Global stability of equilibria of a diffusive SEIR epidemic model with nonlinear incidence

Han, Shuyu; Lei, Chengxia

doi:10.1016/j.aml.2019.05.045

Cited by 45 publications

(18 citation statements)

References 32 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Over the last several decades, infectious disease models have gained increasing recognition as a powerful tool to reveal the mechanism spread of diseases. Based on systems design with deterministic and stochastic models, there are a lot of literatures to investigate the transmission rates of diseases, see [ 1 – 27 ] and the references therein. One of classic epidemic models is the SEIR model, which subdivides a homogeneous host population into categories containing susceptible, exposed, infectious and recovered individuals, with their population sizes denoted by S , E , I and R , respectively.…”

Section: Introductionmentioning

confidence: 99%

A stochastic epidemic model with infectivity in incubation period and homestead–isolation on the susceptible

Shangguan

Liu

Wang

et al. 2021

J. Appl. Math. Comput.

View full text Add to dashboard Cite

A stochastic epidemic model with infectivity rate in incubation period and homestead–isolation on the susceptible is developed with the aim of revealing the effect of stochastic white noise on the long time behavior. A good understanding of extinction and strong persistence in the mean of the disease is obtained. Also, we derive sufficient criteria for the existence of a unique ergodic stationary distribution of the model. Our theoretical results show that the suitably large noise can make the disease extinct while the relatively small noise is advantageous for persistence of the disease and stationary distribution.

show abstract

Section: Introductionmentioning

confidence: 99%

A stochastic epidemic model with infectivity in incubation period and homestead–isolation on the susceptible

Shangguan

Liu

Wang

et al. 2021

J. Appl. Math. Comput.

View full text Add to dashboard Cite

show abstract

“…It includes several basic and improved models, such as susceptible-infected-recovered (SIR), susceptible-infected-susceptible (SIS), SEIR, and so on, among which the SEIR model is a typical example that takes the incubation period into account 19 . The SEIR model has played a positive part in studying the transmission speed and route of infectious diseases, so as to guide the effective prevention and control over the diseases 20,21 . Many scholars have used the SEIR model in the research into the transmission risk of the COVID-19 and in the inoculation of vaccines and control of the epidemic 23 .…”

Section: Introductionmentioning

confidence: 99%

Effect evaluation of non-pharmaceutical interventions taken in China to contain the COVID-19 epidemic based on the susceptible-exposed-infected-recovered model

Shou

Wang

Lou

2021

Technological Forecasting and Social Change

View full text Add to dashboard Cite

This paper takes confirmed cases of COVID-19 from January 20 to March 18, 2020 as the sample set to establish the susceptible-exposed-infected-recovered (SEIR) model. By evaluating effects of different non-pharmaceutical interventions (NPIs), the research expects to provide references to other countries for formulating corresponding policies. This article divides all non-pharmaceutical interventions into three types according to their different roles. The results show that type-A and type-B non-pharmaceutical interventions both can delay the timing of large-scale infections of the susceptible population, timing of the number of exposed individuals to peak, and timing of peaking of the number of infected cases, as well as decrease the peak number of exposed cases. Moreover, type-B non-pharmaceutical interventions have more significant effects on susceptible and exposed populations. Type-C non-pharmaceutical interventions for improving the recovery rate of patients are able to effectively reduce the peak number of patients, greatly decrease the slope of the curve for the number of infected cases, substantially improve the recovery rate, and lower the mortality rate; however, these non-pharmaceutical interventions do not greatly delay the timing of the number of infected cases to peak. And based on the above analysis, we proposed some suggestions.

show abstract

“…Cooke and Driessche [4] proposed and investigated a classical SEIR epidemic model, which has became the most important model in diseases control. Therefore, ODEs, PDEs and SDEs are employed to study SEIR epidemic models, and some results could be found in literatures [5][6][7][8]. Zhao et al [9] investigated an extended SEIR epidemic model with non-communicability in incubation period.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an SEIR model with infectivity in incubation period and homestead-isolation on the susceptible

Jiao

Liu

Cai

2020

Applied Mathematics Letters

View full text Add to dashboard Cite

In this paper, we present an SEIR epidemic model with infectivity in incubation period and homestead-isolation on the susceptible. We prove that the infectionfree equilibrium point is locally and globally asymptotically stable with condition R 0 < 1. We also prove that the positive equilibrium point is locally and globally asymptotically stable with condition R 0 > 1. Numerical simulations are employed to illustrate our results. In the absence of vaccines or antiviral drugs for the virus, our results suggest that the governments should strictly implement the isolation system to make every effort to curb propagation of disease during the epidemic.

show abstract

Global stability of equilibria of a diffusive SEIR epidemic model with nonlinear incidence

Cited by 45 publications

References 32 publications

A stochastic epidemic model with infectivity in incubation period and homestead–isolation on the susceptible

A stochastic epidemic model with infectivity in incubation period and homestead–isolation on the susceptible

Effect evaluation of non-pharmaceutical interventions taken in China to contain the COVID-19 epidemic based on the susceptible-exposed-infected-recovered model

Dynamics of an SEIR model with infectivity in incubation period and homestead-isolation on the susceptible

Contact Info

Product

Resources

About