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Mathematical model, forecast and analysis on the spread of COVID-19

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  • Mishra, Bimal Kumar
  • Keshri, Ajit Kumar
  • Saini, Dinesh Kumar
  • Ayesha, Syeda
  • Mishra, Binay Kumar
  • Rao, Yerra Shankar

Abstract

Pandemic COVID-19 which has infected more than 35,027,546 people and death more than 1,034,837 people in 235 countries as on October 05, 2020 has created a chaos across the globe. In this paper, we develop a compartmental epidemic model to understand the spreading behaviour of the disease in human population with a special case of Bhilwara, a desert town in India where successful control measures TTT (tracking, testing and treatment) was adopted to curb the disease in the very early phase of the spread of the disease in India. Local and global asymptotic stability is established for endemic equilibrium. Extensive numerical simulations with real parametric values are performed to validate the analytical results. Trend analysis of fatality rate, infection rate, and impact of lockdown is performed for USA, European countries, Russia, Iran, China, Japan, S. Korea with a comparative assessment by India. Kruskal - Wallis test is performed to test the null hypothesis for infected cases during the four lockdown phases in India. It has been observed that there is a significant difference at both 95% and 99% confidence interval in the infected cases, recovered cases and the case fatality rate during all the four phases of the lockdown.

Suggested Citation

  • Mishra, Bimal Kumar & Keshri, Ajit Kumar & Saini, Dinesh Kumar & Ayesha, Syeda & Mishra, Binay Kumar & Rao, Yerra Shankar, 2021. "Mathematical model, forecast and analysis on the spread of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:chsofr:v:147:y:2021:i:c:s0960077921003490
    DOI: 10.1016/j.chaos.2021.110995
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    References listed on IDEAS

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    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. Soukhovolsky, Vladislav & Kovalev, Anton & Pitt, Anne & Kessel, Boris, 2020. "A new modelling of the COVID 19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    3. Kassa, Semu M. & Njagarah, John B.H. & Terefe, Yibeltal A., 2020. "Analysis of the mitigation strategies for COVID-19: From mathematical modelling perspective," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Fanelli, Duccio & Piazza, Francesco, 2020. "Analysis and forecast of COVID-19 spreading in China, Italy and France," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    5. Mishra, Bimal Kumar & Keshri, Ajit Kumar & Rao, Yerra Shankar & Mishra, Binay Kumar & Mahato, Buddhadeo & Ayesha, Syeda & Rukhaiyyar, Bansidhar Prasad & Saini, Dinesh Kumar & Singh, Aditya Kumar, 2020. "COVID-19 created chaos across the globe: Three novel quarantine epidemic models," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    6. Tagliazucchi, E. & Balenzuela, P. & Travizano, M. & Mindlin, G.B. & Mininni, P.D., 2020. "Lessons from being challenged by COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 137(C).
    7. 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).
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    Cited by:

    1. Prem Kumar, R. & Santra, P.K. & Mahapatra, G.S., 2023. "Global stability and analysing the sensitivity of parameters of a multiple-susceptible population model of SARS-CoV-2 emphasising vaccination drive," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 741-766.

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