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Mathematical analysis of COVID-19 via new mathematical model

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  • Abdullah,
  • Ahmad, Saeed
  • Owyed, Saud
  • Abdel-Aty, Abdel-Haleem
  • Mahmoud, Emad E.
  • Shah, Kamal
  • Alrabaiah, Hussam

Abstract

We develop a new mathematical model by including the resistive class together with quarantine class and use it to investigate the transmission dynamics of the novel corona virus disease (COVID-19). Our developed model consists of four compartments, namely the susceptible class, S(t), the healthy (resistive) class, H(t), the infected class, I(t) and the quarantine class, Q(t). We derive basic properties like, boundedness and positivity, of our proposed model in a biologically feasible region. To discuss the local as well as the global behaviour of the possible equilibria of the model, we compute the threshold quantity. The linearization and Lyapunov function theory are used to derive conditions for the stability analysis of the possible equilibrium states. We present numerical simulations to support our investigations. The simulations are compared with the available real data for Wuhan city in China, where the infection was initially originated.

Suggested Citation

  • Abdullah, & Ahmad, Saeed & Owyed, Saud & Abdel-Aty, Abdel-Haleem & Mahmoud, Emad E. & Shah, Kamal & Alrabaiah, Hussam, 2021. "Mathematical analysis of COVID-19 via new mathematical model," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309760
    DOI: 10.1016/j.chaos.2020.110585
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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. Yousaf, Muhammad & Zahir, Samiha & Riaz, Muhammad & Hussain, Sardar Muhammad & Shah, Kamal, 2020. "Statistical analysis of forecasting COVID-19 for upcoming month in Pakistan," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    3. Bozkurt, Fatma & Yousef, Ali & Baleanu, Dumitru & Alzabut, Jehad, 2020. "A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    4. Sajjadi, Samaneh Sadat & Baleanu, Dumitru & Jajarmi, Amin & Pirouz, Hassan Mohammadi, 2020. "A new adaptive synchronization and hyperchaos control of a biological snap oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    5. Rahman, Ghaus ur & Shah, Kamal & Haq, Fazal & Ahmad, Naveed, 2018. "Host vector dynamics of pine wilt disease model with convex incidence rate," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 31-39.
    6. 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).
    7. Iqbal, Zafar & Ahmed, Nauman & Baleanu, Dumitru & Adel, Waleed & Rafiq, Muhammad & Aziz-ur Rehman, Muhammad & Alshomrani, Ali Saleh, 2020. "Positivity and boundedness preserving numerical algorithm for the solution of fractional nonlinear epidemic model of HIV/AIDS transmission," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    8. Abdo, Mohammed S. & Shah, Kamal & Wahash, Hanan A. & Panchal, Satish K., 2020. "On a comprehensive model of the novel coronavirus (COVID-19) under Mittag-Leffler derivative," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    9. Khater, Mostafa M.A. & Attia, Raghda A.M. & Abdel-Aty, Abdel-Haleem & Alharbi, W. & Lu, Dianchen, 2020. "Abundant analytical and numerical solutions of the fractional microbiological densities model in bacteria cell as a result of diffusion mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    10. Abdel-Aty, Abdel-Haleem & Khater, Mostafa M.A. & Dutta, Hemen & Bouslimi, Jamel & Omri, M., 2020. "Computational solutions of the HIV-1 infection of CD4+T-cells fractional mathematical model that causes acquired immunodeficiency syndrome (AIDS) with the effect of antiviral drug therapy," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
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    Cited by:

    1. Mitsuhiro Fukao & Etsuro Shioji, 2022. "Is There a Trade‐Off between COVID‐19 Control and Economic Activity? Implications from the Phillips Curve Debate," Asian Economic Policy Review, Japan Center for Economic Research, vol. 17(1), pages 66-85, January.
    2. Rahman, Mati ur & Ahmad, Saeed & Matoog, R.T. & Alshehri, Nawal A. & Khan, Tahir, 2021. "Study on the mathematical modelling of COVID-19 with Caputo-Fabrizio operator," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    3. Otunuga, Olusegun Michael, 2021. "Time-dependent probability distribution for number of infection in a stochastic SIS model: case study COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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