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Mathematical Analysis of SIR Model for COVID-19 Transmission

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  • Mohajan, Haradhan

Abstract

Due to the recent threatening pandemic COVID-19, the research area of this disease is increasing. This paper tries to establish COVID-19 infection transmission by Susceptible-Infectious-Recovered (SIR) compartmental model for epidemic prediction and prevention. The model is built based on the secondary data of the infected persons and discharged patients. It is considered as a valuable tool in public health sector, as it can provide suggestions about the fatality of pandemic to take necessary actions for preventing the infections. COVID-19 is spreading worldwide extremely, and at present it becomes both local and global concern. This model can show the fatality of COVID-19 with time and can predict whether the disease will further spread or abolish completely. This study stresses on vaccination to reduce the infection of the disease. It can provide how many people are needed to be vaccinated to create herd immunity against COVID-19. Overtime the immunity due to vaccination may decrease and after a fixed period the immunity of COVID-19 due to vaccination may extinct completely. The article attempts to give a mathematical presentation to aware the immunity loss individuals with other susceptible. It also tries to alert the people about the re-infection of the previous COVID-19 infected persons. The aim of this study is to minimize both global economic losses and deaths due to COVID-19.

Suggested Citation

  • Mohajan, Haradhan, 2022. "Mathematical Analysis of SIR Model for COVID-19 Transmission," MPRA Paper 114390, University Library of Munich, Germany, revised 10 Jul 2022.
    • Handle: RePEc:pra:mprapa:114390
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    File URL: https://mpra.ub.uni-muenchen.de/114390/1/MPRA_paper_114390.pdf
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    References listed on IDEAS

    as
    1. Haradhan Kumar MOHAJAN, 2018. "Qualitative research methodology in social sciences and related subjects," Journal of Economic Development, Environment and People, Alliance of Central-Eastern European Universities, vol. 7(1), pages 23-48, March.
    2. Mohajan, Haradhan, 2020. "Most Fatal Pandemic COVID-19 Outbreak: An Analysis of Economic Consequences," MPRA Paper 101623, University Library of Munich, Germany, revised 03 Apr 2020.
    3. MOHAJAN, Haradhan Kumar, 2017. "Two Criteria For Good Measurements In Research: Validity And Reliability," Annals of Spiru Haret University, Economic Series, Universitatea Spiru Haret, vol. 17(4), pages 59-82.
    4. Mohajan, Haradhan, 2020. "Quantitative Research: A Successful Investigation in Natural and Social Sciences," MPRA Paper 105149, University Library of Munich, Germany, revised 15 Nov 2020.
    5. Atangana, Abdon, 2020. "Modelling the spread of COVID-19 with new fractal-fractional operators: Can the lockdown save mankind before vaccination?," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    6. Mohajan, Haradhan, 2021. "Global COVID-19 Pandemic: Prevention and Protection Techniques," MPRA Paper 106923, University Library of Munich, Germany, revised 19 Jan 2021.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Situations of Lagrange Multiplier When Costs of Various Inputs Increase for Nonlinear Budget Constraint," MPRA Paper 116879, University Library of Munich, Germany, revised 12 Feb 2023.
    2. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Aspects of Profit Maximization if Cost of Principal Raw Material Increases," MPRA Paper 117453, University Library of Munich, Germany, revised 22 Mar 2023.
    3. Mohajan, Devajit & Mohajan, Haradhan, 2023. "The Responses of an Organization for the Increase in Wage Rates: Profit Maximization Cases," MPRA Paper 118238, University Library of Munich, Germany, revised 10 Jun 2023.
    4. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Glaserian Grounded Theory and Straussian Grounded Theory: Two Standard Qualitative Research Approaches in Social Science," MPRA Paper 117017, University Library of Munich, Germany, revised 20 Feb 2023.
    5. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Broca Index: A Simple Tool to Measure Ideal Body Weight," MPRA Paper 116852, University Library of Munich, Germany, revised 18 Jan 2023.
    6. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Economic Investigation of Lagrange Multiplier if Cost of Inputs and Budget Size of a Firm Increase: A Profit Maximization Endeavor," MPRA Paper 117993, University Library of Munich, Germany, revised 07 May 2023.
    7. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Mathematical Model for Nonlinear Budget Constraint: Economic Activities on Increased Budget," MPRA Paper 117299, University Library of Munich, Germany, revised 17 Mar 2023.
    8. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Obesity and Its Related Diseases: A New Escalating Alarming in Global Health," MPRA Paper 116797, University Library of Munich, Germany, revised 05 Feb 2023.
    9. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Long-Term Regular Exercise Increases V̇O2max for Cardiorespiratory Fitness," MPRA Paper 116962, University Library of Munich, Germany, revised 04 Feb 2023.
    10. Mohajan, Haradhan, 2022. "Maximum profit ensured for industry sustainability," MPRA Paper 114801, University Library of Munich, Germany, revised 15 May 2022.
    11. Mohajan, Devajit & Mohajan, Haradhan, 2022. "Mathematical Analysis of SEIR Model to Prevent COVID-19 Pandemic," MPRA Paper 115858, University Library of Munich, Germany, revised 25 Aug 2022.
    12. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Various Problems Arise in Industrial Economics If Wage Rate Increases: A Study for Nonlinear Budget Constraint," MPRA Paper 117553, University Library of Munich, Germany, revised 04 Apr 2023.
    13. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Nonlinear Budget Constraint of a Local Industrial Firm of Bangladesh: A Profit Maximization Investigation," MPRA Paper 117324, University Library of Munich, Germany, revised 27 Mar 2023.
    14. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis for Utility Maximization: A Study on Lagrange Multipliers and Commodity Coupons," MPRA Paper 117077, University Library of Munich, Germany, revised 06 Jan 2023.
    15. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Effects of Various Inputs for Increased Interest Rate of Capital: A Nonlinear Budget Constraint Consideration," MPRA Paper 118134, University Library of Munich, Germany, revised 06 May 2023.
    16. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis of Inputs of an Organization: A Profit Maximization Exploration," MPRA Paper 117121, University Library of Munich, Germany, revised 12 Mar 2023.
    17. Mohajan, Devajit & Mohajan, Haradhan, 2023. "An Economical Study When Cost of Irregular Raw Materials of an Industry Increases for Nonlinear Budget Constraint," MPRA Paper 118176, University Library of Munich, Germany, revised 05 May 2023.
    18. Mohajan, Devajit & Mohajan, Haradhan, 2023. "A Study on Body Fat Percentage for Physical Fitness and Prevention of Obesity: A Two Compartment Model," MPRA Paper 117158, University Library of Munich, Germany, revised Feb 2023.
    19. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Bulimia Nervosa: A Psychiatric Problem of Disorder," MPRA Paper 117258, University Library of Munich, Germany, revised 17 Mar 2023.
    20. Mohajan, Devajit & Mohajan, Haradhan, 2023. "Sensitivity Analysis between Lagrange Multipliers and Consumer Budget: Utility Maximization Case," MPRA Paper 116907, University Library of Munich, Germany, revised 19 Feb 2023.

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    More about this item

    Keywords

    COVID-19; SARS-CoV-2; SIR Model; Immunity; Pandemics; Vaccination; Basic Reproduction Number;
    All these keywords.

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • I15 - Health, Education, and Welfare - - Health - - - Health and Economic Development
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

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