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Introduction to Compartmental Models in Epidemiology Read chapter Read first chapter

2021 | OriginalPaper | Chapter

4. Transmission Dynamics of Covid-19 from Environment with Red Zone, Orange Zone, Green Zone Using Mathematical Modelling

Authors : Bijal M. Yeolekar, Nita H. Shah

Published in: Mathematical Analysis for Transmission of COVID-19

Publisher: Springer Singapore

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Abstract

The novel corona virus or Covid-19 spread had its inception in November of 2019, and in March 2020, it was declared as a pandemic. Since its initial stage, it has now already infected over 5 million people, leading to the lockdown of countries around the world, and a halt on global as well as national travel across the globe. Based on this, the research proposes a mathematical Covid-19 model to study the outcome of these classified zones under different control strategies. In the nonlinear mathematical model, the total population has been divided into seven compartments, namely Susceptible, Exposed, Red zone, Orange zone, Green zone, Hospitalized, and Recovered. The spectral radius is calculated to analyze dynamics of the Covid-19. To control the spread of the virus, the parameters of controls are Medical Intervention, Partial Lockdown, and Strict Lockdown. This model has been validated with numerical data. The conclusion validates the implementation of lockdown in curbing Covid-19 cases.

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previous chapter Modeling the Spread of COVID-19 Among Doctors from the Asymptomatic Individuals
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Literature
1.
2.
Castillo-Chavez, C., Blower, S., Driessche, P., Kirschner, D., & Yakubu, A. A. (Eds.). (2002). Mathematical approaches for emerging and reemerging infectious diseases: Models, methods, and theory. New York: Springer.MATH
3.
Funk, S., Gilad, E., Watkins, C., & Jansen, V. A. A. (2009). The spread of awareness and its impact on epidemic outbreaks. Proceedings of the National Academy of Sciences of the United States of America, 106, 6872–6877.CrossRef
4.
Jiang, F., Deng, L., Zhang, L., Cai, Y., Cheung, C. W., & Xia, Z. (2020). Review of the clinical characteristics of coronavirus disease 2019 (COVID-19). Journal of General Internal Medicine, 35(5), 1545–1549.
5.
Muniz-Rodriguez, K., Chowell, G., Cheung, C.-H., Jia, D., Po-Kumar, A., Srivastava, P. K., & Takeuchi, Y. (2017). Modeling the role of information and limited optimal treatment on disease prevalence. Journal of Theoretical Biology, 414, 103–119.
6.
Pontriagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mishchenko, E. F. (1986). The mathematical theory of optimal process (pp. 4–5). New York: Gordon and Breach Science Publishers.
7.
Safi, M. A., & Gumel, A. B. (2013). Dynamics of a model with quarantine-adjusted incidence and quarantine of susceptible individuals. Journal of Mathematical Analysis and Applications, 399(2), 565–575.MathSciNetCrossRef
8.
Fuk-Woo, C. J., et al. (2020). A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: A study of a family cluster. Lancet, 395, 514–523.CrossRef
9.
Chan, J. F.-W., Yuan, S., Kok, K.-H., To, K. K.-W., Chu, H., Yang, J., et al. (2020). A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: A study of a family cluster. Lancet, 395, 514–523.
10.
Wu, J. T., Leung, K., & Leung, G. M. (2020). Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: A modelling study. Lancet, 395, 689–697.
11.
12.
13.
Egger, M., Johnson, L., Althaus, C., Schni, A., Salanti, G., Low, N. & Norris, S. L. (2017). Developing WHO guidelines: Time to formally include evidence from mathematical modelling studies. F1000Research, 6, 1584.
14.
Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180, 29–48.MathSciNetCrossRef
15.
Freedman, H. I., Ruan, S., & Tang, M. (1994). Uniform persistence and flows near a closed positively invariant set. Journal of Dynamics and Differential Equations, 6(4), 583–600.MathSciNetCrossRef
16.
Heffernan, L., Smith, R., & Wahl, L. (2005). Perspectives on the basic reproduction ratio. Journal of the Royal Society Interface, 2, 281–293; Sanche, S., Lin, Y. T., Xu, C., Romero-Severson, E., Hengartner, N. W., & Ke, R. (2020). The novel coronavirus, 2019-nCoV, is highly contagious and more infectious than initially estimated.
17.
Hethcote, H. W. (2000). The mathematics of infectious diseases. Society for Industrial and Applied Mathematics Review, 42(4), 599–653.MathSciNetMATH
18.
Sahu, G. P., & Dhar, J. (2012). Analysis of an SVEIS epidemic model with partial temporary immunity and saturation incidence rate. Applied Mathematical Modelling, 36(3), 908–923.MathSciNetCrossRef
19.
Shah, N. H., Patel, Z. A., & Yeolekar, B. M. (2016). Stability analysis of vertical transmission of HIV with delays in treatment and Pre-AIDS. Journal of Basic and Applied Research International, 88–102.
20.
Shah, N. H., Satia, M. H., & Yeolekar, B. M. (2017). Optimum control for spread of pollutants through forest resources. Applied Mathematics, 8(5), 607–620.CrossRef
21.
Shah, N. H., Thakkar, F. A., & Yeolekar, B. M. (2017). Simulation of dengue disease with control. International Journal of Scientific and Innovative Mathematical Research, 5(7), 14–28.
22.
Shah, N. H., Yeolekar, B. M., & Patel, Z. A. (2020). Mathematical model to analyze effect of demonetization. In Mathematical models of infectious diseases and social issues (pp. 270–286). Pennsylvania: IGI Global.
23.
Shah, N. H., Yeolekar, B. M., & Shukla, N. J. (2015). Liquor habit transmission model. Applied Mathematics, 6(08), 1208.CrossRef
24.
Shah, N. H., Yeolekar, B. M., & Patel, Z. A. (2016). Stability analysis of vertical transmission of HIV with delays in treatment and pre-AIDS. Journal of Basic and Applies Research International, 17(2), 88–102.
25.
Chen, T., Rui, J., Wang, Q., Zhao, Z., Cui, J., & Yin, L. (2020). A mathematical model for simulating the phase-based transmissibility of a novel coronavirus. Infectious Diseases Poverty, 9, 24.CrossRef
26.
(2020) Coronavirus in Vietnam. New England Journal of Medicine, 382, 872–874.
27.
28.
Mandal, S., Bhatnagar, T., Arinaminpathy, N., Agarwal, A., Chowdhury, A., Murhekar, M., et al. (2020). Prudent public health intervention strategies to control the coronavirus disease 2019 transmission in India: A mathematical model-based approach. Indian Journal of Medical Research. https://​doi.​org/​10.​4103/​ijmr.​IJMR-504-20. medRxiv preprint.
29.
Phan Lan, T., Nguyen Thuong, V., Luong Quang, C., et al. (2020). Importation and human-to-human transmission of a novel coronavirus in Vietnam. New England Journal of Medicine, 382, 872–874.CrossRef
30.
Van den Driessche, P., & Watmough, J. (2002). Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical Biosciences, 180(1), 29–48.MathSciNetCrossRef
31.
Victor, A. (2020). Mathematical predictions for COVID-19 as a global pandemic. Available at SSRN 3555879.
32.
Yang, Y., Lu, Q., Liu, M., Wang, Y., Zhang, A., Jalali, N, & Zhang, X. (2020). Epidemiological and clinical features of the 2019 novel coronavirus outbreak in China. MedRxiv.
33.
Xiao, X., Tang, S., & Wu, J. (2015). Media impact switching surface during an infectious disease outbreak. Scientific Reports, 5, 7838.CrossRef
34.
Gumel, A. B., Ruan, S., Day, T., Watmough, J., Brauer, F., Van den Driessche, P., et al. (2004). Modelling strategies for controlling SARS outbreaks. Proceedings of the Royal Society of London, Series B: Biological Sciences, 271, 2223–2232.CrossRef
35.
Nishiura, H., Linton, N. M., & Akhmetzhanov, A. R. (2020). Serial interval of novel coronavirus (2019-ncov) infections. medRxiv.
36.
Lewis, F. L., & Syrmos, V. L. (1995). Optimal control. Hoboken: Wiley.
37.
Simonsen, & Fung, I. C.-H. (2020). Epidemic doubling time of the 2019 novel spread of the 2019-nCoV outbreak originating in Wuhan, China: a modeling study. The Lancet, 395, 689–697.
38.
Sanche, S., Lin, Y. T., Xu, C., Romero-Severson, E., NickSun, C., Yang, W., et al. (2011). Effect of media-induced social distancing on disease transmission in a two patch setting. Mathematical Biosciences, 230, 87–95.
39.
Guan, W., Ni, Z., Hu, Y., et al. Clinical characteristics of 2019 novel coronavirus infection in China. MedRxiv.
40.
Zhu, N., Zhang, D., Wang, W., Li, X., Yang, B., Song, J. ... Tan, W. (2020). A novel coronavirus from patients with pneumonia in China, 2019. New England Journal of Medicine.
41.
Tang, B., Wang, X., Li, Q., Bragazzi, N. L., Tang, S., Xiao, Y., & Wu, J. (2020). Estimation of the transmission risk of the 2019-ncov and its implication for public health interventions. Journal of Clinical Medicine, 9(2), 462.CrossRef
42.
Nadim, S. K., Ghosh, I., & Chattopadhyay, J. (2020). Short-term predictions and prevention strategies for COVID-2019: A model based study. arXiv:​2003.​08150.
43.
44.
d’Onofrio, A., & Manfredi, P. (2009). Information-related changes in contact patterns may trigger oscillations in the endemic prevalence of infectious diseases. Journal of Theoretical Biology, 256, 473–478.MathSciNetCrossRef
45.
Buonomo, B., d’Onofrio, A., & Lacitignola, D. (2008). Global stability of an SIR epidemic model with information dependent vaccination. Mathematical Biosciences, 216, 9–16.MathSciNetCrossRef
46.
47.
Das, D. K., Khajanchi, S., & Kar, T. K. (2020). The impact of the media awareness and optimal strategy on the prevalence of tuberculosis. Applied Mathematics and Computation, 366, 124732.MathSciNetCrossRef
48.
Sun, C., Yang, W., Arino, J., & Khan, K. (2011). Effect of media-induced social distancing on disease transmission in a two patch setting. Mathematical Biosciences, 230, 87–95.MathSciNetCrossRef
49.
Fleming, W. H., & Rishel, R. W. (2012). Deterministic and stochastic optimal control (Vol. 1). Berlin: Springer Science and Business Media.
50.
Lukes, D. L. (1982). Differential equations: Classical to controlled (Vol. 162). Cambridge: Academic Press.
51.
Hartl, R. F., & Sethi, S. P. (1983). A note on the free terminal time transversality condition. Zeitschrift für Operations Research, 27(1), 203–208.MathSciNetMATH
52.
53.
Liu, Z., Magal, P., Seydi, O., & Webb, G. (2020). Predicting the cumulative number of cases for the COVID-19 epidemic in China from early data. arXiv:​2002.​12298.
54.
Metadata
Title
Transmission Dynamics of Covid-19 from Environment with Red Zone, Orange Zone, Green Zone Using Mathematical Modelling
Authors
Bijal M. Yeolekar
Nita H. Shah
Copyright Year
2021
Publisher
Springer Singapore
Book
Mathematical Analysis for Transmission of COVID-19

Print ISBN: 978-981-336-263-5

Electronic ISBN: 978-981-336-264-2

Copyright Year: 2021

DOI
https://doi.org/10.1007/978-981-33-6264-2_4

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