Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Modeling of contact tracing in epidemic populations structured by disease age

Pages: 1685 - 1713, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1685

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Xi Huo - Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States (email)

Abstract: We consider an age-structured epidemic model with two basic public health interventions: (i) identifying and isolating symptomatic cases, and (ii) tracing and quarantine of the contacts of identified infectives. The dynamics of the infected population are modeled by a nonlinear infection-age-dependent partial differential equation, which is coupled with an ordinary differential equation that describes the dynamics of the susceptible population. Theoretical results about global existence and uniqueness of positive solutions are proved. We also present two practical applications of our model: (1) we assess public health guidelines about emergency preparedness and response in the event of a smallpox bioterrorist attack; (2) we simulate the 2003 SARS outbreak in Taiwan and estimate the number of cases avoided by contact tracing. Our model can be applied as a rational basis for decision makers to guide interventions and deploy public health resources in future epidemics.

Keywords:  Age since infection, epidemic disease, contact tracing, quarantine, SARS, smallpox.
Mathematics Subject Classification:  Primary: 92D30; Secondary: 35Q92.

Received: July 2014;      Revised: October 2014;      Available Online: June 2015.