Identification of transmission rates and reproduction number in a SARS-CoV-2 epidemic model

Gabriela Marinoschi

doi:10.3934/dcdss.2022128

Article Contents

2022, Volume 15, Issue 12: 3735-3744. Doi: 10.3934/dcdss.2022128

This issue Previous Article Global existence for equivalent nonlinear special scale invariant damped wave equations Next Article Existence of minimizers for a quasilinear elliptic system of gradient type

Identification of transmission rates and reproduction number in a SARS-CoV-2 epidemic model

Gabriela Marinoschi

"Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics, and Applied Mathematics of the Romanian Academy, Calea 13 Septembrie 13, Bucharest, Romania

Received: August 2021

Early access: June 2022

Published: December 2022

This work was supported by a grant of the Ministry of Research, Innovation and Digitization, CNCS - UEFISCDI, project number PN-III-P4-PCE-2021-0006, within PNCDI III

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Abstract

We consider a compartment mathematical model for a SARS-CoV-2 epidemic involving five classes considered to be essential to depict the feature of the epidemic. A first goal is to approach by an optimal control technique the identification of two essential transmission rates in the model, that is the average number of individuals infected in unit time by an infected symptomatic and by an asymptomatic, respectively. These are provided by the first-order conditions of optimality corresponding to the minimization problem introduced for formulating the identification objective. The discussion of the asymptotic stability of the system done for the case when life immunity is gained reveals an asymptotic extinction of the disease, with a well determined reproduction number.

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Mathematics Subject Classification: Primary: 49N45; Secondary: 49Jxx, 49K15, 92D30.

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