Modeling of contact tracing in epidemic populations structured by disease age

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-agedependent 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.2010 Mathematics Subject Classification. Primary: 92D30; Secondary: 35Q92.

A model for an epidemic with contact tracing and cluster isolation, and a detection paradox

“…This aspect will be useful in the forthcoming Section 5.1. In this area, we further refer to [7] for a different model for contact tracing in an epidemic in terms of a disease age-structured population.…”

A model for an epidemic with contact tracing and cluster isolation, and a detection paradox

“…This aspect will be useful in the forthcoming Section 5.1. In this area, we further refer to [5] for a different model for contact tracing in an epidemic in terms of a disease age structured population.…”

“…Predicting and controlling the evolution of epidemics has motivated mathematical contributions for a long time and generated a huge literature; let us merely point at the lecture notes [4] and references therein. Models involving contact tracing and isolation, which aims at reducing the transmissibility of infections, have raised a significant interest; see notably among others [1,2,3,5,10,11,12,14]. We present below a toy model in this framework, which is solvable in the sense that many quantities of interest can be computed explicitly.…”

A Model of the 2014 Ebola Epidemic in West Africa with Contact Tracing

“…It is possible to generalize the model further by tracking the disease stage of all infected individuals, particularly contact traced individuals. Such a model is best treated with an age of infection variable, which allows tracking of the incubation and infectious disease stages [6]. In future work we will develop these models, with age of infection as a continuum independent variable.…”