Transient prophylaxis and multiple epidemic waves

Rebecca C. Tyson; Noah D. Marshall; Bert O. Baumgaertner; Rebecca C. Tyson; Noah D. Marshall; Bert O. Baumgaertner

doi:10.3934/math.2022311

AIMS Mathematics

2022, Volume 7, Issue 4: 5616-5633. doi: 10.3934/math.2022311

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Research article Special Issues

Transient prophylaxis and multiple epidemic waves

1.
CMPS Department (Mathematics), University of British Columbia Okanagan, Kelowna, BC, Canada
2.
Department of Mathematics and Statistics, McGill University, Montreal, Quebec, Canada
3.
Department of Politics and Philosophy, University of Idaho, Moscow, Idaho, USA

Received: 06 January 2021 Revised: 21 May 2021 Accepted: 06 October 2021 Published: 10 January 2022
MSC : 91D10, 92D30

Public opinion and opinion dynamics can have a strong effect on the transmission rate of an infectious disease for which there is no vaccine. The coupling of disease and opinion dynamics however, creates a dynamical system that is complex and poorly understood. We present a simple model in which susceptible groups adopt or give up prophylactic behaviour in accordance with the influence related to pro- and con-prophylactic communication. This influence varies with disease prevalence. We observe how the speed of the opinion dynamics affects the total size and peak size of the epidemic. We find that more reactive populations will experience a lower peak epidemic size, but possibly a larger final size and more epidemic waves, and that an increase in polarization results in a larger epidemic.
- epidemiology,
- disease modelling,
- ordinary differential equations,
- opinion dynamics,
- non-pharmaceutical interventions,
- personal protective behaviours,
- transient behaviour
Citation: Rebecca C. Tyson, Noah D. Marshall, Bert O. Baumgaertner. Transient prophylaxis and multiple epidemic waves[J]. AIMS Mathematics, 2022, 7(4): 5616-5633. doi: 10.3934/math.2022311

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Abstract

Public opinion and opinion dynamics can have a strong effect on the transmission rate of an infectious disease for which there is no vaccine. The coupling of disease and opinion dynamics however, creates a dynamical system that is complex and poorly understood. We present a simple model in which susceptible groups adopt or give up prophylactic behaviour in accordance with the influence related to pro- and con-prophylactic communication. This influence varies with disease prevalence. We observe how the speed of the opinion dynamics affects the total size and peak size of the epidemic. We find that more reactive populations will experience a lower peak epidemic size, but possibly a larger final size and more epidemic waves, and that an increase in polarization results in a larger epidemic.

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