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

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...

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Bibliographic Details
Published in:Journal of mathematical biology 2019-08, Vol.79 (3), p.1077-1104
Main Authors: Miyaoka, Tiago Yuzo, Lenhart, Suzanne, Meyer, João F. C. A.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Aquatic insects
Computer simulation
Cost analysis
Diffusion
Diffusion models
Disease transmission
Immunity
Infections
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Microencephaly
Mosquitoes
Neonates
Optimal control
Outbreaks
Parameter estimation
Sexual transmission
Vaccines
Vector-borne diseases
Vectors
Viruses
Zika virus
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Summary: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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-019-01390-z