With the continuous evolution of the coronavirus, the Omicron variant has gradually replaced the Delta variant as the prevalent strain. Their inducing epidemics last longer, have a higher number of asymptomatic cases, and are more serious. In this article, we proposed a nonautonomous time-delayed susceptible-infected-removed (NATD-SIR) model to predict them in different regions of China. We obtained the maximum and its time of current infected persons, the final size, and the end time of COVID-19 epidemics from January 2022 in China. The method of the fifth-order moving average was used to preprocess the time series of the numbers of current infected and removed cases to obtain more accurate parameter estimations. We found that usually the transmission rate $ \beta(t) $ was a piecewise exponential decay function, but due to multiple bounces in Shanghai City, $ \beta(t) $ was approximately a piecewise quadratic function. In most regions, the removed rate $ \gamma(t) $ was approximately equal to a piecewise linear increasing function of (a*t+b)*H(t-k), but in a few areas, $ \gamma(t) $ displayed an exponential increasing trend. For cases where the removed rate cannot be obtained, we proposed a method for setting the removed rate, which has a good approximation. Using the numerical solution, we obtained the prediction results of the epidemics. By analyzing those important indicators of COVID-19, we provided valuable suggestions for epidemic prevention and control and the resumption of work and production.
Citation: Zhiliang Li, Lijun Pei, Guangcai Duan, Shuaiyin Chen. A non-autonomous time-delayed SIR model for COVID-19 epidemics prediction in China during the transmission of Omicron variant[J]. Electronic Research Archive, 2024, 32(3): 2203-2228. doi: 10.3934/era.2024100
With the continuous evolution of the coronavirus, the Omicron variant has gradually replaced the Delta variant as the prevalent strain. Their inducing epidemics last longer, have a higher number of asymptomatic cases, and are more serious. In this article, we proposed a nonautonomous time-delayed susceptible-infected-removed (NATD-SIR) model to predict them in different regions of China. We obtained the maximum and its time of current infected persons, the final size, and the end time of COVID-19 epidemics from January 2022 in China. The method of the fifth-order moving average was used to preprocess the time series of the numbers of current infected and removed cases to obtain more accurate parameter estimations. We found that usually the transmission rate $ \beta(t) $ was a piecewise exponential decay function, but due to multiple bounces in Shanghai City, $ \beta(t) $ was approximately a piecewise quadratic function. In most regions, the removed rate $ \gamma(t) $ was approximately equal to a piecewise linear increasing function of (a*t+b)*H(t-k), but in a few areas, $ \gamma(t) $ displayed an exponential increasing trend. For cases where the removed rate cannot be obtained, we proposed a method for setting the removed rate, which has a good approximation. Using the numerical solution, we obtained the prediction results of the epidemics. By analyzing those important indicators of COVID-19, we provided valuable suggestions for epidemic prevention and control and the resumption of work and production.
| [1] |
S. Y. Ren, W. B. Wang, R. D. Gao, A. M. Zhou, Omicron variant (B. 1.1. 529) of SARS-CoV-2: mutation, infectivity, transmission, and vaccine resistance, World J. Clin. Cases, 10 (2022), 1–11. https://doi.org/10.12998/wjcc.v10.i1.1 doi: 10.12998/wjcc.v10.i1.1
|
| [2] |
L. Lu, B. W. Y. Mok, L. L. Chen, J. M. C. Chan, O. T. Y. Tsang, B. H. S. Lam, et al., Neutralization of severe acute respiratory syndrome coronavirus 2 omicron variant by sera from BNT162b2 or CoronaVac vaccine recipients, Clin. Infect. Dis., 75 (2022), e822–e826. https://doi.org/10.1093/cid/ciab1041 doi: 10.1093/cid/ciab1041
|
| [3] |
H. F. Tseng, B. K. Ackerson, Y. Luo, L. S. Sy, C. A. Talarico, Y. Tian, et al., Effectiveness of mRNA-1273 against SARS-CoV-2 Omicron and Delta variants, Nat. Med., 28 (2022), 1063–1071. https://doi.org/10.1038/s41591-022-01753-y doi: 10.1038/s41591-022-01753-y
|
| [4] |
W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. R. Soc. A, 115 (1927), 700–721. https://doi.org/10.1098/rspa.1927.0118 doi: 10.1098/rspa.1927.0118
|
| [5] |
K. L. Cooke, Stability analysis for a vector disease model, Rocky Mountain J. Math., 9 (1979), 31–42. https://doi.org/10.1216/RMJ-1979-9-1-31 doi: 10.1216/RMJ-1979-9-1-31
|
| [6] |
N. Guglielmi, E. Iacomini, A. Viguerie, Delay differential equations for the spatially resolved simulation of epidemics with specific application to COVID-19, Math. Methods Appl. Sci., 45 (2022), 4752–4771. https://doi.org/10.1002/mma.8068 doi: 10.1002/mma.8068
|
| [7] |
L. Dell'Anna, Solvable delay model for epidemic spreading: the case of COVID-19 in Italy, Sci. Rep., 10 (2020), 15763. https://doi.org/10.1038/s41598-020-72529-y doi: 10.1038/s41598-020-72529-y
|
| [8] |
I. Rahimi, F. Chen, A. H. Gandomi, A review on COVID-19 forecasting models, Neural Comput. Appl., 35 (2023), 23671–23681. https://doi.org/10.1007/s00521-020-05626-8 doi: 10.1007/s00521-020-05626-8
|
| [9] |
Z. Lv, J. Zeng, Y. Ding, X. Liu, Stability analysis of time-delayed SAIR model for duration of vaccine in the context of temporary immunity for COVID-19 situation, Electron. Res. Arch., 31 (2023), 1004–1030. https://doi.org/10.3934/era.2023050 doi: 10.3934/era.2023050
|
| [10] |
Y. Mohamadou, A. Halidou, P. T. Kapen, A review of mathematical modeling, artificial intelligence and datasets used in the study, prediction and management of COVID-19, Appl. Intell., 50 (2020), 3913–3925. https://doi.org/10.1007/s10489-020-01770-9 doi: 10.1007/s10489-020-01770-9
|
| [11] |
T. T. Marinov, R. S. Marinova, Dynamics of COVID-19 using inverse problem for coefficient identification in SIR epidemic models, Chaos, Solitons Fractals:X, 5 (2020), 100041. https://doi.org/10.1016/j.csfx.2020.100041 doi: 10.1016/j.csfx.2020.100041
|
| [12] |
M. Karim, A. Kouidere, M. Rachik, K. Shah, T. Abdeljawad, Inverse problem to elaborate and control the spread of COVID-19: a case study from Morocco, AIMS Math., 8 (2023), 23500–23518. https://doi.org/10.3934/math.20231194 doi: 10.3934/math.20231194
|
| [13] |
A. Comunian, R. Gaburro, M. Giudici, Inversion of a SIR-based model: a critical analysis about the application to COVID-19 epidemic, Physica D, 413 (2020), 132674. https://doi.org/10.1016/j.physd.2020.132674 doi: 10.1016/j.physd.2020.132674
|
| [14] |
I. Cooper, A. Mondal, C. G. Antonopoulos, A SIR model assumption for the spread of COVID-19 in different communities, Chaos, Solitons Fractals, 139 (2020), 110057. https://doi.org/10.1016/j.chaos.2020.110057 doi: 10.1016/j.chaos.2020.110057
|
| [15] |
F. S. Lobato, G. M. Platt, G. B. Libotte, A. J. S. NETO, Formulation and solution of an inverse reliability problem to simulate the dynamic behavior of COVID-19 pandemic, Trends Comput. Appl. Math., 22 (2021), 91–107. https://doi.org/10.5540/tcam.2021.022.01.00091 doi: 10.5540/tcam.2021.022.01.00091
|
| [16] |
C. C. Pacheco, C. R. de Lacerda, Function estimation and regularization in the SIRD model applied to the COVID-19 pandemics, Inverse Probl. Sci. Eng., 29 (2021), 1613–1628. https://doi.org/10.1080/17415977.2021.1872563 doi: 10.1080/17415977.2021.1872563
|
| [17] |
F. S. Lobato, G. B. Libotte, G. M. Platt, Identification of an epidemiological model to simulate the COVID-19 epidemic using robust multiobjective optimization and stochastic fractal search, Comput. Math. Methods Med., 2020 (2020), 9214159. https://doi.org/10.1155/2020/9214159 doi: 10.1155/2020/9214159
|
| [18] |
L. J. Pei, Y. H. Hu, Long-term prediction of the sporadic COVID-19 epidemics induced by $\delta$-virus in China based on a novel non-autonomous delayed SIR model, Eur. Phys. J. Spec. Top., 231 (2022), 3649–3662. https://doi.org/10.1140/epjs/s11734-022-00622-6 doi: 10.1140/epjs/s11734-022-00622-6
|
| [19] |
L. J. Pei, M. Y. Zhang, Long-term predictions of current confirmed and dead cases of COVID-19 in China by the non-autonomous delayed epidemic models, Cognit. Neurodyn., 16 (2022), 229–238. https://doi.org/10.1007/s11571-021-09701-1 doi: 10.1007/s11571-021-09701-1
|
| [20] |
L. J. Pei, M. Y. Zhang, Long-term predictions of COVID-19 in some countries by the SIRD model, Complexity, 2021 (2021), 6692678. https://doi.org/10.1155/2021/6692678 doi: 10.1155/2021/6692678
|
| [21] |
H. Jahanshahi, J. M. Munoz-Pacheco, S. Bekiros, N. D. Alotaibi, A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19, Chaos, Solitons Fractals, 143 (2021), 110632. https://doi.org/10.1016/j.chaos.2020.110632 doi: 10.1016/j.chaos.2020.110632
|
| [22] |
C. Anastassopoulou, L. Russo, A. Tsakris, C. Siettos, Data-based analysis, modelling and forecasting of the COVID-19 outbreak, PLoS One, 15 (2020), e0230405. https://doi.org/10.1371/journal.pone.0230405 doi: 10.1371/journal.pone.0230405
|
| [23] |
S. He, Y. X. Peng, K. H. Sun, SEIR modeling of the COVID-19 and its dynamics, Nonlinear Dyn., 101 (2020), 1667–1680. https://doi.org/10.1007/s11071-020-05743-y doi: 10.1007/s11071-020-05743-y
|
| [24] |
Z. Yang, Z. Q. Zeng, K. Wang, S. S. Wong, W. Liang, M. Zanin, et al., Modified SEIR and AI prediction of the epidemics trend of COVID-19 in China under public health interventions, J. Thoracic Dis., 12 (2020), 165–174. https://doi.org/10.21037/jtd.2020.02.64 doi: 10.21037/jtd.2020.02.64
|
| [25] |
S. Annas, M. I. Pratama, M. Rifandi, W. Sanusi, S. Side, Stability analysis and numerical simulation of SEIR model for pandemic COVID-19 spread in Indonesia, Chaos, Solitons Fractals, 139 (2020), 110072. https://doi.org/10.1016/j.chaos.2020.110072 doi: 10.1016/j.chaos.2020.110072
|
| [26] |
R. Engbert, M. M. Rabe, R. Kliegl, S. Reich, Sequential data assimilation of the stochastic SEIR epidemic model for regional COVID-19 dynamics, Bull. Math. Biol., 83 (2021), 1. https://doi.org/10.1007/s11538-020-00834-8 doi: 10.1007/s11538-020-00834-8
|
| [27] |
S. Margenov, N. Popivanov, I. Ugrinova, S. Harizanov, T. Hristov, Mathematical and computer modeling of COVID-19 transmission dynamics in Bulgaria by time-depended inverse SEIR model, AIP Conf. Proc., 2333 (2021), 090024. https://doi.org/10.1063/5.0041868 doi: 10.1063/5.0041868
|
| [28] |
E. Li, Q. Zhang, Global dynamics of an endemic disease model with vaccination: analysis of the asymptomatic and symptomatic groups in complex networks, Electron. Res. Arch., 31 (2023), 6481–6504. https://doi.org/10.3934/era.2023328 doi: 10.3934/era.2023328
|
| [29] |
G. Fan, N. Li, Application and analysis of a model with environmental transmission in a periodic environment, Electron. Res. Arch., 31 (2023), 5815–5844. https://doi.org/10.3934/era.2023296 doi: 10.3934/era.2023296
|
| [30] |
W. P. Jia, K. Han, Y. Song, W. Z. Cao, S. S. Wang, S. S. Yang, et al., Extended SIR prediction of the epidemics trend of COVID-19 in Italy and compared with Hunan, China, Front. Med., 7 (2020), 169. https://doi.org/10.3389/fmed.2020.00169 doi: 10.3389/fmed.2020.00169
|
| [31] |
M. Turkyilmazoglu, An extended epidemic model with vaccination: weak-immune SIRVI, Physica A, 598 (2022), 127429. https://doi.org/10.1016/j.physa.2022.127429 doi: 10.1016/j.physa.2022.127429
|
| [32] |
C. Iwendi, A. K. Bashir, A. Peshkar, R. Sujatha, J. M. Chatterjee, S. Pasupuleti, et al., COVID-19 patient health prediction using boosted random forest algorithm, Front. Public Health, 8 (2020), 357. https://doi.org/10.3389/fpubh.2020.00357 doi: 10.3389/fpubh.2020.00357
|
| [33] |
G. Pinter, I. Felde, A. Mosavi, P. Ghamisi, R. Gloaguen, COVID-19 pandemic prediction for hungary; a hybrid machinelearning approach, Mathematics, 8 (2020), 890. https://doi.org/10.3390/math8060890 doi: 10.3390/math8060890
|
| [34] |
M. Zivkovic, N. Bacanin, K. Venkatachalam, A. Nayyar, A. Djordjevic, I. Strumberger, et al., COVID-19 cases prediction by using hybrid machine learning and beetle antennae search approach, Sustainable Cities Soc., 66 (2021), 102669. https://doi.org/10.1016/j.scs.2020.102669 doi: 10.1016/j.scs.2020.102669
|
| [35] |
A. S. Kwekha-Rashid, H. N. Abduljabbar, B. Alhayani, Coronavirus disease (COVID-19) cases analysis using machine learning applications, Appl. Nanosci., 13 (2023), 2013–2015. https://doi.org/10.1007/s13204-021-01868-7 doi: 10.1007/s13204-021-01868-7
|
| [36] |
F. Rustam, A. A. Reshi, A. Mehmood, S. Ullah, B. W. On, W. Aslam, et al., COVID-19 future forecasting using supervised machine learning models, IEEE Access, 8 (2020), 101489–101499. https://doi.org/10.1109/ACCESS.2020.2997311 doi: 10.1109/ACCESS.2020.2997311
|
| [37] |
R. Salgotra, M. Gandomi, A. H. Gandomi, Time series analysis and forecast of the COVID-19 pandemic in India using genetic programming, Chaos, Solitons Fractals, 138 (2020), 109945. https://doi.org/10.1016/j.chaos.2020.109945 doi: 10.1016/j.chaos.2020.109945
|
| [38] |
H. Abbasimehr, R. Paki, Prediction of COVID-19 confirmed cases combining deep learning methods and Bayesian optimization, Chaos, Solitons Fractals, 142 (2021), 110511. https://doi.org/10.1016/j.chaos.2020.110511 doi: 10.1016/j.chaos.2020.110511
|
| [39] |
M. Turkyilmazoglu, A highly accurate peak time formula of epidemic outbreak from the SIR model, Chin. J. Phys., 84 (2023), 39–50. https://doi.org/10.1016/j.cjph.2023.05.009 doi: 10.1016/j.cjph.2023.05.009
|
| [40] |
M. Turkyilmazoglu, Explicit formulae for the peak time of an epidemic from the SIR model, Physica D, 422 (2021), 132902. https://doi.org/10.1016/j.physd.2021.132902 doi: 10.1016/j.physd.2021.132902
|
| [41] |
Z. Guo, S. Zhao, C. K. P. Mok, R. T. Y. So, C. H. K. Yam, T. Y. Chow, et al., Comparing the incubation period, serial interval, and infectiousness profile between SARS-CoV-2 Omicron and Delta variants, J. Med. Virol., 95 (2023), e28648. https://doi.org/10.1002/jmv.28648 doi: 10.1002/jmv.28648
|
Figures(5) / Tables(7)
Zhiliang Li, Lijun Pei, Guangcai Duan, Shuaiyin Chen. A non-autonomous time-delayed SIR model for COVID-19 epidemics prediction in China during the transmission of Omicron variant[J]. Electronic Research Archive, 2024, 32(3): 2203-2228. doi: 10.3934/era.2024100
DownLoad: