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Calibration of a SEIR–SEI epidemic model to describe the Zika virus outbreak in Brazil

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  • Dantas, Eber
  • Tosin, Michel
  • Cunha Jr, Americo

Abstract

Multiple instances of Zika virus epidemic have been reported around the world in the last two decades, turning the related illness into an international concern. In this context the use of mathematical models for epidemics is of great importance, since they are useful tools to study the underlying outbreak numbers and allow one to test the effectiveness of different strategies used to combat the associated diseases. This work deals with the development and calibration of an epidemic model to describe the 2016 outbreak of Zika virus in Brazil. A system of 8 differential equations with 8 parameters is employed to model the evolution of the infection through two populations. Nominal values for the model parameters are estimated from the literature. An inverse problem is formulated and solved by comparing the system response to real data from the outbreak. The calibrated results presents realistic parameters and returns reasonable descriptions, with the curve shape similar to the outbreak evolution and peak value close to the highest number of infected people during 2016. Considerations about the lack of data for some initial conditions are also made through an analysis over the response behavior according to their change in value.

Suggested Citation

  • Dantas, Eber & Tosin, Michel & Cunha Jr, Americo, 2018. "Calibration of a SEIR–SEI epidemic model to describe the Zika virus outbreak in Brazil," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 249-259.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:249-259
    DOI: 10.1016/j.amc.2018.06.024
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    References listed on IDEAS

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    4. Diaz, Paul & Constantine, Paul & Kalmbach, Kelsey & Jones, Eric & Pankavich, Stephen, 2018. "A modified SEIR model for the spread of Ebola in Western Africa and metrics for resource allocation," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 141-155.
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    Cited by:

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    2. Ariful Kabir, K.M. & Tanimoto, Jun, 2021. "A cyclic epidemic vaccination model: Embedding the attitude of individuals toward vaccination into SVIS dynamics through social interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
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    4. AlShamrani, N.H. & Elaiw, A.M. & Batarfi, H. & Hobiny, A.D. & Dutta, H., 2020. "Global stability analysis of a general nonlinear scabies dynamics model," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Gergo Pinter & Imre Felde & Amir Mosavi & Pedram Ghamisi & Richard Gloaguen, 2020. "COVID-19 Pandemic Prediction for Hungary; A Hybrid Machine Learning Approach," Mathematics, MDPI, vol. 8(6), pages 1-20, June.
    6. Jabili Angina & Anish Bachhu & Eesha Talati & Rishi Talati & Jan Rychtář & Dewey Taylor, 2022. "Game-Theoretical Model of the Voluntary Use of Insect Repellents to Prevent Zika Fever," Dynamic Games and Applications, Springer, vol. 12(1), pages 133-146, March.
    7. Kabir, K.M. Ariful & Kuga, Kazuki & Tanimoto, Jun, 2019. "Analysis of SIR epidemic model with information spreading of awareness," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 118-125.
    8. Yunhwan Kim & Ana Vivas Barber & Sunmi Lee, 2020. "Modeling influenza transmission dynamics with media coverage data of the 2009 H1N1 outbreak in Korea," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-21, June.

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