Computational and Applied Mathematics

, Volume 37, Issue 2, pp 2112–2128 | Cite as

Multiobjective optimization to a TB-HIV/AIDS coinfection optimal control problem

  • Roman Denysiuk
  • Cristiana J. Silva
  • Delfim F. M. Torres


We consider a recent coinfection model for Tuberculosis (TB), Human Immunodeficiency Virus (HIV) infection, and Acquired Immunodeficiency Syndrome (AIDS) proposed in Silva and Torres (Discr Contin Dyn Syst 35(9):4639–4663, 2015). We introduce and analyze a multiobjective formulation of an optimal control problem, where the two conflicting objectives are minimization of the number of HIV-infected individuals with AIDS clinical symptoms and coinfected with AIDS and active TB; and costs related to prevention and treatment of HIV and/or TB measures. The proposed approach eliminates some limitations of previous works. The results of the numerical study provide comprehensive insights about the optimal treatment policies and the population dynamics resulting from their implementation. Some nonintuitive conclusions are drawn. Overall, the simulation results demonstrate the usefulness and validity of the proposed approach.


Tuberculosis HIV Epidemic model Treatment strategies Optimal control theory Multiobjective optimization 

Mathematics Subject Classification

90C29 92C50 



Silva and Torres were supported by Portuguese funds through the Center for Research and Development in Mathematics and Applications (CIDMA) and the Portuguese Foundation for Science and Technology (FCT), within project UID/MAT/04106/2013; and by the FCT project TOCCATA, ref. PTDC/EEI-AUT/2933/2014. Silva is also grateful to the FCT post-doc fellowship SFRH/ BPD/72061/2010. The authors would like to thank two anonymous referees for valuable comments and suggestions.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2017

Authors and Affiliations

  1. 1.Algoritmi R&D CenterUniversity of MinhoBragaPortugal
  2. 2.Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA)University of AveiroAveiroPortugal

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