Incorporating changeable attitudes toward vaccination into compartment models for infectious diseases

Yi Jiang; Kristin M. Kurianski; Jane HyoJin Lee; Yanping Ma; Daniel Cicala; Glenn Ledder; Yi Jiang; Kristin M. Kurianski; Jane HyoJin Lee; Yanping Ma; Daniel Cicala; Glenn Ledder

doi:10.3934/mbe.2025011

Mathematical Biosciences and Engineering

2025, Volume 22, Issue 2: 260-289. doi: 10.3934/mbe.2025011

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Incorporating changeable attitudes toward vaccination into compartment models for infectious diseases

1.
Department of Mathematics and Statistics, Southern Illinois University Edwardsville, 6 Hairpin Drive, Edwardsville, IL 62026, USA
2.
Department of Mathematics, California State University, Fullerton, 800 N State College Blvd, Fullerton, CA 92831, USA
3.
Department of Mathematics, Stonehill College, 320 Washington Street, Easton, MA 02357, USA
4.
Department of Mathematics, Loyola Marymount University, 1 LMU Drive, Los Angeles, CA 90045, USA
5.
Department of Mathematics, Southern Connecticut State University, 501 Crescent Street, New Haven, CT 06515, USA
6.
Department of Mathematics, University of Nebraska–Lincoln, 203 Avery Hall, Lincoln, NE 68588, USA

Academic Editor: Yang Kuang

Received: 02 August 2024 Revised: 30 December 2024 Accepted: 03 January 2025 Published: 21 January 2025

We develop a mechanistic model that classifies individuals both in terms of epidemiological status (SIR) and vaccination attitude (Willing or Unwilling/Unable), with the goal of discovering how disease spread is influenced by changing opinions about vaccination. Analysis of the model identifies the existence and stability criteria for both disease-free and endemic disease equilibria. The analytical results, supported by numerical simulations, show that attitude changes induced by disease prevalence can destabilize endemic disease equilibria, resulting in limit cycles.
- compartment models,
- endemic disease models,
- vaccination,
- stability analysis
Citation: Yi Jiang, Kristin M. Kurianski, Jane HyoJin Lee, Yanping Ma, Daniel Cicala, Glenn Ledder. Incorporating changeable attitudes toward vaccination into compartment models for infectious diseases[J]. Mathematical Biosciences and Engineering, 2025, 22(2): 260-289. doi: 10.3934/mbe.2025011

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Abstract

We develop a mechanistic model that classifies individuals both in terms of epidemiological status (SIR) and vaccination attitude (Willing or Unwilling/Unable), with the goal of discovering how disease spread is influenced by changing opinions about vaccination. Analysis of the model identifies the existence and stability criteria for both disease-free and endemic disease equilibria. The analytical results, supported by numerical simulations, show that attitude changes induced by disease prevalence can destabilize endemic disease equilibria, resulting in limit cycles.

References

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