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Synchronization and Self-organization in Complex Networks for a Tuberculosis Model

Abstract

In this work, we propose and analyze the dynamics of a complex network built with non identical instances of a tuberculosis (TB) epidemiological model, for which we prove the existence of non-negative and bounded global solutions. A two nodes network is analyzed where the nodes represent the TB epidemiological situation of the countries Angola and Portugal. We analyze the effect of different coupling and intensity of migratory movements between the two countries and explore the effect of seasonal migrations. For a random complex network setting, we show that it is possible to reach a synchronization state by increasing the coupling strength and test the influence of the topology in the dynamics of the complex network. All the results are analyzed through numerical simulations where the given algorithms are implemented with the python 3.5 language, in a Debian/GNU-Linux environment.

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Notes

  1. Angola is in the 30 high TB burden countries. of WHO’s Global tuberculosis report 2018 [15].

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Acknowledgements

This work is partially supported by The Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT—Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020. Silva is also supported by national funds (OE), through FCT, I.P., in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article 23, of the Decree-Law 57/2016, of August 29, changed by Law 57/2017, of July 19. Silva is also grateful to the support of the COST Action CA16227—Investigation and Mathematical Analysis of Avant-garde Disease Control via Mosquito Nano-Tech-Repellents (WG2 on ?Structured Models & Optimal Control?).

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Correspondence to Cristiana J. Silva.

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Silva, C.J., Cantin, G. Synchronization and Self-organization in Complex Networks for a Tuberculosis Model. Math.Comput.Sci. 15, 107–120 (2021). https://doi.org/10.1007/s11786-020-00472-2

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  • DOI: https://doi.org/10.1007/s11786-020-00472-2

Keywords

  • Complex network
  • Graph topology
  • Python
  • Tuberculosis

Mathematics Subject Classification

  • 34A34
  • 34C60
  • 92B05