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Coupled contagion dynamics of fear and disease: mathematical and computational explorations.

Epstein JM, Parker J, Cummings D, Hammond RA - PLoS ONE (2008)

Bottom Line: In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics.They do not endogenously engage, for example, in social distancing based on fear.Our main point is that behavioral adaptation of some sort must be considered.

View Article: PubMed Central - PubMed

Affiliation: Center on Social and Economic Dynamics, The Brookings Institution, Washington DC, United States of America. jepstein@brookings.edu

ABSTRACT

Background: In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics. They do not endogenously engage, for example, in social distancing based on fear. Yet, adaptive behavior is well-documented in true epidemics. We explore the effect of including such behavior in models of epidemic dynamics.

Methodology/principal findings: Using both nonlinear dynamical systems and agent-based computation, we model two interacting contagion processes: one of disease and one of fear of the disease. Individuals can "contract" fear through contact with individuals who are infected with the disease (the sick), infected with fear only (the scared), and infected with both fear and disease (the sick and scared). Scared individuals--whether sick or not--may remove themselves from circulation with some probability, which affects the contact dynamic, and thus the disease epidemic proper. If we allow individuals to recover from fear and return to circulation, the coupled dynamics become quite rich, and can include multiple waves of infection. We also study flight as a behavioral response.

Conclusions/significance: In a spatially extended setting, even relatively small levels of fear-inspired flight can have a dramatic impact on spatio-temporal epidemic dynamics. Self-isolation and spatial flight are only two of many possible actions that fear-infected individuals may take. Our main point is that behavioral adaptation of some sort must be considered.

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Related in: MedlinePlus

In the idealized run of figure 3, susceptible individuals (blue-curve) self-isolate (black curve) through fear as the infection of disease proper grows (red curve).Emboldened by the falling disease incidence, these susceptibles return (prematurely) to circulation (the blue hump). But, this offers fuel to the remaining embers of infection (at time 100), and a second wave ensues.
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pone-0003955-g003: In the idealized run of figure 3, susceptible individuals (blue-curve) self-isolate (black curve) through fear as the infection of disease proper grows (red curve).Emboldened by the falling disease incidence, these susceptibles return (prematurely) to circulation (the blue hump). But, this offers fuel to the remaining embers of infection (at time 100), and a second wave ensues.

Mentions: Finally, multiple waves of infection of the sort that occurred in 1918 are easily generated in this model. For example, it suffices to , with a = 150 and b = 8. In the idealized run of figure 3, susceptible individuals (blue-curve) self-isolate (yellow curve) through fear as the infection of disease proper grows (red curve). Emboldened by the falling disease incidence, these susceptibles return (prematurely) to circulation (the blue hump). But, this offers fuel to the remaining embers of infection (at time 100), and a second wave ensues. This reflects the counterintuitive and crucial insight of the original Kermack-McKendrick model, that the epidemic threshold is not the infective level, but rather the susceptible one. Authorities in 1918 did not have the benefit of this insight, and in a number of cities lifted quarantines prematurely, with the same effect: multiple waves.


Coupled contagion dynamics of fear and disease: mathematical and computational explorations.

Epstein JM, Parker J, Cummings D, Hammond RA - PLoS ONE (2008)

In the idealized run of figure 3, susceptible individuals (blue-curve) self-isolate (black curve) through fear as the infection of disease proper grows (red curve).Emboldened by the falling disease incidence, these susceptibles return (prematurely) to circulation (the blue hump). But, this offers fuel to the remaining embers of infection (at time 100), and a second wave ensues.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC2596968&req=5

pone-0003955-g003: In the idealized run of figure 3, susceptible individuals (blue-curve) self-isolate (black curve) through fear as the infection of disease proper grows (red curve).Emboldened by the falling disease incidence, these susceptibles return (prematurely) to circulation (the blue hump). But, this offers fuel to the remaining embers of infection (at time 100), and a second wave ensues.
Mentions: Finally, multiple waves of infection of the sort that occurred in 1918 are easily generated in this model. For example, it suffices to , with a = 150 and b = 8. In the idealized run of figure 3, susceptible individuals (blue-curve) self-isolate (yellow curve) through fear as the infection of disease proper grows (red curve). Emboldened by the falling disease incidence, these susceptibles return (prematurely) to circulation (the blue hump). But, this offers fuel to the remaining embers of infection (at time 100), and a second wave ensues. This reflects the counterintuitive and crucial insight of the original Kermack-McKendrick model, that the epidemic threshold is not the infective level, but rather the susceptible one. Authorities in 1918 did not have the benefit of this insight, and in a number of cities lifted quarantines prematurely, with the same effect: multiple waves.

Bottom Line: In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics.They do not endogenously engage, for example, in social distancing based on fear.Our main point is that behavioral adaptation of some sort must be considered.

View Article: PubMed Central - PubMed

Affiliation: Center on Social and Economic Dynamics, The Brookings Institution, Washington DC, United States of America. jepstein@brookings.edu

ABSTRACT

Background: In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics. They do not endogenously engage, for example, in social distancing based on fear. Yet, adaptive behavior is well-documented in true epidemics. We explore the effect of including such behavior in models of epidemic dynamics.

Methodology/principal findings: Using both nonlinear dynamical systems and agent-based computation, we model two interacting contagion processes: one of disease and one of fear of the disease. Individuals can "contract" fear through contact with individuals who are infected with the disease (the sick), infected with fear only (the scared), and infected with both fear and disease (the sick and scared). Scared individuals--whether sick or not--may remove themselves from circulation with some probability, which affects the contact dynamic, and thus the disease epidemic proper. If we allow individuals to recover from fear and return to circulation, the coupled dynamics become quite rich, and can include multiple waves of infection. We also study flight as a behavioral response.

Conclusions/significance: In a spatially extended setting, even relatively small levels of fear-inspired flight can have a dramatic impact on spatio-temporal epidemic dynamics. Self-isolation and spatial flight are only two of many possible actions that fear-infected individuals may take. Our main point is that behavioral adaptation of some sort must be considered.

Show MeSH
Related in: MedlinePlus