Abstract
BackgroundIn 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 FindingsUsing 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/SignificanceIn 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.
Highlights
In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics
We explore the impact of differing levels of flight on the epidemic dynamics
The results from this agent model highlight the importance of flight as a topic for research—even a small amount of flight can have a dramatic impact on epidemic dynamics
Summary
Motivation In classical mathematical epidemiology–the tradition of ordinary differential equations with perfect mixing (mass action kinetics) beginning with the 1927 Kermack-McKendrick model– individuals do not adapt their contact behavior during epidemics [1,2,3] They do not endogenously engage, for example, in social distancing (protective sequestration) based on disease prevalence. In the model introduced here, we expand the behavioral response repertoire of agents infected with fear to include both flight and protective self-isolation. (Bear in mind that the model does not require that the event sparking the fear epidemic be a disease, contagious or otherwise It could be a radiological, or seismic event, for example.) Individuals contract disease only through contact with the disease-infected (the sick). We specify below the parameters controlling the rate at which individuals self-isolate due to fear and recover from fear and return to circulation: lF: Rate of removal to self-isolation of those infected with fear only lP: Rate of removal from infection with pathogen lPF: Rate of removal to self-isolation of those infected with fear and pathogen
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