A compartmental model for COVID-19 to assess the effects of non-pharmaceutical interventions with emphasis on contact-based quarantine

Authors

  • Saumen BARUA Bolyai Institute, University of Szeged, Hungary. Email: baruasaumen@yahoo.com. https://orcid.org/0000-0002-2585-6249
  • Bornali DAS National Laboratory for Health Security, Bolyai Institute, University of Szeged, Hungary. Email: das.bornali19@gmail.com.
  • Attila DÉNES National Laboratory for Health Security, Bolyai Institute, University of Szeged, Hungary. Email: denesa@math.u-szeged.hu. https://orcid.org/0000-0003-1827-7932

DOI:

https://doi.org/10.24193/subbmath.2023.3.15

Keywords:

COVID-19, compartmental model, quarantine, data fitting.

Abstract

Relative to the number of casualties, COVID-19 ranks among the ten most devastating plagues in history. The pandemic hit the South Asian nation of Bangladesh in early March 2020 and has greatly impacted the socio-economic status of the country. In this article, we propose a compartmental model for COVID-19 dynamics, introducing a separate class for quarantined susceptibles, synonymous to isolation of individuals who have been exposed and are suspected of being infected. The current model assumes a perfect quarantine based on contact with infectious individuals. Numerical simulation is conducted to investigate the efficiency of disease control by segregating suspected individuals and other non-pharmaceutical interventions. In addition, we assort quantitatively the importance of parameters that influence the dynamics of the system. Fitting the system to the early phase of COVID-19 outbreaks in Bangladesh, by taking into account the cumulative number of cases with the data of the first 17-week period, the basic reproduction number is estimated as 1.69.

Mathematics Subject Classification (2010): 92D30, 34A99.

References

Barbarossa, M.V., Bogya, N., Dénes, A., et al., Fleeing lockdown and its impact on the size of epidemic outbreaks in the source and target regions – A COVID-19 lesson, Sci. Rep., 11(2021), no. 9233, https://doi.org/10.1038/s41598-021-88204-9.

Barbarossa, M.V., Fuhrmann, J., Meinke, J.H., et al., Modeling the spread of COVID- 19 in Germany: Early assessment and possible scenarios, PloS One, 15(2020), no. 9, e0238559, https://doi.org/10.1371/journal.pone.0238559.

Byrne, A.W., McEvoy, D., Collins, A.B., et al., Inferred duration of infectious period of SARS-COV-2: Rapid scoping review and analysis of available evidence for asymptomatic and symptomatic COVID-19 cases, BMJ Open, 10(2020), no. e039856, https://doi.org/10.1136/bmjopen-2020-039856.

Chen, S.J., Wang, S.C., Chen, Y.C., Novel antiviral strategies in the treatment of COVID-19: A Review, Microorganisms, 8(2020), no. 9, 1259, https://doi.org/10.3390/microorganisms8091259.

Chen, T.M., Rui, J., Wang, Q.P. et al., A mathematical model for simulating the phase- based transmissibility of a novel coronavirus, Infect. Dis. Poverty, 9(2020), no. 1, 24, https://doi.org/10.1186/s40249-020-00640-3.

Chen, Y.-H., Fang, C.-T., Huang, Y.-L., Effect of non-lockdown social distancing and testing-contact tracing during a covid-19 outbreak in Daegu, South Korea, February to April 2020: A modeling study, International J. Infect. Dis., 110(2021), 213-221, https://doi.org/10.1016/j.ijid.2021.07.058.

Cheng, C., Zhang, D.D., Dang, D., et al., The incubation period of COVID-19: A global meta-analysis of 53 studies and a Chinese observation study of 11545 patients, Infect. Dis. Poverty, 10(2021), no. 1, 119, https://doi.org/10.1186/s40249-021-00901-9.

Datta, S., Saratchand, C., Non-pharmaceutical interventions in a generalized model of interactive dynamics between COVID-19 and the economy, Nonlinear Dyn., 105(2021), no. 3, 2795-2810, https://doi.org/10.1007/s11071-021-06712-9.

Dénes, A., Gumel, A.B., Modeling the impact of quarantine during an outbreak of Ebola virus disease, Infect. Dis. Model., 4(2019), 12-27, https://doi.org/10.1016/j.idm.2019.01.003.

Diekmann, O., Heesterbeek, J.A., Roberts, M.G., The construction of next-generation matrices for compartmental epidemic models, J. R. Soc. Interface, 7(2009), no. 47, 873- 885, https://doi.org/10.1098/rsif.2009.0386.

van den Driessche, P., Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180(2002), no. 1-2, 29-48, https://doi.org/10.1016/s0025-5564(02)00108-6.

Ferguson, N., Laydon, D., Nedjati Gilani, G., et al., Report 9: Impact of non- pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, In: Spiral. (2020), http://spiral.imperial.ac.uk/handle/10044/1/77482.

Fokas, A.S., Dikaios, N., Kastis, G.A., Mathematical models and deep learning for predicting the number of individuals reported to be infected with SARS-COV-2, J.R. Soc. Interface, 17(2020), 169, https://doi.org/10.1098/rsif.2020.0494.

Gaudart, J., Landier, J., Huiart, L., et al., Factors associated with the spatial heterogeneity of the first wave of COVID-19 in France: A nationwide geo-epidemiological study, Lancet Public Health, 6(2021), no. 4, e222-e231, https://doi.org/10.1016/s2468-2667(21)00006-2.

Holshue, M.L., DeBolt, C., Lindquist, S., et al., First case of 2019 novel coronavirus in the United States, N. Engl. J. Med., 382(2020), no. 10, 929-936, https://doi.org/10.1056/nejmoa2001191.

Huo, X., Chen, J., Ruan, S., Estimating asymptomatic, undetected and total cases for the COVID-19 outbreak in Wuhan: A mathematical modeling study, BMC Infect. Dis., 21(2021), no. 1, 476, https://doi.org/10.1186/s12879-021-06078-8.

Ibrahim, M.A., Al-Najafi, A., Modeling, control, and prediction of the spread of COVID- 19 using compartmental, logistic, and Gauss models: A case study in Iraq and Egypt, Processes, 8(2020), no. 11, 1400, https://doi.org/10.3390/pr8111400.

Ivorra, B., Ferrández, M.R., Vela-Pérez, M., Ramos, A.M., Mathematical modeling of the spread of the coronavirus disease 2019 (COVID-19) taking into account the undetected infections. The case of China, Commun. Nonlinear Sci. Numer. Simul., 88(2020), 105303, https://doi.org/10.1016/j.cnsns.2020.105303.

Jin, Y.H., Cai, L., Cheng, Z.S., et al., A rapid advice guideline for the diagnosis and treatment of 2019 novel coronavirus (2019-nCoV) infected pneumonia (standard version), Mil. Med. Res., 7(2020), no. 1, https://doi.org/10.1186/s40779-020-0233-6.

Li, C., Zhu, Y., Qi, C., et al., Estimating the prevalence of asymptomatic COVID-19 cases and their contribution in transmission – using Henan Province, China, as an example, Front. Med., 8(2021), https://doi.org/10.3389/fmed.2021.591372.

Lipsitch, M., Cohen, T., Cooper, B., et al., Transmission dynamics and control of severe acute respiratory syndrome, Science, 300(2003), no. 5627, 1966-1970, https://doi.org/10.1126/science.1086616.

Masud, M.A., Islam, M.H., Mamun, K.A., et al., COVID-19 transmission: Bangladesh perspective, Mathematics, 8(2020), no. 10, 1793, https://doi.org/10.3390/math8101793.

Mizumoto, K., Kagaya, K., Zarebski, A., Chowell, G., Estimating the asymptomatic proportion of coronavirus disease 2019 (COVID-19) cases on board the Diamond Princess cruise ship, Yokohama, Japan, 2020, Euro Surveill., 25(2020), no. 10, https://doi.org/10.2807/1560-7917.es.2020.25.10.2000180.

Mubayi, A., Zaleta, C.K., Martcheva, M., Chávez, C.C., A cost-based comparison of quarantine strategies for new emerging diseases, Math. Biosci. Eng., 7(2010), no. 3, 687- 717, https://doi.org/10.3934/mbe.2010.7.687.

Ndaïrou, F., Area, I., Nieto, J.J., Torres, D.F.M., Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan, Chaos Solitons and Fractals, 135(2020), 109846, https://doi.org/10.1016/j.chaos.2020.109846.

Nishiura, H., Kobayashi, T., Miyama, T., et al., Estimation of the asymptomatic ratio of novel coronavirus infections (COVID-19), Int. J. Infect Dis., 94(2020), 154-155, https://doi.org/10.1016/j.ijid.2020.03.020.

Oloniiju, S.D., Otegbeye, O., Ezugwu, A.E., Investigating the impact of vaccination and non-pharmaceutical measures in curbing COVID-19 spread: A South Africa perspective, Math. Biosci. Eng., 19(2021), no. 1, 1058-1077, https://doi.org/10.3934/mbe.2022049.

Safi, M.A., Gumel, A.B., Dynamics of a model with quarantine-adjusted incidence and quarantine of susceptible individuals, J. Math. Anal. Appl., 399(2013), no. 2, 565-575, https://doi.org/10.1016/j.jmaa.2012.10.015.

Shahrear, P., Rahman, S.M., Nahid, M.M., Prediction and mathematical analysis of the outbreak of coronavirus (COVID-19) in Bangladesh, Results Appl. Math., 10(2021), no. 100145, https://doi.org/10.1016/j.rinam.2021.100145.

Stebbing, J., Phelan, A., Griffin, I., et al., Covid-19: Combining antiviral and anti- inflammatory treatments, Lancet Infect. Dis., 20(2020), no. 4, 400-402, https://doi. org/10.1016/s1473-3099(20)30132-8.

Wang, S., Pan, Y., Wang, Q., et al., Modeling the viral dynamics of SARS-COV-2 infection, Math. Biosci., 328(2020), no. 108438, https://doi.org/10.1016/j.mbs.2020. 108438.

Zhao, S., Chen, H., Modeling the epidemic dynamics and control of covid-19 outbreak in China, Quant. Biol., 8(2020), no. 1, 11-19, https://doi.org/10.1007/s40484-020-0199-0.

Bangladesh: WHO coronavirus disease (COVID-19) dashboard with vaccination data, In: World Health Organization, https://covid19.who.int/region/searo/country/bd.

Cabinet Division, In: Cabinet Division Government of the Peoples Republic of Bangladesh, https://cabinet.gov.bd/site/view/noticesarchive. Accessed 22 May 2022.

Coronavirus cases: In: Worldometer, https://www.worldometers.info/coronavirus/Worldometers, COVID-19 pandemic update.

Coronavirus disease (COVID-19): Vaccines, In: World Health Organization, https://www.who.int/news-room/questions-and-answers/item/coronavirus-disease-(covid-19)-vaccines?topicsurvey=v8kj13.

Ministry of Public Administration (Sl 48-51,53-55). In: Ministry of Public Administration, Government of the Peoples Republic of Bangladesh, https://mopa.gov.bd/site/view/publicholidayarchive?page=3&rows=20. Accessed 22 May 2022.

World Health Organization, Origin of SARS-CoV-2, https://apps.who.int/iris/bitstream/handle/10665/332197/WHO-2019-nCoV-FAQ-Virus_origin-2020.1-eng. pdf.

Downloads

Published

2023-09-30

How to Cite

BARUA, S. ., DAS, B. ., & DÉNES, A. . (2023). A compartmental model for COVID-19 to assess the effects of non-pharmaceutical interventions with emphasis on contact-based quarantine. Studia Universitatis Babeș-Bolyai Mathematica, 68(3), 679–697. https://doi.org/10.24193/subbmath.2023.3.15

Issue

Section

Articles

Similar Articles

1 2 3 4 > >> 

You may also start an advanced similarity search for this article.