Optimal Control Measures for Tuberculosis in a Population Affected with Insurgency

  • A. O. Egonmwan
  • D. OkuonghaeEmail author
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 200)


In this chapter, optimal control theory is applied to a mathematical model describing the population dynamics of tuberculosis (TB) with variability in susceptibility due to difference in awareness level. Seeking to minimize the number of high-risk susceptible individuals with low level of TB awareness and to maximize the number of isolated actively-infected individuals placed under Directly Observed Treatment Short-Course (DOTS), we incorporated time-dependent control functions that represent educational campaign programs in the midst of insurgency, and case finding techniques for chronic TB cases, as they affect the dynamics of TB in a population. A particular case of the TB model without controls is presented and analyzed. Furthermore, the optimal controls are characterized in terms of the optimality systems, which are solved numerically for several scenarios using an iterative method with Runge-Kutta fourth order scheme. Numerical simulations were performed for various setting to illustrate the effect of the controls on the population dynamics of the disease in a given population.


Tuberculosis Mathematical model Awareness campaign Case finding techniques Insurgency Optimal control theory Numerical simulations 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of BeninBenin CityNigeria

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