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A Multi-strain Model for COVID-19

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Applied Analysis, Optimization and Soft Computing (ICNAAO 2021)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 419))

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Abstract

The main objective of this work is to propose and analyze a multi-compartment ordinary differential equation model for multi-strain epidemic disease. The proposed model mainly focuses on the epidemic disease spread due to SARS-CoV-2, and the recurrent outbreaks are due to the emergence of a new strain. The possibility of reinfection of the recovered individuals is considered in the model. The multi-strain model is validated with the help of strain-specific daily infection data from France and Italy.

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References

  1. https://www.who.int/en/activities/tracking-SARS-CoV-2-variants/

  2. https://covid.ourworldindata.org

  3. https://nextstrain.org/ncov/gisaid/global/6m

  4. https://ourworldindata.org/grapher/covid-cases-omicron?time=2022-01-24&country=GBR~FRA~BEL~DEU~ITA~ESP~USA~ZAF~BWA~AUS

  5. Abu-Raddad, L.J., Chemaitelly, H., Ayoub, H.H., Tang, P., Coyle, P., Hasan, M.R., Yassine, H.M., Benslimane, F.M., Al Khatib, H.A., Al Kanaani, Z., et al.: Effect of vaccination and of prior infection on infectiousness of vaccine breakthrough infections and reinfections. medRxiv (2021)

    Google Scholar 

  6. Anderson, R.M., May, R.M.: Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford (1992)

    Google Scholar 

  7. Aniţa, S., Banerjee, M., Ghosh, S., Volpert, V.: Vaccination in a two-group epidemic model. Appl. Math. Lett. 119, 107197 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  8. Banerjee, M., Ghosh, S., Volpert, V.: Epidemic progression in a heterogeneously distributed population (2021)

    Google Scholar 

  9. Banerjee, M., Lipniacki, T., d’Onofrio, A., Volpert, V.: Epidemic model with a strain-dependent transmission rate. Commun. Nonlinear Sci. Num. Simul. 114, 106641 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  10. Brauer, F., Castillo-Chavez, C., Feng, Z.: Mathematical Models in Epidemiology, vol. 32. Springer, Berlin (2019)

    Google Scholar 

  11. Chintu, C., Athale, U.H., Patil, P.: Childhood cancers in zambia before and after the hiv epidemic. Arch. Dis. Childhood 73(2), 100–105 (1995)

    Article  Google Scholar 

  12. Diekmann, O., Heesterbeek, J.A.P.: Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation, vol. 5. Wiley, New York (2000)

    Google Scholar 

  13. Van den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180(1–2), 29–48 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Fisher-Hoch, S., Hutwagner, L.: Opportunistic candidiasis: an epidemic of the 1980s. Clin. Infecti. Dis. 21(4), 897–904 (1995)

    Article  Google Scholar 

  15. Ghosh, S., Banerjee, M., Volpert, V.: Immuno-epidemiological model-based prediction of further covid-19 epidemic outbreaks due to immunity waning. Math. Modell. Nat. Phenom. 17, 9 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  16. Keeling, M.J., Rohani, P.: Modeling Infectious Diseases in Humans and Animals. Princeton University Press, Princeton (2011)

    Google Scholar 

  17. Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. Ser. A Contain. Papers Math. Phys. Character 115(772), 700–721 (1927)

    Google Scholar 

  18. Kermack, W.O., McKendrick, A.G.: Contributions to the mathematical theory of epidemics. ii.-the problem of endemicity. Proc. R. Soc. Lond. Ser. A Contain. Papers Math. Phys. Character 138(834), 55–83 (1932)

    Google Scholar 

  19. Kermack, W.O., McKendrick, A.G.: Contributions to the mathematical theory of epidemics. iii.-further studies of the problem of endemicity. Proc. R. Soc. Lond. Ser. A Contain. Papers Math. Phys. Character 141(843), 94–122 (1933)

    Google Scholar 

  20. Kim, P., Gordon, S.M., Sheehan, M.M., Rothberg, M.B.: Duration of sars-cov-2 natural immunity and protection against the delta variant: a retrospective cohort study. Clin. Inf. Dis. (2021)

    Google Scholar 

  21. de León, U.A.P., Pérez, Á.G., Avila-Vales, E.: An seiard epidemic model for covid-19 in mexico: mathematical analysis and state-level forecast. Chaos Solitons Fractals 140, 110165 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  22. Mahase, E.: Covid-19: past infection provides 83% protection for five months but may not stop transmission, study finds (2021)

    Google Scholar 

  23. Martcheva, M.: An Introduction to Mathematical Epidemiology, vol. 61. Springer, Berlin (2015)

    Google Scholar 

  24. Murray, J.: Mathematical Biology, vol. 1. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  25. Parolini, N., Dede’, L., Antonietti, P.F., Ardenghi, G., Manzoni, A., Miglio, E., Pugliese, A., Verani, M., Quarteroni, A.: Suihter: a new mathematical model for covid-19. application to the analysis of the second epidemic outbreak in Italy. Proc. R. Soc. A 477(2253), 20210027 (2021)

    Google Scholar 

  26. Patterson, K.D., Pyle, G.F.: The geography and mortality of the 1918 influenza pandemic. Bull. Hist. Med. 65(1), 4–21 (1991)

    Google Scholar 

  27. Sharma, S., Volpert, V., Banerjee, M.: Extended seiqr type model for covid-19 epidemic and data analysis. Math. Biosci. Eng. (2020)

    Google Scholar 

  28. Volpert, V., Banerjee, M., Sharma, S.: Epidemic progression and vaccination in a heterogeneous population. application to the covid-19 epidemic. Ecolog. Compl. 47, 100940 (2021)

    Google Scholar 

  29. Wang, K., Ding, L., Yan, Y., Dai, C., Qu, M., Jiayi, D., Hao, X.: Modelling the initial epidemic trends of covid-19 in Italy, Spain, Germany, and France. PLoS One 15(11), e0241743 (2020)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Statistics, IIT Kanpur, Kanpur, 208016, India

    Samiran Ghosh & Malay Banerjee

Authors
  1. Samiran Ghosh
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  2. Malay Banerjee
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Corresponding author

Correspondence to Malay Banerjee .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, Uttar Pradesh, India

    Tanmoy Som

  2. Department of Mathematical Sciences, Indian Institute of Technology, BHU, Varanasi, Uttar Pradesh, India

    Debdas Ghosh

  3. Research Chair of Graduate Studies, Tijuana Institute of Technology, Tijuana, Mexico

    Oscar Castillo

  4. Faculty of Mathematics and Computer Sci., Babes-Bolyai University, Cluj-Napoca, Romania

    Adrian Petrusel

  5. Department of Mathematics, Banaras Hindu University, Varanasi, India

    Dayaram Sahu

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Ghosh, S., Banerjee, M. (2023). A Multi-strain Model for COVID-19. In: Som, T., Ghosh, D., Castillo, O., Petrusel, A., Sahu, D. (eds) Applied Analysis, Optimization and Soft Computing. ICNAAO 2021. Springer Proceedings in Mathematics & Statistics, vol 419. Springer, Singapore. https://doi.org/10.1007/978-981-99-0597-3_10

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