Pattern mechanism in stochastic SIR networks with ER connectivity

Zheng, Qianqian; Shen, Jianwei; Xu, Yong; Pandey, V. C.; Guan, Linan

doi:10.1016/j.physa.2022.127765

Cited by 14 publications

(6 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further increase in susceptibility rate induce subcritical Hopf bifurcation (figure 2(d)) leading to endemic state (figure 2(c)). This endemic state suppresses the periodic outbreaks [39]. The evolution of the epidemic initially shows outbreaks with small amplitude and then a periodic explosion as (figure 2(d)) for k 2 = 0.1, and eventually, large outbreaks lead to endemic.…”

Section: Driving Factors Causing Periodic Covid-19 Wavesmentioning

confidence: 90%

Spatiotemporal dynamics of periodic waves in SIR model with driving factors

et al. 2023

View full text Add to dashboard Cite

The world is facing Covid-19 waves and the overall pattern of confirmed cases shows periodic oscillations. In this paper, we investigate the spatio-temporal spread of Covid-19 in the network-organized SIR model with an extrinsic incubation period of the driving factors. Firstly, Our analysis shows the occurrence of Hopf bifurcation and periodic outbreaks which is consistent with the actual spread of Covid-19. And we investigate periodic waves on spatial scales using Turing instability, and the spread of infected individuals increases the localized hot spots. We study the effect of the incubation period, more incubation periods generate Turing instability resulting in periodic outbreaks. There is an occurrence of bursting states at peaks of periodic waves due to small diffusion of infected and susceptible, which means stable and unstable areas try to convert each other due to high competition among nodes. Also, We note the disappearance of these bursts when infected and susceptible individuals' movements are easier, thus dominance of infected individuals prevails everywhere. Effective policy interventions and seasonality can cause periodic perturbations in the model, and therefore we study the impact of these perturbations on the spread of Covid-19. Periodic perturbations on the driving factors, infected individuals show co-existing spatial patterns. Chaotic outbreak becomes periodic outbreaks through alternating periodic or period-2 outbreaks as we regulate the amplitude and frequency of infected individuals. In short, regulations can erase period-2 and chaotic spread through policy interventions.

show abstract

Section: Driving Factors Causing Periodic Covid-19 Wavesmentioning

confidence: 90%

Spatiotemporal dynamics of periodic waves in SIR model with driving factors

et al. 2023

View full text Add to dashboard Cite

show abstract

“…However, the diffusion process may affect the stationary behavior of the epidemic model in the small-size network under some specific control parameters. Zheng et al found periodic outbreaks via Turing instabilities caused by the diffusion, delay, and driving factors [14][15][16]. The equations for network-averaged densities are written as…”

Section: Hmf Analysismentioning

confidence: 99%

“…In the metapopulation models, we consider that individuals randomly move to connected nodes after all processes are completed in every node. Recently, Zheng et al presented the effects of the diffusion, delay, and driving factors on the stationary behavior of epidemic model on the small-size network with 100 nodes by calculating the eigenvalues of the Laplacian matrix of the network [14][15][16]. Infection processes are assumed to be frequency-dependent, which means that infection rate does not depend on the population [4].…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium phase transitions in metapopulation models of infectious diseases on heterogeneous networks

Kwon,

Park

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

We study two meta-population models of infectious diseases in heterogeneous networks. We distinguish between asymptomatic and symptomatic infections and these two go through the diﬀerent courses of infection and recovery. We consider that asymptomatic infections are described by an SIS model and symptomatic infections by an SIR or SIRS model depending on the immunity upon recovery. By introducing the probability of being infected asymptomatically, we combine an SIS model for asymptomatic infections with an SIR or SIRS model for symptomatic infections to obtain the SIS-SIR and SIS-SIRS models. We use a heterogeneous mean-ﬁeld theory and Monte Carlo simulations to analyze two models and ﬁnd that both models undergo nonequilibrium continuous phase transitions from the endemic phase to the disease-free phase at certain critical thresholds as we vary the proportion of asymptomatic infections. It suggests that it may be possible to maintain the population in the disease-free phase by controlling the proportion of asymptomatic infections. The SIS-SIRS model shows that asymptomatic infection drives symptomatic infection and vice versa. In addition, the spreading of infections eventually ceases as the population decreases even at a ﬁxed proportion of asymptomatic infections corresponding to the endemic phase. The results provide a theoretical basis for understanding the epidemiological facts that social distancing and reducing asymptomatic infections are important factors in optimizing quarantine measures to prevent the epidemic outbreaks of infectious diseases.epidemic outbreaks of infectious diseases.

show abstract

“…Zheng et al constructed a network-organized SIR model to show the effects of the network structured entropy and diffusion on the bifurcation and Turing instability. They explained the dynamical mechanism of the periodic outbreak and endemic diseases through wavenumber [15], after that, the influences of directed network [16], driving factors [17] and time-delay network [18] on the pattern formation of epidemic model are given. Pattern formation provides new insight into the spread of infectious diseases, and relationships between pattern formation and the region of infectious diseases were introduced in the SIR reaction-diffusion model, which provided an optimal control method for the epidemic [19].…”

Section: Introductionmentioning

confidence: 99%

Hopf bifurcation and patterns in a modified SIR model

Yang,

Zheng,

Shen

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

Infectious diseases have constantly threatened human safety because the diffusion of the susceptible and infected may make more individuals infected and even die. In this paper, a modified SIR model with both external stimulus and diffusion is considered to illustrate the dynamical mechanism of the periodic outbreak and pattern formation. Firstly, we propose a modified SIR model based on the propagation behavior of infectious diseases to show the effects of the different parameters and diffusion on the outbreak. The Hopf bifurcation and multiscale methods are performed to analyze the stability of this model, which explains the dynamical mechanism of the periodic outbreak. Then the pattern formation and Turing instability are discussed through comparison principles to reveal the role of periodic disturbances and diffusion in selecting pattern formation. Also, we find rich patterns that may occur when the frequency modulation is close to the intrinsic frequency. Finally, our theoretical results are verified by numerical simulation. 2010 MSC: 34F10, 35B36, 92C42.

show abstract

Pattern mechanism in stochastic SIR networks with ER connectivity

Cited by 14 publications

References 37 publications

Spatiotemporal dynamics of periodic waves in SIR model with driving factors

Spatiotemporal dynamics of periodic waves in SIR model with driving factors

Nonequilibrium phase transitions in metapopulation models of infectious diseases on heterogeneous networks

Hopf bifurcation and patterns in a modified SIR model

Contact Info

Product

Resources

About