# American Institute of Mathematical Sciences

doi: 10.3934/dcdss.2022128
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## Identification of transmission rates and reproduction number in a SARS-CoV-2 epidemic model

 "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

Fund Project: 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

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.

Citation: Gabriela Marinoschi. Identification of transmission rates and reproduction number in a SARS-CoV-2 epidemic model. Discrete and Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2022128
##### References:
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show all references

##### References:
 [1] C. Anastassopoulou, L. Russo, A. Tsakris and C. Siettos, Data-based analysis, modelling and forecasting of the COVID-19 outbreak, PLoS One, 15 (2020), e0230405.  doi: 10.1371/journal.pone.0230405. [2] E. Armstrong, M. Runge and J. Gerardin, Identifying the measurements required to estimate rates of COVID-19 transmission, infection, and detection, using variational data assimilation, Infectious Disease Modelling, 6 (2021), 133-147.  doi: 10.1016/j.idm.2020.10.010. [3] F. Casella, Can the COVID-19 epidemic be managed on the basis of daily data?, IEEE Control Syst. Lett., 5 (2021), 1079–1084. arXiv: 2003.06967. doi: 10.1109/LCSYS.2020.3009912. [4] M. Cascella, M. Rajnik, A. Cuomo, S. C. Dulebohn and R. Di Napoli, Features, Evaluation and Treatment of Coronavirus (COVID-19), StatPearls Publishing, 2020. [5] G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, A. Di Matteo and M. Colaneri, Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy, Nat Med, 26 (2020), 855-860.  doi: 10.1038/s41591-020-0883-7. [6] M. Iannelli and A. Pugliese, An Introduction to Mathematical Population Dynamics, Springer, 2014. doi: 10.1007/978-3-319-03026-5. [7] Q. Lin, S. Zhao, D. Gao, Y. Lou, S. Yang, S. S. Musa, M. H. Wang, Y. Cai, W. Wang, L. Yang and D. He, A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action, Int. J. Inf. Dis., 93 (2020), 211-216. [8] N. Linton, T. Kobayashi, Y. Yang, K. Hayashi, A. R. Akhmetzhanov, S.-M. Jung, B. Yuan, R. Kinoshita and H. Nishiura, Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: A statistical analysis of publicly available case data, J. Clin. Med., 9 (2020), 538.  doi: 10.3390/jcm9020538. [9] G. Marinoschi, Parameter estimation of an epidemic model with state constraints, Appl. Math. Optimiz., 84 (2021), S1903-S1923.  doi: 10.1007/s00245-021-09815-2. [10] F. Ndaïrou, I. Area, J. J. Nieto and D. F. M. Torres, Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan, Chaos, Solitons and Fractals, 135 (2020), 109846, 6 pp. doi: 10.1016/j.chaos.2020.109846. [11] A. Pugliese and S. Sottile, Inferring the COVID-19 infection curve in Italy, preprint, 2020, arXiv: 2004.09404. [12] P. van den Driessche, Reproduction numbers of infectious disease models, Infect Dis Model, 2 (2017), 288-303.  doi: 10.1016/j.idm.2017.06.002. [13] C. Yang and J. Wang, Modeling the transmission of COVID-19 in the USA case study, Infectious Disease Modelling, 6 (2021), 195-211.
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