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Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks

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  • Arenas, Alex
  • Garijo, Antonio
  • Gómez, Sergio
  • Villadelprat, Jordi

Abstract

The dynamics of many epidemic compartmental models for infectious diseases that spread in a single host population present a second-order phase transition. This transition occurs as a function of the infectivity parameter, from the absence of infected individuals to an endemic state. Here, we study this transition, from the perspective of dynamical systems, for a discrete-time compartmental epidemic model known as Microscopic Markov Chain Approach, whose applicability for forecasting future scenarios of epidemic spreading has been proved very useful during the COVID-19 pandemic. We show that there is an endemic state which is stable and a global attractor and that its existence is a consequence of a transcritical bifurcation. This mathematical analysis grounds the results of the model in practical applications.

Suggested Citation

  • Arenas, Alex & Garijo, Antonio & Gómez, Sergio & Villadelprat, Jordi, 2023. "Bifurcation analysis of the Microscopic Markov Chain Approach to contact-based epidemic spreading in networks," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    • Handle: RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011006
    DOI: 10.1016/j.chaos.2022.112921
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    References listed on IDEAS

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    1. J. Gómez-Gardeñes & P. Echenique & Y. Moreno, 2006. "Immunization of real complex communication networks," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 49(2), pages 259-264, January.
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    Cited by:

    1. Zhiyong Hong & Huiyu Zhou & Zhishuang Wang & Qian Yin & Jingang Liu, 2023. "Coupled Propagation Dynamics of Information and Infectious Disease on Two-Layer Complex Networks with Simplices," Mathematics, MDPI, vol. 11(24), pages 1-17, December.

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