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Epidemics with Behavior

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  • Satoshi Fukuda
  • Nenad Kos
  • Christoph Wolf

Abstract

We study equilibrium distancing during epidemics. Distancing reduces the individual's probability of getting infected but comes at a cost. It creates a single-peaked epidemic, flattens the curve and decreases the size of the epidemic. We examine more closely the effects of distancing on the outset, the peak and the final size of the epidemic. First, we define a behavioral basic reproduction number and show that it is concave in the transmission rate. The infection, therefore, spreads only if the transmission rate is in the intermediate region. Second, the peak of the epidemic is non-monotonic in the transmission rate. A reduction in the transmission rate can lead to an increase of the peak. On the other hand, a decrease in the cost of distancing always flattens the curve. Third, both an increase in the infection rate as well as an increase in the cost of distancing increase the size of the epidemic. Our results have important implications on the modeling of interventions. Imposing restrictions on the infection rate has qualitatively different effects on the trajectory of the epidemics than imposing assumptions on the cost of distancing. The interventions that affect interactions rather than the transmission rate should, therefore, be modeled as changes in the cost of distancing.

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  • Satoshi Fukuda & Nenad Kos & Christoph Wolf, 2021. "Epidemics with Behavior," Papers 2103.00591, arXiv.org.
    • Handle: RePEc:arx:papers:2103.00591
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    Cited by:

    1. Christoph Carnehl & Satoshi Fukuda & Nenad Kos, 2022. "Time-varying Cost of Distancing: Distancing Fatigue and Lockdowns," Papers 2206.03847, arXiv.org, revised Sep 2023.

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    JEL classification:

    • I12 - Health, Education, and Welfare - - Health - - - Health Behavior
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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