Estimating the time-dependent effective reproduction number and vaccination rate for COVID-19 in the USA and India

Sarita Bugalia; Jai Prakash Tripathi; Hao Wang; Sarita Bugalia; Jai Prakash Tripathi; Hao Wang

doi:10.3934/mbe.2023216

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 3: 4673-4689. doi: 10.3934/mbe.2023216

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Research article

Estimating the time-dependent effective reproduction number and vaccination rate for COVID-19 in the USA and India

1.
Department of Mathematics, Central University of Rajasthan, Bandar Sindri, Kishangarh-305817, Ajmer, Rajasthan, India
2.
Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB T6G 2G1, Canada

Received: 29 October 2022 Revised: 08 December 2022 Accepted: 19 December 2022 Published: 28 December 2022

The effective reproduction number, $ R_t $, is a vital epidemic parameter utilized to judge whether an epidemic is shrinking, growing, or holding steady. The main goal of this paper is to estimate the combined $ R_t $ and time-dependent vaccination rate for COVID-19 in the USA and India after the vaccination campaign started. Accounting for the impact of vaccination into a discrete-time stochastic augmented SVEIR (Susceptible-Vaccinated-Exposed-Infectious-Recovered) model, we estimate the time-dependent effective reproduction number $ (R_t) $ and vaccination rate $ (\xi_t) $ for COVID-19 by using a low pass filter and the Extended Kalman Filter (EKF) approach for the period February 15, 2021 to August 22, 2022 in India and December 13, 2020 to August 16, 2022 in the USA. The estimated $ R_t $ and $ \xi_t $ show spikes and serrations with the data. Our forecasting scenario represents the situation by December 31, 2022 that the new daily cases and deaths are decreasing for the USA and India. We also noticed that for the current vaccination rate, $ R_t $ would remain greater than one by December 31, 2022. Our results are beneficial for the policymakers to track the status of the effective reproduction number, whether it is greater or less than one. As restrictions in these countries ease, it is still important to maintain safety and preventive measures.
- COVID-19,
- SVEIR model,
- effective reproduction number,
- time-dependent vaccination rate
Citation: Sarita Bugalia, Jai Prakash Tripathi, Hao Wang. Estimating the time-dependent effective reproduction number and vaccination rate for COVID-19 in the USA and India[J]. Mathematical Biosciences and Engineering, 2023, 20(3): 4673-4689. doi: 10.3934/mbe.2023216

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Abstract

The effective reproduction number, $ R_t $, is a vital epidemic parameter utilized to judge whether an epidemic is shrinking, growing, or holding steady. The main goal of this paper is to estimate the combined $ R_t $ and time-dependent vaccination rate for COVID-19 in the USA and India after the vaccination campaign started. Accounting for the impact of vaccination into a discrete-time stochastic augmented SVEIR (Susceptible-Vaccinated-Exposed-Infectious-Recovered) model, we estimate the time-dependent effective reproduction number $ (R_t) $ and vaccination rate $ (\xi_t) $ for COVID-19 by using a low pass filter and the Extended Kalman Filter (EKF) approach for the period February 15, 2021 to August 22, 2022 in India and December 13, 2020 to August 16, 2022 in the USA. The estimated $ R_t $ and $ \xi_t $ show spikes and serrations with the data. Our forecasting scenario represents the situation by December 31, 2022 that the new daily cases and deaths are decreasing for the USA and India. We also noticed that for the current vaccination rate, $ R_t $ would remain greater than one by December 31, 2022. Our results are beneficial for the policymakers to track the status of the effective reproduction number, whether it is greater or less than one. As restrictions in these countries ease, it is still important to maintain safety and preventive measures.

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