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

Yanfei Zhao; Yepeng Xing

doi:10.3934/dcdsb.2021278

Article Contents

2022, Volume 27, Issue 10: 5367-5387. Doi: 10.3934/dcdsb.2021278

This issue Previous Article Next Article Nonstationary homoclinic orbit for an infinite-dimensional fractional reaction-diffusion system

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

Yanfei Zhao and
Yepeng Xing^,

Department of Applied Mathematics, Shanghai Normal University, Road Guilin No.100, 200234, Shanghai, China

^* Corresponding author: Yepeng Xing
^* Corresponding author: Yepeng Xing

Received: May 31, 2021

Revised: September 30, 2021

Early access: November 2021

Published: October 2022

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

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Abstract

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.

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

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

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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 $

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

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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

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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

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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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