulative case data from the Werder district of the Somali regional state health officials. The model is developed using a system of nonlinear ordinary differential equations and basic reproduction number is determine to perform analysis for both local and global stability of the equilibrium points of the model. In addition to this, sensitivity analysis is studied based on the reproduction number to reveal influential parameters of transmission dynamics of tuberculosis. Then the optimal control strategy was found by minimizing the number of exposed and infected individual populations with tuberculosis taking into account the cost of implementation. The existence of optimal control and characterization was established with the help of Pontryagin's Maximum Principle and we conducted different numerical simulation cases to see agreements with analytical results. Moreover, the model was calibrated with real data collected from the Werder district of the Somali regional state health office from 2016 – 2022. The simulation results also clearly shown that the tuberculosis can be minimized by applying TB prevention programs to susceptible individuals and preventing the failure of treatment in active tuberculosis individuals through continuous supervision and helping patients during treatment period with optimal implementation cost. Furthermore, the optimal control model also predicted that tuberculosis is under control in Werder district.
Abstract: Tuberculosis (TB) is an infectious disease caused by mycobacterium tuberculosis bacteria (tubercle bacilli) and spreads through the air from an infectious person to a susceptible person. This research aims to investigate the transmission dynamics of tuberculosis (TB) using a mathematical model with optimal control and to estimate the reproduction n...
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