A Theoretical Model of Public Response to the Homeland Security Advisory System

Abstract

Using a differential equation modeling approach, this paper explores the issue of public response to, and confidence in, anti-threat warnings. The effects of anti-threat warnings and their associated public confidence levels are modeled as a group of nonlinear differential equations. The analytical solutions of these nonlinear differential equations are derived to show how warning frequency and the duration of a warning affect public confidence, and how the effects of anti-threat warnings are constrained by the degree of public concern as the threat level changes. Phase plane analysis suggests that the number of warnings for a particular type of threat has a threshold level. Below this threshold, increasing the number of reliable warnings can improve the credibility and effectiveness of the warning system. However, once the number of warnings exceeds the threshold, the greater the number of warnings issued the less the public responds and the lower public confidence becomes. The resulting graphic representation is an easy-to-understand method for authorities to use to issue advisory warnings while maintaining the public's confidence in the system.