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

Alex Arenas, Antonio Garijo, Sergio Gómez and Jordi Villadelprat

Chaos, Solitons & Fractals, 2023, vol. 166, issue C

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.

Keywords: Transcritical bifurcation; Epidemic spreading; Discrete-map; Complex networks (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:166:y:2023:i:c:s0960077922011006

DOI: 10.1016/j.chaos.2022.112921

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