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.
Highlights
The purpose of this paper is to quantify the infection of an epidemic in its different phases by providing appropriate estimators of the infection parameter for each of these phases
The epidemic is modeled by a Markovian process of order d 1 with Poissonian transitions, which can be seen as a multitype Bienayme-Galton-Watson (BGW) branching process with d types
This model is suitable for any rare transmissible SEIR disease in a large branching population following a Reed-Frost model for the infection ([11])
Summary
The purpose of this paper is to quantify the infection of an epidemic in its different phases (growth and decay) by providing appropriate estimators of the infection parameter for each of these phases. These two estimators are especially suitable for a long growth phase of the epidemic. This estimator is designed for a long decay phase of the epidemic. We describe the practical interest of each of these estimators, and illustrate on a simulated multi-phase epidemic which one should be chosen on which type of data
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