COVID-19 pandemic control using restrictions and vaccination

Vinicius Piccirillo; Vinicius Piccirillo

doi:10.3934/mbe.2022062

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 2: 1355-1372. doi: 10.3934/mbe.2022062

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Research article

COVID-19 pandemic control using restrictions and vaccination

Vinicius Piccirillo ^,

Department of Mathematics, Federal Technological University of Parana UTFPR, 84016 - 210, Ponta Grossa – PR, Brazil

Received: 28 September 2021 Accepted: 24 November 2021 Published: 03 December 2021

This work deals with the impact of the vaccination in combination with a restriction parameter that represents non-pharmaceutical interventions measures applied to the compartmental SEIR model in order to control the COVID-19 epidemic. This restriction parameter is used as a control parameter, and the univariate autoregressive integrated moving average (ARIMA) is used to forecast the time series of vaccination of all individuals of a specific country. Having in hand the time series of the population fully vaccinated (real data + forecast), the Levenberg–Marquardt algorithm is used to fit an analytic function that models this evolution over time. Here, it is used two time series of real data that refer to a slow vaccination obtained from India and Brazil, and two faster vaccination as observed in Israel and the United States of America. Together with vaccination, two different control approaches are presented in this paper, which enable reduces the infected people successfully: namely, the feedback and nonfeedback control methods. Numerical results predict that vaccination can reduce the peaks of infections and the duration of the pandemic, however, a better result is achieved when the vaccination is combined with any restrictions or prevention policy.
- COVID-19,
- Vaccination,
- Mathematical model,
- Control of infection spread
Citation: Vinicius Piccirillo. COVID-19 pandemic control using restrictions and vaccination[J]. Mathematical Biosciences and Engineering, 2022, 19(2): 1355-1372. doi: 10.3934/mbe.2022062

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Abstract

This work deals with the impact of the vaccination in combination with a restriction parameter that represents non-pharmaceutical interventions measures applied to the compartmental SEIR model in order to control the COVID-19 epidemic. This restriction parameter is used as a control parameter, and the univariate autoregressive integrated moving average (ARIMA) is used to forecast the time series of vaccination of all individuals of a specific country. Having in hand the time series of the population fully vaccinated (real data + forecast), the Levenberg–Marquardt algorithm is used to fit an analytic function that models this evolution over time. Here, it is used two time series of real data that refer to a slow vaccination obtained from India and Brazil, and two faster vaccination as observed in Israel and the United States of America. Together with vaccination, two different control approaches are presented in this paper, which enable reduces the infected people successfully: namely, the feedback and nonfeedback control methods. Numerical results predict that vaccination can reduce the peaks of infections and the duration of the pandemic, however, a better result is achieved when the vaccination is combined with any restrictions or prevention policy.

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