The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

Abstract Background The global spread of the novel coronavirus pneumonia is still continuing, and a new round of more serious outbreaks has even begun in some countries. In this context, this paper studies the dynamics of a type of delayed reaction-diffusion novel coronavirus pneumonia model with re...

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Autores principales:	Cheng-Cheng Zhu, Jiang Zhu
Formato:	article
Lenguaje:	EN
Publicado:	BMC 2021
Materias:	Self-limiting epidemics COVID-19 Global exponential attractor Delayed Temporal-spatial heterogeneous Infectious and parasitic diseases RC109-216
Acceso en línea:	https://doaj.org/article/9060e9ff7720400f90fbc99cc3724178
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spelling	oai:doaj.org-article:9060e9ff7720400f90fbc99cc37241782021-11-14T12:44:14ZThe effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous10.1186/s12879-021-06670-y1471-2334https://doaj.org/article/9060e9ff7720400f90fbc99cc37241782021-11-01T00:00:00Zhttps://doi.org/10.1186/s12879-021-06670-yhttps://doaj.org/toc/1471-2334Abstract Background The global spread of the novel coronavirus pneumonia is still continuing, and a new round of more serious outbreaks has even begun in some countries. In this context, this paper studies the dynamics of a type of delayed reaction-diffusion novel coronavirus pneumonia model with relapse and self-limiting treatment in a temporal-spatial heterogeneous environment. Methods First, focus on the self-limiting characteristics of COVID-19, incorporate the relapse and self-limiting treatment factors into the diffusion model, and study the influence of self-limiting treatment on the diffusion of the epidemic. Second, because the traditional Lyapunov stability method is difficult to determine the spread of the epidemic with relapse and self-limiting treatment, we introduce a completely different method, relying on the existence conditions of the exponential attractor of our newly established in the infinite-dimensional dynamic system to determine the diffusion of novel coronavirus pneumonia. Third, relapse and self-limiting treatment have led to a change in the structure of the delayed diffusion COVID-19 model, and the traditional basic reproduction number $$R_0$$ R 0 no longer has threshold characteristics. With the help of the Krein-Rutman theorem and the eigenvalue method, we studied the threshold characteristics of the principal eigenvalue and found that it can be used as a new threshold to describe the diffusion of the epidemic. Results Our results prove that the principal eigenvalue $$\uplambda ^{*}$$ λ ∗ of the delayed reaction-diffusion COVID-19 system with relapse and self-limiting treatment can replace the basic reproduction number $$R_0$$ R 0 to describe the threshold effect of disease transmission. Combine with the latest official data and the prevention and control strategies, some numerical simulations on the stability and global exponential attractiveness of the diffusion of the COVID-19 epidemic in China and the USA are given. Conclusions Through the comparison of numerical simulations, we find that self-limiting treatment can significantly promote the prevention and control of the epidemic. And if the free activities of asymptomatic infected persons are not restricted, it will seriously hinder the progress of epidemic prevention and control.Cheng-Cheng ZhuJiang ZhuBMCarticleSelf-limiting epidemicsCOVID-19Global exponential attractorDelayedTemporal-spatial heterogeneousInfectious and parasitic diseasesRC109-216ENBMC Infectious Diseases, Vol 21, Iss 1, Pp 1-22 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Self-limiting epidemics COVID-19 Global exponential attractor Delayed Temporal-spatial heterogeneous Infectious and parasitic diseases RC109-216
spellingShingle	Self-limiting epidemics COVID-19 Global exponential attractor Delayed Temporal-spatial heterogeneous Infectious and parasitic diseases RC109-216 Cheng-Cheng Zhu Jiang Zhu The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous
description	Abstract Background The global spread of the novel coronavirus pneumonia is still continuing, and a new round of more serious outbreaks has even begun in some countries. In this context, this paper studies the dynamics of a type of delayed reaction-diffusion novel coronavirus pneumonia model with relapse and self-limiting treatment in a temporal-spatial heterogeneous environment. Methods First, focus on the self-limiting characteristics of COVID-19, incorporate the relapse and self-limiting treatment factors into the diffusion model, and study the influence of self-limiting treatment on the diffusion of the epidemic. Second, because the traditional Lyapunov stability method is difficult to determine the spread of the epidemic with relapse and self-limiting treatment, we introduce a completely different method, relying on the existence conditions of the exponential attractor of our newly established in the infinite-dimensional dynamic system to determine the diffusion of novel coronavirus pneumonia. Third, relapse and self-limiting treatment have led to a change in the structure of the delayed diffusion COVID-19 model, and the traditional basic reproduction number $$R_0$$ R 0 no longer has threshold characteristics. With the help of the Krein-Rutman theorem and the eigenvalue method, we studied the threshold characteristics of the principal eigenvalue and found that it can be used as a new threshold to describe the diffusion of the epidemic. Results Our results prove that the principal eigenvalue $$\uplambda ^{*}$$ λ ∗ of the delayed reaction-diffusion COVID-19 system with relapse and self-limiting treatment can replace the basic reproduction number $$R_0$$ R 0 to describe the threshold effect of disease transmission. Combine with the latest official data and the prevention and control strategies, some numerical simulations on the stability and global exponential attractiveness of the diffusion of the COVID-19 epidemic in China and the USA are given. Conclusions Through the comparison of numerical simulations, we find that self-limiting treatment can significantly promote the prevention and control of the epidemic. And if the free activities of asymptomatic infected persons are not restricted, it will seriously hinder the progress of epidemic prevention and control.
format	article
author	Cheng-Cheng Zhu Jiang Zhu
author_facet	Cheng-Cheng Zhu Jiang Zhu
author_sort	Cheng-Cheng Zhu
title	The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous
title_short	The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous
title_full	The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous
title_fullStr	The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous
title_full_unstemmed	The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous
title_sort	effect of self-limiting on the prevention and control of the diffuse covid-19 epidemic with delayed and temporal-spatial heterogeneous
publisher	BMC
publishDate	2021
url	https://doaj.org/article/9060e9ff7720400f90fbc99cc3724178
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The effect of self-limiting on the prevention and control of the diffuse COVID-19 epidemic with delayed and temporal-spatial heterogeneous

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