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 of individuals 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 include multiple waves of infection, such as occurred in the 1918 flu pandemic. We also study flight as a behavioral response. In a spatially extended setting, even relatively small levels of fear-inspired flight can have a dramatic impact on spatio-temporal epidemic dynamics.
Motivation In classical mathematical epidemiology, individuals do not adapt their contact behavior during epidemics. They do not endogenously engage, for example, in social distancing (protective sequestration) based on disease prevalence. Rather, they simply continue mixing (often uniformly) as if no epidemic were under way. This may be a reasonable assumption for non-lethal infections such as the common cold, but for lethal diseases such as AIDS, it is known to fail; and for other lethal disease threats, like pandemic influenza or bioterrror smallpox, it seems likely to. People may be expected to adapt their contact patterns, and this will feed back to alter epidemic dynamics.
Homo EconomSickus
Economists have begun to address this issue, introducing the notion of prevalence elastic behavior into epidemic models. For example, as AIDS prevalence grows in a community, people may reduce their number of sexual partners. On prevalence elastic partner selection in AIDS, for example, see Kremer (1996). Predictably, economic epidemiology, as this subfield is called, posits optimizing behavior on the part of individuals. In effect, it models how canonically rational individuals would behave given some level of disease prevalence. They behave as homo economicus would behave given the associated health risks and costs of protection (e.g., vaccine-seeking). A term used for the resulting dynamics is rational epidemics. This literature includes elegant mathematical work, and captures—in the notion of prevalence elasticity—a clearly important phenomenon.