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Large-sample analysis for a stochastic epidemic model and its parameter estimators
1Instituto de Matemáticas, Universidad Católica de Valparaíso, Chile.
Journal of Mathematical Biology
|January 1, 1996
Summary
This study models epidemic spread using stochastic methods, providing approximations for epidemic size and analyzing contact rate estimators. These findings offer insights into disease dynamics and public health interventions.
Area of Science:
- Epidemiology
- Stochastic Processes
- Mathematical Biology
Background:
- Understanding epidemic dynamics is crucial for public health.
- Stochastic models offer a framework for analyzing disease spread in populations.
- Previous models often lacked detailed analysis of epidemic size distribution.
Purpose of the Study:
- To develop and analyze a simple stochastic model for epidemic spread.
- To approximate the probability distribution of epidemic size.
- To investigate asymptotic properties of epidemic size and related variables.
Main Methods:
- Utilizing a stochastic model for a homogeneously mixing population.
- Applying approximate methods for calculating epidemic size distribution.
- Employing functional central limit theorem and large deviation principles.
Main Results:
- A global approximation for epidemic size was obtained.
- Asymptotic properties of epidemic size were analyzed.
- Two sequences of contact rate estimators were derived and their behavior analyzed.
Conclusions:
- The developed methods provide accurate approximations for epidemic size.
- The study offers insights into the asymptotic behavior of epidemic processes.
- The derived estimators are valuable for analyzing disease transmission rates.