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.
Highlights
Our aim is to develop a model to assess the effectiveness of two public health interventions in controlling epidemic outbreaks: (i) identifying and isolating symptomatic cases, and (ii) tracing of their contacts, followed by isolation, quarantine, or vaccination
Ordinary differential equation models were used in modeling SARS, and in particular to investigate the impact of quarantining asymptomatic infectives (Hethcote et al 2002; Wang and Ruan 2003; Hsieh et al 2004; Gumel et al 2004; Nishiura et al 2004; Fraser et al 2004; Day et al 2006; Hsu and Hsieh 2006; Arino et al 2006; Feng et al 2007, 2009, 2011)
We introduce a general epidemic model that takes age since infection into consideration, to model interventions such as contact tracing, quarantine, and vaccination
Summary
Our aim is to develop a model to assess the effectiveness of two public health interventions in controlling epidemic outbreaks: (i) identifying and isolating symptomatic cases, and (ii) tracing of their contacts, followed by isolation, quarantine, or vaccination. Our model is applicable to general epidemics for which quarantine or vaccination are available as control measures. Isolation of symptomatic cases is important in controlling infectious diseases, and important may be the vaccination and quarantine of traced contacts of known infectives. We use a partial differential equation model with a variable of disease age (or age since infection), with nonlinear rates of contact tracing infectives and quarantining susceptibles dependent on the rate of identifying symptomatic cases
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