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A mathematical model for COVID-19 transmission dynamics with a case study of India

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  • Samui, Piu
  • Mondal, Jayanta
  • Khajanchi, Subhas

Abstract

The ongoing COVID-19 has precipitated a major global crisis, with 968,117 total confirmed cases, 612,782 total recovered cases and 24,915 deaths in India as of July 15, 2020. In absence of any effective therapeutics or drugs and with an unknown epidemiological life cycle, predictive mathematical models can aid in understanding of both coronavirus disease control and management. In this study, we propose a compartmental mathematical model to predict and control the transmission dynamics of COVID-19 pandemic in India with epidemic data up to April 30, 2020. We compute the basic reproduction number R0, which will be used further to study the model simulations and predictions. We perform local and global stability analysis for the infection free equilibrium point E0 as well as an endemic equilibrium point E* with respect to the basic reproduction number R0. Moreover, we showed the criteria of disease persistence for R0 > 1. We conduct a sensitivity analysis in our coronavirus model to determine the relative importance of model parameters to disease transmission. We compute the sensitivity indices of the reproduction number R0 (which quantifies initial disease transmission) to the estimated parameter values. For the estimated model parameters, we obtained R0=1.6632, which shows the substantial outbreak of COVID-19 in India. Our model simulation demonstrates that the disease transmission rate βs is more effective to mitigate the basic reproduction number R0. Based on estimated data, our model predict that about 60 days the peak will be higher for COVID-19 in India and after that the curve will plateau but the coronavirus diseases will persist for a long time.

Suggested Citation

  • Samui, Piu & Mondal, Jayanta & Khajanchi, Subhas, 2020. "A mathematical model for COVID-19 transmission dynamics with a case study of India," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305695
    DOI: 10.1016/j.chaos.2020.110173
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    References listed on IDEAS

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    1. Khajanchi, Subhas & Das, Dhiraj Kumar & Kar, Tapan Kumar, 2018. "Dynamics of tuberculosis transmission with exogenous reinfections and endogenous reactivation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 52-71.
    2. 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).
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    15. Bera, Sovan & Khajanchi, Subhas & Roy, Tapan Kumar, 2022. "Dynamics of an HTLV-I infection model with delayed CTLs immune response," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    16. Zhang, Zhenzhen & Ma, Xia & Zhang, Yongxin & Sun, Guiquan & Zhang, Zi-Ke, 2023. "Identifying critical driving factors for human brucellosis in Inner Mongolia, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 626(C).
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    18. El-Mesady, A. & Elsonbaty, Amr & Adel, Waleed, 2022. "On nonlinear dynamics of a fractional order monkeypox virus model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
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