An optimal control problem and cost-effectiveness analysis of malaria disease with vertical transmission applied to San Andrés de Tumaco (Colombia)

  • Jhoana P. Romero-LeitonEmail author
  • Jairo Eloy Castellanos
  • Eduardo Ibargüen-Mondragón


In this work, we studied malaria disease in San Andrés de Tumaco-Colombia (Tumaco) using mathematical modeling with the objective of contributing to the understanding its transmission dynamics and to the development of control strategies. To this end, we formulated a system of ordinary differential equations that describe the malaria disease transmission dynamics in Tumaco and considered both vectorial and vertical transmission of disease. We performed a sensitivity analysis of parameters that allowed us to define the following control variables: indoor residual spraying (IRS), bed nets (BN), intermittent prophylactic treatment in pregnancy (IPTp) and antimalarial treatment (AT). Using previously identified control variables, we formulated an optimal control problem with different control strategies. We analytically and numerically solved the optimal control problem and generated a cost-effectiveness analysis of these strategies using data from rural areas of Tumaco. The results suggested that simultaneous implementation of IRS, BN, IPTp and AT strategies are the best options.


Malaria Sensitivity analysis of parameters Optimal control Cost-effectiveness analysis 

Mathematics Subject Classification

92B05 49J15 



Jhoana P. Romero-Leiton acknowledges for the scholarship Jóvenes Investigadores e innovadores granted by Fundación CEIBA. E. Ibargüen acknowledges support from Project No. 114-19/10/2017 (VIPRI-UDENAR). This work is dedicated to the memory of Ph.D Anthony Uyi Afuwape who in life helped us unconditionally.


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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  • Jhoana P. Romero-Leiton
    • 1
    Email author
  • Jairo Eloy Castellanos
    • 2
  • Eduardo Ibargüen-Mondragón
    • 3
  1. 1.Escuela de ciencias matemáticas y computacionalesUniversidad de Investigación y Tecnología Experimental Yachay TechUrcuquíEcuador
  2. 2.Instituto de matemáticasUniversidad de AntioquiaMedellinColombia
  3. 3.Departamento de matemáticasUniversidad de NariñoPastoColombia

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