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An epidemiological MSEIR model described by the Caputo fractional derivative

  • Ricardo AlmeidaEmail author
  • Artur M. C. Brito da Cruz
  • Natália Martins
  • M. Teresa T. Monteiro
Article

Abstract

A fractional MSEIR model is presented, involving the Caputo fractional derivative. The equilibrium points and the basic reproduction number are computed. An analysis of the local asymptotic stability at the disease free equilibrium is given. Finally a numerical simulation, using Matlab based on optimization techniques, of the varicella outbreak among Shenzhen school children, China, is carried out.

Keywords

Fractional calculus Fractional differential equations Epidemics MSEIR model Local stability 

Mathematics Subject Classification

26A33 92D30 37N25 

Notes

Acknowledgements

R. Almeida, A.M.C. Brito da Cruz and N. Martins were supported by Portuguese funds through the CIDMA—Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), within project UID/MAT/04106/2019; M. T. Monteiro by COMPETE: POCI-01-0145-FEDER-007043 and FCT-Fundação para a Ciência e a Tecnologia within the Project Scope: UID/CEC/00319/2013. The authors are grateful to two anonymous referees for valuable comments and suggestions. ©2017 The MathWorks, Inc. MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See mathworks.com/trademarks for a list of additional trademarks. Other product or brand names may be trademarks or registered trademarks of their respective holders.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Center for Research and Development in Mathematics and Applications (CIDMA)University of AveiroAveiroPortugal
  2. 2.Escola Superior de Tecnologia de SetúbalSetúbalPortugal
  3. 3.Department of Production and Systems, Algoritmi R&D CenterUniversity of MinhoBragaPortugal

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