PHASE TRANSITIONS OF THE SIR RUMOR SPREADING MODEL WITH A VARIABLE TRUST RATE

Sun Ho Choi, Hyowon Seo, Minha Yoo

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We study a threshold phenomenon of rumor outbreak on the SIR rumor spreading model with a variable trust rate depending on the populations of ignorants and spreaders. Rumor outbreak in the SIR rumor spreading model is defined as a persistence of the final rumor size in the large population limit or thermodynamics limit (n → ∞), where 1/n is the initial population of spreaders. We present a rigorous proof for the existence of threshold on the final size of the rumor with respect to the basic reproduction number R0. Moreover, we prove that a phase transition phenomenon occurs for the final size of the rumor (as an order parameter) with respect to the basic reproduction number and provide a criterion to determine whether the phase transition is of first or second order. Precisely, we prove that there is a critical number R1 such that if R1 > 1, then the phase transition is of the first order, i.e., the limit of the final size is not a continuous function with respect to R0. The discontinuity is a jump-type discontinuity and it occurs only at R0 = 1. If R1 < 1, then the phase transition is second order, i.e., the limit of the final size is continuous with respect to R0 and its derivative exists, except at R0 = 1, and the derivative is not continuous at R0 = 1. We also present numerical simulations to demonstrate our analytical results for the threshold phenomena and phase transition order criterion.

Original languageEnglish
Pages (from-to)1827-1851
Number of pages25
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume27
Issue number3
DOIs
Publication statusPublished - Mar 2022

Bibliographical note

Publisher Copyright:
© 2022 American Institute of Mathematical Sciences. All rights reserved.

Keywords

  • Phase transition order
  • SIR type rumor spreading model
  • Thermodynamic limit
  • Variable trust rate

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