Complex dynamics induced by delayed adaptive behavior during epidemics

Ronan F. Arthur; James H. Jones; Matthew H. Bonds; Marcus W. Feldman

Interactions between behavior-mediated transmission and the prevalence of disease depend on the nature and timing of an outbreak of infectious disease. Given enough time for response, behavior is prevalence-elastic. If the behavior in question is slow-changing, it may effectively be regarded as a parameter rather than a variable in a fast-acting outbreak [9] , although it may still be important to the long-term interaction between economics, the environment, and disease [24] . Continuous-time modeling of epidemics and adaptive behavior generally assumes perfect instantaneous information and immediate response and does not allow for delay of information or reactions. However, in reality, information about the state of an epidemic can take time to collect and distribute, and the reaction to this information may also be delayed. For example, if behavior responds to mortality rates, there will inevitably be a lag with an average duration of of the incubation period plus the life expectancy upon becoming infected. In a tightly interdependent system, reacting to outdated information can result in an irrational response.