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A model based study on the dynamics of COVID-19: Prediction and control

Author

Listed:
  • Mandal, Manotosh
  • Jana, Soovoojeet
  • Nandi, Swapan Kumar
  • Khatua, Anupam
  • Adak, Sayani
  • Kar, T.K.

Abstract

As there is no vaccination and proper medicine for treatment, the recent pandemic caused by COVID-19 has drawn attention to the strategies of quarantine and other governmental measures, like lockdown, media coverage on social isolation, and improvement of public hygiene, etc to control the disease. The mathematical model can help when these intervention measures are the best strategies for disease control as well as how they might affect the disease dynamics. Motivated by this, in this article, we have formulated a mathematical model introducing a quarantine class and governmental intervention measures to mitigate disease transmission. We study a thorough dynamical behavior of the model in terms of the basic reproduction number. Further, we perform the sensitivity analysis of the essential reproduction number and found that reducing the contact of exposed and susceptible humans is the most critical factor in achieving disease control. To lessen the infected individuals as well as to minimize the cost of implementing government control measures, we formulate an optimal control problem, and optimal control is determined. Finally, we forecast a short-term trend of COVID-19 for the three highly affected states, Maharashtra, Delhi, and Tamil Nadu, in India, and it suggests that the first two states need further monitoring of control measures to reduce the contact of exposed and susceptible humans.

Suggested Citation

  • Mandal, Manotosh & Jana, Soovoojeet & Nandi, Swapan Kumar & Khatua, Anupam & Adak, Sayani & Kar, T.K., 2020. "A model based study on the dynamics of COVID-19: Prediction and control," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    • Handle: RePEc:eee:chsofr:v:136:y:2020:i:c:s0960077920302897
    DOI: 10.1016/j.chaos.2020.109889
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    References listed on IDEAS

    as
    1. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Torres, Delfim F.M., 2020. "Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Fanelli, Duccio & Piazza, Francesco, 2020. "Analysis and forecast of COVID-19 spreading in China, Italy and France," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    3. Chakraborty, Tanujit & Ghosh, Indrajit, 2020. "Real-time forecasts and risk assessment of novel coronavirus (COVID-19) cases: A data-driven analysis," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    4. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
    5. Ribeiro, Matheus Henrique Dal Molin & da Silva, Ramon Gomes & Mariani, Viviana Cocco & Coelho, Leandro dos Santos, 2020. "Short-term forecasting COVID-19 cumulative confirmed cases: Perspectives for Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    6. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
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