Optimal control of vaccination in a vector-borne reaction–diffusion model applied to Zika virus

  • Tiago Yuzo MiyaokaEmail author
  • Suzanne Lenhart
  • João F. C. A. Meyer


Zika virus has acquired worldwide concern after a recent outbreak in Latin America that started in Brazil, with associated neurological conditions such as microcephaly in newborns from infected mothers. The virus is transmitted mainly by Aedes aegypti mosquitoes, but direct (sexual) transmission has been documented. We formulate a reaction diffusion model that considers spatial movement of humans and vectors, with local contact transmission of Zika virus. Vaccination is introduced as a control variable, giving immunity to susceptible humans, in order to characterize an optimal vaccination strategy that minimizes the costs associated with infections and vaccines. The optimal control characterization is obtained in terms of state and adjoint equations. Parameter estimation and numerical simulations are carried out using data for the initial 2015 Zika outbreak in the state of Rio Grande do Norte in Brazil. Several scenarios are considered and analyzed in terms of number of new infections and costs, showing that the optimal control application is successful, significantly reducing these quantities.


Zika virus Optimal control Vaccination Partial differential equations Numerical methods 

Mathematics Subject Classification

35K51 49J20 92D30 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Applied Mathematics, IMECCUniversity of CampinasCampinasBrazil
  2. 2.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

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