Research article Special Issues

A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic

  • Received: 31 August 2020 Accepted: 16 November 2020 Published: 26 November 2020
  • In this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the states of Maharashtra, Delhi, Tamil Nadu and overall India, and estimate the rate of infection of susceptible with symptomatic population and recovery rate of quarantined individuals. We also estimate basic reproduction number to illustrate the epidemiological status of the regions under study. Our simulations infer that the infective population will be on increasing curve for Maharashtra and India, and settling for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Our results reveal that to curtail the disease burden in India, specific control strategies should be implemented effectively so that the basic reproduction number is decreased below unity. The three control strategies are shown to be important preventive measures to lower disease transmission rate. The model is further extended to its stochastic counterpart to encapsulate the variation or uncertainty observed in the disease transmissibility. We observe the variability in the infective population and found their distribution at certain fixed time, which shows that for small populations, the stochasticity will play an important role.

    Citation: Akhil Kumar Srivastav, Pankaj Kumar Tiwari, Prashant K Srivastava, Mini Ghosh, Yun Kang. A mathematical model for the impacts of face mask, hospitalization and quarantine on the dynamics of COVID-19 in India: deterministic vs. stochastic[J]. Mathematical Biosciences and Engineering, 2021, 18(1): 182-213. doi: 10.3934/mbe.2021010

    Related Papers:

  • In this paper, we propose a mathematical model to assess the impacts of using face masks, hospitalization of symptomatic individuals and quarantine of asymptomatic individuals in combating the COVID-19 pandemic in India. We calibrate the proposed model to fit the four data sets, viz. data for the states of Maharashtra, Delhi, Tamil Nadu and overall India, and estimate the rate of infection of susceptible with symptomatic population and recovery rate of quarantined individuals. We also estimate basic reproduction number to illustrate the epidemiological status of the regions under study. Our simulations infer that the infective population will be on increasing curve for Maharashtra and India, and settling for Tamil Nadu and Delhi. Sophisticated techniques of sensitivity analysis are employed to determine the impacts of model parameters on basic reproduction number and symptomatic infected individuals. Our results reveal that to curtail the disease burden in India, specific control strategies should be implemented effectively so that the basic reproduction number is decreased below unity. The three control strategies are shown to be important preventive measures to lower disease transmission rate. The model is further extended to its stochastic counterpart to encapsulate the variation or uncertainty observed in the disease transmissibility. We observe the variability in the infective population and found their distribution at certain fixed time, which shows that for small populations, the stochasticity will play an important role.


    加载中


    [1] N. M. Ferguson, D. Laydon, G. Nedjati-Gilani, N. Imai, K. Ainslie, M. Baguelin, et al., Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand, London: Imperial College COVID-19 Response Team, March 16, 2020.
    [2] M. McKee, D. Stuckler, If the world fails to protect the economy, COVID-19 will damage health not just now but also in the future, Nat. Med., 26 (2020), 640-642. doi: 10.1038/s41591-020-0863-y
    [3] M. Nicola, Z. Alsafi, C. Sohrabi, A. Kerwan, A. Al-Jabir, C. Iosifidis, et al., The socio-economic implications of the coronavirus pandemic (COVID-19): A review, Int. J. Surg., 78 (2020), 185-193. doi: 10.1016/j.ijsu.2020.04.018
    [4] N. van Doremalen, T. Bushmaker, D. H. Morris, M. G. Holbrook, A. Gamble, B. N. Williamson, et al., Aerosol and surface stability of SARS-CoV-2 as compared with SARS-CoV-1, N. Engl. J. Med., 382 (2020), 1564-1567. doi: 10.1056/NEJMc2004973
    [5] World Health Organization, Coronavirus disease 2019 (COVID-19). WHO situation report - 73, 2020. Avaiable from: https://www.who.int/docs/default-source/coronaviruse/situation-reports/20200402-sitrep-73-covid-19.pdf.
    [6] X. Liu, S. Zhang, COVID-19: face masks and human-to-human transmission. Influenza Other Respir Viruses, 2020. Avaiable from: http://doi.wiley.com/10.1111/irv.12740.
    [7] C. J. Noakes, C. B. Beggs, P. A. Sleigh, K. G. Kerr, Modelling the transmission of airborne infections in enclosed spaces, Epidemiol. Infect., 134 (2006), 1082-1091. doi: 10.1017/S0950268806005875
    [8] C. J. Noakes, P. A. Sleigh, Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards, J. R. Soc. Interface, 6 (2009), S791-S800.
    [9] R. Chetty, M. Stepner, S. Abraham, S. Lin, B. Scuderi, N. Turner, et al., The association between income and life expectancy in the United States, 2001-2014, JAMA, 315 (2016), 1750. doi: 10.1001/jama.2016.4226
    [10] R. O. Stutt, R. Retkute, M. Bradley, C. A. Gilligan, J. Colvin, A modelling framework to assess the likely effectiveness of facemasks in combination with 'lock-down'in managing the COVID-19 pandemic, Proc. R. Soc. A, 476 (2020), 20200376. doi: 10.1098/rspa.2020.0376
    [11] D. K. Chu, E. A. Akl, S. Duda, K. Solo, S. Yaacoub, H. J. Schunemann, et al., Physical distancing, face masks, and eye protection to prevent person-to-person transmission of SARS-CoV-2 and COVID-19: a systematic review and meta-analysis, The Lancet, 395 (2020), 1973-1987. doi: 10.1016/S0140-6736(20)31142-9
    [12] C. N. Ngonghala, E. Iboi, S. Eikenberry, M. Scotch, C. R. MacIntyre, M. H. Bonds, et al., Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel Coronavirus, Math. Biosci., 325 (2020), 108364. doi: 10.1016/j.mbs.2020.108364
    [13] S. E. Eikenberry, M. Mancuso, E. Iboi, T. Phan, K. Eikenberry, Y. Kuang, et al., To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic, Infect. Dis. Model., 5 (2020), 293-308.
    [14] E. A. Iboi, O. O. Sharomi, C. N. Ngonghala, A. B. Gumel, Mathematical modeling and analysis of COVID-19 pandemic in Nigeria, Math. Biosci. Eng., 17 (2020), 7192-7220.
    [15] D. Okuonghae, A. Omame, Analysis of a mathematical model for COVID-19 population dynamics in Lagos, Nigeria, Chaos Soliton. Fract., 139 (2020), 110032. doi: 10.1016/j.chaos.2020.110032
    [16] B. J. Cowling, K. H. Chan, V. J. Fang, C. K. Cheng, R. O. Fung, W. Wai, et al., Facemasks and hand hygiene to prevent influenza transmission in households: a cluster randomized trial, Ann. Intern. Med., 151 (2009), 437-446. doi: 10.7326/0003-4819-151-7-200910060-00142
    [17] M. Lipsitch, T. Cohen, B. Cooper, J. M. Robins, S. Ma, L. James, et al., Transmission dynamics and control of severe acute respiratory syndrome, Science, 300 (2003), 1966-1970. doi: 10.1126/science.1086616
    [18] S. Zhao, L. Stone, D. Gao, S. S. Musa, M. K. Chong, D. He, et al., Imitation dynamics in the mitigation of the novel coronavirus disease (COVID-19) outbreak in Wuhan, China from 2019 to 2020, Ann. Transl. Med., 8 (2020), 448. doi: 10.21037/atm.2020.03.168
    [19] S. H. A. Khoshnaw, R. H. Salih, S. Sulaimany, Mathematical modeling for coronavirus disease (COVID-19) in predicting future behaviours and sensitivity analysis, Math. Model. Nat. Phenom., 15 (2020), 1-13. doi: 10.1051/mmnp/2019006
    [20] M. Serhani, H. Labbardi, Mathematical modeling of COVID-19 spreading with asymptomatic infected and interacting peoples, J. Appl. Math. Comput., 17 (2020), 1-20.
    [21] C. Huang, Y. Wang, X. Li, L. Ren, J. Zhao, Y. Hu, et al., Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China, Lancet, 395 (2020), 497-506. doi: 10.1016/S0140-6736(20)30183-5
    [22] P. van den Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6
    [23] COVID 2019, India, available from: https://www.covid19india.org/.
    [24] L. F. White, M. Pagano, A likelihood-based method for real-time estimation of the serial interval and reproductive number of an epidemic, Stat. Med., 27 (2008), 2999-3016. doi: 10.1002/sim.3136
    [25] A. Davies, K. A. Thompson, K. Giri, G. Kafatos, J. Walker, A. Bennett, Testing the efficacy of homemade masks: would they protect in an influenza pandemic?, Disaster Med. Public Health Prep., 7 (2013), 413-418. doi: 10.1017/dmp.2013.43
    [26] C. N. Ngonghala, E. Iboi, S. Eikenberry, M. Scotch, C. R. MacIntyre, M. H. Bonds, et al., Mathematical assessment of the impact of non-pharmaceutical interventions on curtailing the 2019 novel coronavirus, Math. Biosci., 325 (2020), 108364. doi: 10.1016/j.mbs.2020.108364
    [27] S. A. Lauer, K. H. Grantz, Q. Bi, F. K. Jones, Q. Zheng, H. R. Meredith, et al., The incubation period of coronavirus disease 2019 (COVID-19) from publicly reported confirmed cases: estimation and application, Ann. Intern. Med., 172 (2020), 577-582. doi: 10.7326/M20-0504
    [28] R. Li, S. Pei, B. Chen, Y. Song, T. Zhang, W. Yang, et al., Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2), Science, 368 (2020), 489-493. doi: 10.1126/science.abb3221
    [29] F. Zhou, T. Yu, R. Du, G. Fan, Y. Liu, Z. Liu, et al., Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study, Lancet, 395 (2020), 1054-1062. doi: 10.1016/S0140-6736(20)30566-3
    [30] B. Tang, X. Wang, Q. Li, N. L. Bragazzi, S. Tang, Y. Xiao, et al., Estimation of the transmission risk of the 2019-nCoV and its implication for public health interventions, J. Clin. Med., 9 (2020), 462. doi: 10.3390/jcm9020462
    [31] D. Aldila, M. Z. Ndii, B. M. Samiadji, Optimal control on COVID-19 eradication program in Indonesia under the effect of community awareness, Math. Biosci. Eng., 17 (2020), 6355-6389. doi: 10.3934/mbe.2020335
    [32] D. He, S. Zhao, X. Xu, Q. Lin, Z. Zhuang, P. Cao, et al., Low dispersion in the infectiousness of COVID-19 cases implies difficulty in control, BMC Public Health, 20 (2020), 1558. doi: 10.1186/s12889-020-09624-2
    [33] I. Ghosh, P. K. Tiwari, J. Chattopadhyay, Effect of active case finding on dengue control: Implications from a mathematical model, J. Theor. Biol., 464 (2019), 50-62. doi: 10.1016/j.jtbi.2018.12.027
    [34] S. M. Blower, H. Dowlatabadi, Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example, Int. Stat. Rev., 62 (1994), 229-243. doi: 10.2307/1403510
    [35] S. Marino, I. B. Hogue, C. J. Ray, D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, J. Theor. Biol., 254 (2008), 178-196. doi: 10.1016/j.jtbi.2008.04.011
    [36] Y. Yuan, L. J. S. Allen, Stochastic models for virus and immune system dynamics, Math. Biosci., 234 (2011), 84-94. doi: 10.1016/j.mbs.2011.08.007
  • Reader Comments
  • © 2021 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)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(1198) PDF downloads(327) Cited by(1)

Article outline

Figures and Tables

Figures(17)  /  Tables(5)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog