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Optimal Control Measures for Tuberculosis in a Population Affected with Insurgency

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Mathematics Applied to Engineering, Modelling, and Social Issues

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 200))

Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Benin, P.M.B. 1154, Benin City, Nigeria

    A. O. Egonmwan & D. Okuonghae

Authors
  1. A. O. Egonmwan
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  2. D. Okuonghae
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Correspondence to D. Okuonghae .

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Editors and Affiliations

  1. Department of Mathematics, University College London, London, UK

    Frank T. Smith

  2. Department of Mathematics, Gauhati University, Guwahati, Assam, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

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Egonmwan, A.O., Okuonghae, D. (2019). Optimal Control Measures for Tuberculosis in a Population Affected with Insurgency. In: Smith, F.T., Dutta, H., Mordeson, J.N. (eds) Mathematics Applied to Engineering, Modelling, and Social Issues. Studies in Systems, Decision and Control, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-030-12232-4_19

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  • DOI: https://doi.org/10.1007/978-3-030-12232-4_19

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-12231-7

  • Online ISBN: 978-3-030-12232-4

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