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Using a Stochastic SIR Model to Design Optimal Vaccination Campaigns via Multiobjective Optimization

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Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment (BIOMAT 2019)

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Abstract

The design of optimal vaccination campaigns using mathematical and computational models has given concrete suggestions to politicians and other ones responsible on how it should be implemented in a better way, given a certain allowed level of infected persons within the whole population. In this paper, a multiobjective impulsive control scheme in an open-loop continuous-variable dynamic optimization procedure is proposed to cope with this problem, having the NSGA-II (Non-dominated Sorting Genetic Algorithm) as an optimization machinery and the SIR (Susceptible–Infectious–Recovered) model describing the behavior of a disease in a population, extended to analyze the effects of impulsive vaccination on the population. Furthermore, a stochastic SIR model is adapted in order to calculate the probability of eradication to each non-dominated vaccination policy came from the NSGA-II, as decision criteria. The target of the analysis is to give concrete suggestions to politicians or decision-makers how optimal vaccination campaigns should be implemented, given a certain probability of eradication or an allowed level of infected persons within the whole population.

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Acknowledgements

R. T. N. Cardoso thanks the International Union of Biological Sciences (IUBS) for partial support of living expenses in Szeged, during the 19th BIOMAT International Symposium, October 20–26, 2019.

The authors would thank to the Brazilian Agencies CAPES, CNPq, FAPEMIG, and to CEFET-MG for financial support.

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Authors and Affiliations

  1. Centro Federal de Educação Tecnológica de Minas Gerais, Belo Horizonte, MG, Brazil

    A. C. S. Dusse & R. T. N. Cardoso

Authors
  1. A. C. S. Dusse
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  2. R. T. N. Cardoso
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Editors and Affiliations

  1. President, BIOMAT Consortium – International Institute for Interdisciplinary Sciences, Rio de Janeiro, Brazil

    Rubem P. Mondaini

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Dusse, A.C.S., Cardoso, R.T.N. (2020). Using a Stochastic SIR Model to Design Optimal Vaccination Campaigns via Multiobjective Optimization. In: Mondaini, R.P. (eds) Trends in Biomathematics: Modeling Cells, Flows, Epidemics, and the Environment. BIOMAT 2019. Springer, Cham. https://doi.org/10.1007/978-3-030-46306-9_16

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