Application of optimal control to tuberculosis model with parameter estimations: Bayesian approach

  • Goodluck M Mlay Department of Mathematics, University of Dar es Salaam, P. O. Box 35062, Dar es Salaam, Tanzania
  • Alfred K Hugo Department of Mathematics and Statistics, University of Dodoma, P. O. Box 338, Dodoma, Tanzania
Keywords: Tuberculosis, Education campaigns, Chemoprophylaxis, MCMC


In this paper, one-strain tuberculosis (TB) model with two control mechanisms, education campaigns and chemoprophylaxis of TB-infected patients, was studied to determine their effects on the reduction of latent and active TB cases. In the case of analysis, boundedness and positivity of the model solutions were carried out to determine the biological feasibility of the study. Besides, the calibration of the parameters by utilizing the identifiability technique through the Markov chain Monte Carlo (MCMC) was thoroughly analysed. The optimum conditions for controlling TB were derived from the Pontryagin Maximum Principle. The numerical simulations were carried out using the forward-back sweep method with the help of the Runge-Kutta fourth-order numerical schemes. Simulation results showed that the education campaigns strategy is more effective in reducing TB infections than the chemoprophylaxis of TB-infected individuals. The combination of the two control strategies reduces a significant number of infections than when each strategy is used on its own. To minimize the transmission of TB from the community, we recommend the education campaigns strategy be a focal point and treatment of latent TB to be paired with the treatment of active TB cases.

Keywords: Tuberculosis, Education campaigns, Chemoprophylaxis, MCMC


Journal Identifiers

eISSN: 2507-7961
print ISSN: 0856-1761