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A delayed dynamical model for COVID-19 therapy with defective interfering particles and artificial antibodies

  • * Corresponding author: Yepeng Xing

    * Corresponding author: Yepeng Xing

The authors were supported by National Natural Science Foundation of China (No.12071297, No.12171320)

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  • In this paper, we use delay differential equations to propose a mathematical model for COVID-19 therapy with both defective interfering particles and artificial antibodies. For this model, the basic reproduction number $ \mathcal{R}_0 $ is given and its threshold properties are discussed. When $ \mathcal{R}_0<1 $, the disease-free equilibrium $ E_0 $ is globally asymptotically stable. When $ \mathcal{R}_0>1 $, $ E_0 $ becomes unstable and the infectious equilibrium without defective interfering particles $ E_1 $ comes into existence. There exists a positive constant $ R_1 $ such that $ E_1 $ is globally asymptotically stable when $ R_1<1<\mathcal{R}_0 $. Further, when $ R_1>1 $, $ E_1 $ loses its stability and infectious equilibrium with defective interfering particles $ E_2 $ occurs. There exists a constant $ R_2 $ such that $ E_2 $ is asymptotically stable without time delay if $ 1<R_1<\mathcal{R}_0<R_2 $ and it loses its stability via Hopf bifurcation as the time delay increases. Numerical simulation is also presented to demonstrate the applicability of the theoretical predictions.

    Mathematics Subject Classification: Primary: 92C60; Secondary: 34k20, 34k60.


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  • Figure 1.  Artificial antibodies block SARS-CoV-2 from infecting cells

    Figure 2.  Pathogen viral particles $ V $ infect normal cells $ T $ producing infected cells $ I $; $ W $ can produce in infected cells; artificial antibodies $ F $ bind to virus, infected cells are able to produce virus $ V $ and defective interfering particles $ W $

    Figure 3.  When $ \mathcal{R}_0<1 $, $ \tau = 1 $, the disease-free equilibrium $ E_0 $ is globally asymptotically stable

    Figure 4.  When $ R_1<1<\mathcal{R}_0 $, $ \tau = 0.8, 1,1.5 $, the infectious equilibrium without defective interfering particles $ E_1 $ is globally asymptotically stable

    Figure 5.  When $ 1<R_1<\mathcal{R}_0 $, $ \tau = 1.6 $, the infectious equilibrium with defective intefering particles $ E_2 $ is locally asymptotically stable

    Figure 6.  When $ 1<R_1<\mathcal{R}_0 $, $ \tau = 1.6 $, the infectious equilibrium with defective interfering particles $ E_2 $ showing bifurcation to a stable limit cycle

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