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A stochastic SIR model with contact-tracing: large population limits and statistical inference
Stéphan Clémençon1, Viet Chi Tran, Hector de Arazoza
1Laboratoire TCI UMR CNRS/Institut Telecom No. 5141, Paris Cedex 13, France. stephan.clemencon@telecom-paristech.fr
Journal of Biological Dynamics
|August 11, 2012
Summary
This study introduces a stochastic epidemic model incorporating contact-tracing to control infectious disease spread. The model, validated with HIV data from Cuba, shows contact-tracing significantly aids epidemic management.
Area of Science:
- Epidemiology
- Mathematical Biology
- Stochastic Processes
Background:
- Infectious disease spread is a major public health concern.
- Contact-tracing is a key strategy for disease control.
- Stochastic modeling provides a framework for understanding disease dynamics.
Purpose of the Study:
- To present and analyze a novel stochastic epidemic model.
- To incorporate the effect of contact-tracing into epidemic modeling.
- To investigate the model's convergence to a deterministic solution and its application to real-world data.
Main Methods:
- Development of a stochastic Markov process model for disease spread.
- Inclusion of a contact-tracing component valued in a space of point measures.
- Analysis of the model's convergence to a partial differential equation (PDE) system for large population sizes.
- Application to HIV epidemic data from Cuba.
Main Results:
- The proposed stochastic model effectively captures epidemic dynamics with contact-tracing.
- The model converges to a deterministic PDE system under specific rate scalings.
- Preliminary statistical results for inference methods are presented.
- Numerical applications demonstrate the model's utility with HIV data.
Conclusions:
- Contact-tracing is a valuable addition to epidemic control strategies.
- The stochastic model provides a robust framework for analyzing epidemic data.
- The model's large-population approximation is a key tool for statistical inference.
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