Dynamics of Epidemic Spreading Model With Distributed Delay on Heterogeneous Network

Liu, Qiming; Sun, Meici

doi:10.1142/s0218339017500097

Cited by 3 publications

(1 citation statement)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One dose of vaccine does not protect all receivers because vaccine-induced immunity is lost after some period of time [17,18]. Time delays are significant in the transmission process of epidemics and arise due to delayed feedback especially the period for waning vaccine-induced immunity, latent period of infection, the infectious period, and the immunity period [19][20][21]. Among the mathematical tools currently used, delay differential models with time delay have attracted attention in the field of science especially modeling infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Mbabazi¹,

Mugisha

Kimathi

2019

Abstract and Applied Analysis

View full text Add to dashboard Cite

In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is asymptotically stable if the control reproduction ratioR0is less than unity and unstable otherwise. The stability of equilibria with delays shows that the endemic equilibrium is locally stable without delays and stable if the delays are under conditions. The existence of Hopf-bifurcation is investigated and transversality conditions are proved. The model results suggest that, as the respective delays exceed some critical value past the endemic equilibrium, the system loses stability through the process of local birth or death of oscillations. Further, a decrease or an increase in the delays leads to asymptotic stability or instability of the endemic equilibrium, respectively. The analytical results are supported by numerical simulations.

show abstract

Section: Introductionmentioning

confidence: 99%

Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Mbabazi¹,

Mugisha

Kimathi

2019

Abstract and Applied Analysis

View full text Add to dashboard Cite

show abstract

A Network Virus Propagation Model with Distributed Infectious Period Delay in Internet

Liu¹

2019

IOP Conf. Ser.: Earth Environ. Sci.

View full text Add to dashboard Cite

An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

Sun¹,

Liu

2021

MBE

View full text Add to dashboard Cite

<abstract><p>An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 < 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 > 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.</p></abstract>

show abstract

Dynamics of Epidemic Spreading Model With Distributed Delay on Heterogeneous Network

Cited by 3 publications

References 23 publications

Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

Hopf-Bifurcation Analysis of Pneumococcal Pneumonia with Time Delays

A Network Virus Propagation Model with Distributed Infectious Period Delay in Internet

An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

Contact Info

Product

Resources

About