Electronic Journal of Statistics

Estimation of the infection parameter of an epidemic modeled by a branching process

Sophie Pénisson

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Abstract

The aim of this paper is to build estimators of the infection parameter in the different phases of an epidemic (growth and decay phases). The epidemic is modeled by a Markovian process of order $d\geqslant1$, and can be written as a multitype branching process. We propose three estimators suitable for the different classes of criticality of the process, and consequently for different phases of the epidemic. We prove their consistency and asymptotic normality when the number of ancestors (resp. number of generations) tends to infinity.

Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 2158-2187.

Dates
First available in Project Euclid: 29 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1414588190

Digital Object Identifier
doi:10.1214/14-EJS948

Mathematical Reviews number (MathSciNet)
MR3273622

Zentralblatt MATH identifier
1302.62228

Subjects
Primary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J85: Applications of branching processes [See also 92Dxx] 62P10: Applications to biology and medical sciences
Secondary: 62M05: Markov processes: estimation 62F12: Asymptotic properties of estimators 62J02: General nonlinear regression

Keywords
Multitype branching process conditioned branching process CLSE consistency and asymptotic normality epidemiology SEI

Citation

Pénisson, Sophie. Estimation of the infection parameter of an epidemic modeled by a branching process. Electron. J. Statist. 8 (2014), no. 2, 2158--2187. doi:10.1214/14-EJS948. https://projecteuclid.org/euclid.ejs/1414588190


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References

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