Article Contents
Article Contents

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

• * Corresponding author: Yepeng Xing

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

• 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.

 Citation:

• 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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