# American Institute of Mathematical Sciences

doi: 10.3934/dcdsb.2021278
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

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

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

* Corresponding author: Yepeng Xing

Received  June 2021 Revised  October 2021 Early access November 2021

Fund Project: 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.

Citation: Yanfei Zhao, Yepeng Xing. A delayed dynamical model for COVID-19 therapy with defective interfering particles and artificial antibodies. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021278
##### References:

show all references

##### References:
Artificial antibodies block SARS-CoV-2 from infecting cells
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 $W$
When $\mathcal{R}_0<1$, $\tau = 1$, the disease-free equilibrium $E_0$ is globally asymptotically stable
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
When $1<R_1<\mathcal{R}_0$, $\tau = 1.6$, the infectious equilibrium with defective intefering particles $E_2$ is locally asymptotically stable
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
 [1] Nitu Kumari, Sumit Kumar, Sandeep Sharma, Fateh Singh, Rana Parshad. Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021170 [2] Jorge Rebaza. On a model of COVID-19 dynamics. Electronic Research Archive, 2021, 29 (2) : 2129-2140. doi: 10.3934/era.2020108 [3] Hailiang Liu, Xuping Tian. Data-driven optimal control of a seir model for COVID-19. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021093 [4] Tailei Zhang, Zhimin Li. Analysis of COVID-19 epidemic transmission trend based on a time-delayed dynamic model. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021088 [5] Tao Zheng, Yantao Luo, Xinran Zhou, Long Zhang, Zhidong Teng. Spatial dynamic analysis for COVID-19 epidemic model with diffusion and Beddington-DeAngelis type incidence. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021154 [6] Emiliano Alvarez, Juan Gabriel Brida, Lucía Rosich, Erick Limas. Analysis of communities of countries with similar dynamics of the COVID-19 pandemic evolution. Journal of Dynamics & Games, 2022, 9 (1) : 75-96. doi: 10.3934/jdg.2021026 [7] Haitao Song, Fang Liu, Feng Li, Xiaochun Cao, Hao Wang, Zhongwei Jia, Huaiping Zhu, Michael Y. Li, Wei Lin, Hong Yang, Jianghong Hu, Zhen Jin. Modeling the second outbreak of COVID-19 with isolation and contact tracing. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021294 [8] Amin Reza Kalantari Khalil Abad, Farnaz Barzinpour, Seyed Hamid Reza Pasandideh. A novel separate chance-constrained programming model to design a sustainable medical ventilator supply chain network during the Covid-19 pandemic. Journal of Industrial & Management Optimization, 2022  doi: 10.3934/jimo.2021234 [9] John Leventides, Costas Poulios, Georgios Alkis Tsiatsios, Maria Livada, Stavros Tsipras, Konstantinos Lefcaditis, Panagiota Sargenti, Aleka Sargenti. Systems theory and analysis of the implementation of non pharmaceutical policies for the mitigation of the COVID-19 pandemic. Journal of Dynamics & Games, 2021, 8 (3) : 167-186. doi: 10.3934/jdg.2021004 [10] R. Ouifki, M. L. Hbid, O. Arino. Attractiveness and Hopf bifurcation for retarded differential equations. Communications on Pure & Applied Analysis, 2003, 2 (2) : 147-158. doi: 10.3934/cpaa.2003.2.147 [11] Sun Yi, Patrick W. Nelson, A. Galip Ulsoy. Delay differential equations via the matrix lambert w function and bifurcation analysis: application to machine tool chatter. Mathematical Biosciences & Engineering, 2007, 4 (2) : 355-368. doi: 10.3934/mbe.2007.4.355 [12] Janusz Mierczyński, Sylvia Novo, Rafael Obaya. Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations. Communications on Pure & Applied Analysis, 2020, 19 (4) : 2235-2255. doi: 10.3934/cpaa.2020098 [13] Runxia Wang, Haihong Liu, Fang Yan, Xiaohui Wang. Hopf-pitchfork bifurcation analysis in a coupled FHN neurons model with delay. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 523-542. doi: 10.3934/dcdss.2017026 [14] Timothy C. Reluga, Jan Medlock, Alison Galvani. The discounted reproductive number for epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (2) : 377-393. doi: 10.3934/mbe.2009.6.377 [15] Dimitri Breda, Sara Della Schiava. Pseudospectral reduction to compute Lyapunov exponents of delay differential equations. Discrete & Continuous Dynamical Systems - B, 2018, 23 (7) : 2727-2741. doi: 10.3934/dcdsb.2018092 [16] Leonid A. Bunimovich. Dynamical systems and operations research: A basic model. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 209-218. doi: 10.3934/dcdsb.2001.1.209 [17] Sigurdur Hafstein, Skuli Gudmundsson, Peter Giesl, Enrico Scalas. Lyapunov function computation for autonomous linear stochastic differential equations using sum-of-squares programming. Discrete & Continuous Dynamical Systems - B, 2018, 23 (2) : 939-956. doi: 10.3934/dcdsb.2018049 [18] Tomás Caraballo, Francisco Morillas, José Valero. On differential equations with delay in Banach spaces and attractors for retarded lattice dynamical systems. Discrete & Continuous Dynamical Systems, 2014, 34 (1) : 51-77. doi: 10.3934/dcds.2014.34.51 [19] Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with state-dependent delay. Discrete & Continuous Dynamical Systems, 2017, 37 (7) : 3939-3961. doi: 10.3934/dcds.2017167 [20] Neville J. Ford, Stewart J. Norton. Predicting changes in dynamical behaviour in solutions to stochastic delay differential equations. Communications on Pure & Applied Analysis, 2006, 5 (2) : 367-382. doi: 10.3934/cpaa.2006.5.367

2020 Impact Factor: 1.327