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Mathematical modelling of COVID-19: A case study of Italy

Author

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  • Ghosh, Jayanta Kumar
  • Biswas, Sudhanshu Kumar
  • Sarkar, Susmita
  • Ghosh, Uttam

Abstract

This manuscript describes a mathematical epidemiological model of COVID-19 to investigate the dynamics of this pandemic disease and we have fitted this model to the current COVID-19 cases in Italy. We have obtained the basic reproduction number which plays a crucial role on the stability of disease free equilibrium point. Backward bifurcation with respect to the cure rate of treatment occurs conditionally. It is clear from the sensitivity analysis that the developments of self immunities with proper maintaining of social distancing of the exposed and asymptomatic individuals play key role for controlling the disease. We have validated the model by considering the COVID-19 cases of Italy and the future situations of epidemicity in Italy have been predicted from the model. We have estimated the basic reproduction number for the COVID-19 outbreak in Italy and effective reproduction number has also been studied. Finally, an optimal control model has been formulated and solved to realize the positive impacts of adapting lock down by many countries for maintaining social distancing.

Suggested Citation

  • Ghosh, Jayanta Kumar & Biswas, Sudhanshu Kumar & Sarkar, Susmita & Ghosh, Uttam, 2022. "Mathematical modelling of COVID-19: A case study of Italy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 1-18.
    • Handle: RePEc:eee:matcom:v:194:y:2022:i:c:p:1-18
    DOI: 10.1016/j.matcom.2021.11.008
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    Cited by:

    1. Ahmed, Marzia & Sulaiman, Mohd Herwan & Mohamad, Ahmad Johari & Rahman, Mostafijur, 2024. "Gooseneck barnacle optimization algorithm: A novel nature inspired optimization theory and application," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 248-265.
    2. 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.
    3. Kumar, Arjun & Dubey, Uma S. & Dubey, Balram, 2024. "The impact of social media advertisements and treatments on the dynamics of infectious diseases with optimal control strategies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 219(C), pages 50-86.
    4. Xu, Changjin & Liu, Zixin & Pang, Yicheng & Akgül, Ali, 2023. "Stochastic analysis of a COVID-19 model with effects of vaccination and different transition rates: Real data approach," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    5. Carmen Legarreta & Manuel De la Sen & Santiago Alonso-Quesada, 2024. "On the Properties of a Newly Susceptible, Non-Seriously Infected, Hospitalized, and Recovered Subpopulation Epidemic Model," Mathematics, MDPI, vol. 12(2), pages 1-34, January.

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