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Stochastic epidemic models featuring contact tracing with delays.
Frank G Ball1, Edward S Knock1, Philip D O'Neill1
1School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, UK.
Mathematical Biosciences
|June 4, 2015
Summary
This study models epidemics using a susceptible-exposed-infective-removed (SEIR) framework with contact tracing. A high contact rate can lead to an infinite reproduction number, impacting epidemic spread and control strategies.
Area of Science:
- Epidemiology
- Mathematical Biology
- Stochastic Processes
Background:
- Understanding epidemic dynamics is crucial for public health interventions.
- Contact tracing is a key strategy to control infectious disease spread.
- Stochastic models provide a framework for analyzing disease transmission variability.
Purpose of the Study:
- To develop and analyze a stochastic SEIR epidemic model incorporating a contact tracing scheme.
- To investigate the impact of contact tracing delays and infectious period distributions on epidemic spread.
- To derive and analyze a type-reproduction number within this model.
Main Methods:
- Development of a stochastic SEIR model with contact tracing.
- Approximation of the epidemic dynamics using a modified birth-death process.
- Derivation of a type-reproduction number based on unnamed individuals.
- Analysis of explicit results for constant and exponentially distributed infectious periods.
Main Results:
- The derived type-reproduction number can become infinite with a sufficiently large contact rate.
- Explicit formulas for epidemic extinction probability were obtained under constant infectious periods.
- Numerical simulations indicate that latent period and delay distributions affect epidemic spread.
- The assumption of delay distribution (same vs. independent) has minimal impact on epidemic dynamics.
Conclusions:
- Contact tracing can significantly alter epidemic trajectories.
- The model highlights the critical role of contact rates in disease transmission.
- Further research can explore more complex contact tracing mechanisms and delay distributions.
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