Skip to main content

A Variational Formulation for a Human Migration Problem

Part of the AIRO Springer Series book series (AIROSS,volume 3)


Many social and economical factors affect the dynamics of human populations, such as poverty, violence, war, dictatorships, persecutions, tsunamis, floods, earthquakes, family reunification as well as economic and educational possibilities or a job. In this paper, we consider a network based model where the aim of each migration class is to maximize the attractiveness of the origin country and we prove that the optimization model can be formulated in terms of a Nash equilibrium problem and a variational inequality. Finally, some numerical results applied to the human migration from Africa to Europe are presented and analyzed.


  • Human migration
  • Nonlinear optimization
  • Network models

This is a preview of subscription content, access via your institution.

Buying options

USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-030-34960-8_17
  • Chapter length: 11 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
USD   139.00
Price excludes VAT (USA)
  • ISBN: 978-3-030-34960-8
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   179.99
Price excludes VAT (USA)
Hardcover Book
USD   179.99
Price excludes VAT (USA)
Fig. 1
Fig. 2


  1. Aleshkovski, I., Iontsev, V.: Mathematical models of migration. Comput. Sci. (2011).

  2. Cojocaru, M.G.: Double-layer dynamics theory and human migration after catastrophic events. In: Nonlinear Analysis with applications in Economics. Energy and Transportation, pp. 65–86. Bergamo University Press, Bergamo (2007)

    Google Scholar 

  3. Cui, S., Bai, M.: Mathematical Analysis of Population Migration and Its Effects to Spread of Epidemics (2014), arXiv:1403.5351 [math.FA]

    Google Scholar 

  4. International Organization for Migration’s Global Migration Data Analysis Centre.

  5. Kalashnykov, V., Kalashnykova, N.: Simulation of a conjectural variations equilibrium in a human migration model. Int. J. Simul. Syst. Sci. Technol. 7(9), 26–39 (2006)

    Google Scholar 

  6. Mediterranean Situation.

  7. Nagurney, A.: A network model of migration equilibrium with movement costs. Math. Comput. Model. 13(5), 79–88 (1990)

    MathSciNet  CrossRef  Google Scholar 

  8. Nagurney, A.: Network Economics: A Variational Inequality Approach, 2nd and revised edn. Kluwer, Boston (1999)

    CrossRef  Google Scholar 

  9. Volpert, V., Petrovskiic, S., Zincenkoc, A.: Interaction of human migration and wealth distribution. Nonlinear Anal. 159, 408–423 (2017). Hal

    MathSciNet  CrossRef  Google Scholar 

Download references


The research of the authors was partially supported by the research project “Modelli Matematici nell’Insegnamento-Apprendimento della Matematica” DMI, University of Catania and by the research project PON SCN 00451 CLARA - CLoud plAtform and smart underground imaging for natural Risk Assessment, Smart Cities and Communities and Social Innovation. These supports are gratefully acknowledged.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Patrizia Daniele .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Verify currency and authenticity via CrossMark

Cite this chapter

Cappello, G., Daniele, P. (2019). A Variational Formulation for a Human Migration Problem. In: Paolucci, M., Sciomachen, A., Uberti, P. (eds) Advances in Optimization and Decision Science for Society, Services and Enterprises. AIRO Springer Series, vol 3. Springer, Cham.

Download citation