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Estimating the infection rate of a SIR epidemic model via differential elimination

Rosane Ushirobira 1 Denis Efimov 1 Pierre-Alexandre Bliman 2
1 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
2 MAMBA - Modelling and Analysis for Medical and Biological Applications
Inria de Paris, LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
Abstract : A SIR epidemic model is one of the most well-known mathematical models that helps to understand the dissemination of an infectious illness. It is a three-compartment model composed by individuals that are susceptible, infective and recovered with respect to the disease. In this work, the infection rate is estimated for a particular SIR epidemic model by using as the output measurement the incidence rate, which is a nonlinear function of the state variables. The aim is then to eliminate variables in the given system for which there are no measurements, such as the proportion of each type of individuals (susceptible, infective and recovered). The method applied here is based on differential elimination concepts from differential algebra, more precisely the Rosenfeld-Gröbner algorithm is employed. Once the input-output (IO) equation is determined, the derivatives of the signal are estimated by a homogeneous finite-time differentiator and a gradient descent method can be applied to solve the IO equation for the infection rate.
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https://hal.inria.fr/hal-02418553
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Submitted on : Wednesday, December 18, 2019 - 10:48:01 PM
Last modification on : Friday, April 10, 2020 - 5:24:30 PM
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Rosane Ushirobira, Denis Efimov, Pierre-Alexandre Bliman. Estimating the infection rate of a SIR epidemic model via differential elimination. ECC 2019 - 18th European Control Conference, Jun 2019, Naples, Italy. ⟨hal-02418553⟩

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