A SEIARQ model combine with Logistic to predict COVID-19 within small-world networks

Qinghua Liu; Siyu Yuan; Xinsheng Wang; Qinghua Liu; Siyu Yuan; Xinsheng Wang

doi:10.3934/mbe.2023187

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 4006-4017. doi: 10.3934/mbe.2023187

Previous Article Next Article

Research article Special Issues

A SEIARQ model combine with Logistic to predict COVID-19 within small-world networks

School of Information Science and Engineering, Harbin Institute of Technology at Weihai, Weihai 264200, China

Received: 26 September 2022 Revised: 13 November 2022 Accepted: 06 December 2022 Published: 16 December 2022

Since the COVID-19 epidemic, mathematical and simulation models have been extensively utilized to forecast the virus's progress. In order to more accurately describe the actual circumstance surrounding the asymptomatic transmission of COVID-19 in urban areas, this research proposes a model called Susceptible-Exposure-Infected-Asymptomatic-Recovered-Quarantine in a small-world network. In addition, we coupled the epidemic model with the Logistic growth model to simplify the process of setting model parameters. The model was assessed through experiments and comparisons. Simulation results were analyzed to explore the main factors affecting the spread of the epidemic, and statistical analysis that was applied to assess the model's accuracy. The results are consistent well with epidemic data from Shanghai, China in 2022. The model can not only replicate the real virus transmission data, but also anticipate the development trend of the epidemic based on available data, so that health policy-makers can better understand the spread of the epidemic.
- SEAIRQ epidemic model,
- small-world networks,
- Logistic growth model,
- COVID-19,
- prediction
Citation: Qinghua Liu, Siyu Yuan, Xinsheng Wang. A SEIARQ model combine with Logistic to predict COVID-19 within small-world networks[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 4006-4017. doi: 10.3934/mbe.2023187

Related Papers:

Abstract

Since the COVID-19 epidemic, mathematical and simulation models have been extensively utilized to forecast the virus's progress. In order to more accurately describe the actual circumstance surrounding the asymptomatic transmission of COVID-19 in urban areas, this research proposes a model called Susceptible-Exposure-Infected-Asymptomatic-Recovered-Quarantine in a small-world network. In addition, we coupled the epidemic model with the Logistic growth model to simplify the process of setting model parameters. The model was assessed through experiments and comparisons. Simulation results were analyzed to explore the main factors affecting the spread of the epidemic, and statistical analysis that was applied to assess the model's accuracy. The results are consistent well with epidemic data from Shanghai, China in 2022. The model can not only replicate the real virus transmission data, but also anticipate the development trend of the epidemic based on available data, so that health policy-makers can better understand the spread of the epidemic.

References

[1]	M. EI-Doma, Analysis of an age-dependent SI epidemic model with disease-induced mortality and proportionate mixing assumption: The case of vertically transmitted diseases, J. Appl. Math., 2004 (2004), 235–254. https://doi.org/10.1155/S1110757X0430118X doi: 10.1155/S1110757X0430118X
[2]	W. O. Kermack, A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc R. Soc. Lond. B Biol. Sci., 115 (1927), 700–721. https://doi.org/10.1098/rspa.1927.0118E. doi: 10.1098/rspa.1927.0118E
[3]	I. Mimmo, M. Y. Kim, J. Park, Asymptotic behavior for an SIS epidemic model and its approximation, Nonlinear Anal. Theory Methods Appl., 35 (1999), 797–814. https://doi.org/10.1016/S0362-546X(97)00597-X doi: 10.1016/S0362-546X(97)00597-X
[4]	I. B. Schwartz, H. L. Smith, Infinite subharmonic bifurcation in an SEIR epidemic model, J. Math. Biol., 18 (1983), 233–253. https://doi.org/10.1007/BF00276090 doi: 10.1007/BF00276090
[5]	R. A. Brown, A simple model for control of COVID-19 infections on an urban campus, Proc. Natl. Acad. Sci. U S A, 118 (2021), e2105292118. https://doi.org/10.1073/pnas.2105292118 doi: 10.1073/pnas.2105292118
[6]	X. X. Liu, S. J. Fong, N. Dey, R. G. Crespo, E. H. Viedma, A new SEAIRD pandemic prediction model with clinical and epidemiological data analysis on COVID-19 outbreak, Appl. Intell., 51 (2021), 4162–4198. https://doi.org/10.1007/s10489-020-01938-3 doi: 10.1007/s10489-020-01938-3
[7]	D. J. Watts, S. H. Strogatz, Collective dynamics of small-world9 networks, Nature, 393 (1998), 440–442. https://doi.org/10.1038/30918 doi: 10.1038/30918
[8]	L. A. Amaral, A. Scala, M. Barthelemy, H. E. Stanley, Classes of small-world networks, Proc. Natl. Acad. Sci. U S A, 97 (2000), 11149–11152. https://doi.org/10.1073/pnas.200327197 doi: 10.1073/pnas.200327197
[9]	M. Liu, Y. Xiao, Modeling and analysis of epidemic diffusion within small-world network, J. Appl. Math., 2012 (2012), 841531. https://doi.org/10.1155/2012/841531 doi: 10.1155/2012/841531
[10]	F. Z. Younsi, A. Bounnekar, D. Hamdadou, O. Boussaid, SEIR-SW, simulation model of influenza spread based on the Small World network, Tsinghua Sci. Technol., 20 (2015), 460–473. https://doi.org/10.1109/TST.2015.7297745 doi: 10.1109/TST.2015.7297745
[11]	J. Saramäki, K. Kaski, Modelling development of epidemics with dynamic small-world networks, J. Theor. Biol., 234 (2005), 413–421. https://doi.org/10.1016/j.jtbi.2004.12.003 doi: 10.1016/j.jtbi.2004.12.003
[12]	S. Ren, W. Wang, R. Gao, A. 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
[13]	H. W. Hethcote, The mathematics of infectious diseases, SIAM Rev., 42 (2000), 599–653, https://doi.org/10.1137/S0036144500371907. doi: 10.1137/S0036144500371907
[14]	P. Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29–48. https://doi.org/10.1016/S0025-5564(02)00108-6 doi: 10.1016/S0025-5564(02)00108-6
[15]	O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz, On the definition and the computation of the basic reproduction ratio R₀ in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365–382. https://doi.org/10.1007/BF00178324 doi: 10.1007/BF00178324
[16]	E. Y. Boateng, D. A. Abaye, A review of the Logistic Regression model with emphasis on medical research, J. Data Anal. Inform. Proc., 7 (2019), 190–207. https://doi.org/10.4236/jdaip.2019.74012 doi: 10.4236/jdaip.2019.74012
[17]	S. A. Morsi, M. E. Alzahrani, Advanced computing approach for modeling and prediction COVID-19 pandemic, Appl. Bionics and Biomech., 2022 (2022), 6056574. https://doi.org/10.1155/2022/6056574 doi: 10.1155/2022/6056574
[18]	Shanghai Municipal Health Commission, Shanghai Municipal Bureau Statistics: From epidemic notification. Available from: https://wsjkw.sh.gov.cn.
[19]	Y. Ma, S. Xu, Q. An, M. Qin, S. Li, K. Lu, et al., Coronavirus disease 2019 epidemic prediction in Shanghai under the dynamic zero-COVID policy using time-dependent SEAIQR model, J. Biosaf. Biosecur., 4 (2022), 105–113. https://doi.org/10.1016/j.jobb.2022.06.002 doi: 10.1016/j.jobb.2022.06.002
[20]	World Health Organization: WHO Coronavirus (COVID-19) Dashboard with Vaccination Data, 2022. Available from: https://covid19.who.int.

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)