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

Identifier:  imarina:9287404

Handle: https://hdl.handle.net/20.500.11797/imarina9287404

Authors:  Arenas, Alex; Garijo, Antonio; Gomez, 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.