Hopf bifurcation and patterns in a modified SIR model DOI Creative Commons
Wenjie Yang, Qianqian Zheng, Jianwei Shen

et al.

Research Square (Research Square), Journal Year: 2023, Volume and Issue: unknown

Published: July 31, 2023

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

Language: Английский

Dynamics of delayed and diffusive FitzHugh–Nagumo network DOI

Shaoyang Gao,

Jianwei Shen, Xiao Hu

et al.

The European Physical Journal Special Topics, Journal Year: 2024, Volume and Issue: unknown

Published: June 18, 2024

Language: Английский

Citations

2
Turing instability and pattern formation induced by noise in the modified SIR model DOI
Quan Zheng, Jianwei Shen,

Linan Guan

et al.

Nonlinear Dynamics, Journal Year: 2024, Volume and Issue: unknown

Published: July 6, 2024

Language: Английский

Citations

2
Turing instability induced by crossing curves in network-organized system DOI Creative Commons
Xi Li, Jianwei Shen, Qianqian Zheng

et al.

Advances in Continuous and Discrete Models, Journal Year: 2024, Volume and Issue: 2024(1)

Published: Aug. 13, 2024

Several factors significantly contribute to the onset of infectious diseases, including direct and indirect transmissions their respective impacts on incubation periods. The intricate interplay these within social networks remains a puzzle yet be unraveled. In this study, we conduct stability analysis network-organized SIR model incorporating dual delays explore influence periods disease spread. Additionally, investigate how compound affect critical period. Our findings reveal several vital insights. First, by examining crossing curves dispersion equation, establish conditions for Turing instability delineate stable regions associated with delays. Second, ascertain that value exhibits an inverse relationship network's eigenvalues, indicating Laplacian matrix does not solely dictate periodic behavior in context Furthermore, our study elucidates impact pattern formation, revealing distinct types across different regions. Specifically, observations suggest effectively curtailing spread diseases during outbreak is more achievable when period contact shorter longer. Namely, network framework enables regulation optimal combination $(\tau _{1},\tau _{2})$ mitigate risk diseases. summary, results offer valuable theoretical insights can inform strategies preventing managing

Language: Английский

Citations

2
Hopf bifurcation and patterns in a modified SIR model DOI Creative Commons
Wenjie Yang, Qianqian Zheng, Jianwei Shen

et al.

Frontiers in Physics, Journal Year: 2023, Volume and Issue: 11

Published: Nov. 1, 2023

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

Language: Английский

Citations

2
Nonequilibrium phase transitions in metapopulation models of infectious diseases on heterogeneous networks DOI Creative Commons
Sungchul Kwon, Jeong-Man Park

Journal of Physics A Mathematical and Theoretical, Journal Year: 2023, Volume and Issue: 56(37), P. 375001 - 375001

Published: Aug. 11, 2023

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

Language: Английский

Citations

1
Bifurcation and pattern dynamics in the nutrient-plankton network DOI Creative Commons
Wenjie Yang, Qianqian Zheng, Jianwei Shen

et al.

Mathematical Biosciences & Engineering, Journal Year: 2023, Volume and Issue: 20(12), P. 21337 - 21358

Published: Jan. 1, 2023

This paper used a Holling-IV nutrient-plankton model with network to describe algae's spatial and temporal distribution variation in specific sea area. The stability bifurcation of the nonlinear dynamic harmful algal blooms (HABs) were analyzed using theory de-eutrophication's effect on behavior. conditions for equilibrium points (local global), saddle-node, transcritical, Hopf-Andronov Bogdanov-Takens (B-T) obtained. limit cycle was then judged rich complex phenomenon obtained by numerical simulations, which revealed robustness system switching between nodes. Also, these results show relationship HABs bifurcation, has important guiding significance solving environmental problems caused abnormal increase phytoplankton.

Language: Английский

Citations

1
Network topology and double delays in Turing instability and pattern formation DOI
Q Q Zheng, Xiaohui Li, Jianwei Shen

et al.

Journal of Physics A Mathematical and Theoretical, Journal Year: 2024, Volume and Issue: 57(39), P. 395203 - 395203

Published: Aug. 30, 2024

Abstract Investigating Turing patterns in complex networks presents a significant challenge, particularly understanding the transition from simple to systems. We examine network-organized SIR model, incorporating Matthew effect and double delays, demonstrate how network structures directly impact critical delay values, providing insights into historical of disease spread. The study reveals that both susceptible infected individuals experience latent period due interactions between incubation, mirroring observed seasonal flu outbreaks. emergence chaotic states is when two delays intersect curves, highlighting dynamics can arise epidemic models. A novel approach introduced, utilizing eigenvalue ratios minimum/maximum Laplacian matrices (excluding 0) identify stable regions within systems, new tool for epidemiological analysis. paper further explores dynamic biological mechanisms, discussing these findings inform contemporary strategies managing infectious

Language: Английский

Citations

0
The spatiotemporal dynamics of a diffusive predator-prey model with double Allee effect DOI Creative Commons
Lingling Li, Xuechen Li

AIMS Mathematics, Journal Year: 2024, Volume and Issue: 9(10), P. 26902 - 26915

Published: Jan. 1, 2024

<p>We introduce a diffusive predator-prey system with the double Allee effect, focusing on stability and sufficient conditions for coexistence of prey predator. Subsequently, we derived amplitude equation explore secondary-order dynamic properties using methods such as Taylor series expansion multiscaling. The novel approach outlined above provides precise means to thoroughly analyze model. Through this analysis, demonstrated that inclusion effect diffusion leads exhibiting more intricate behaviors compared systems lacking these factors. On one hand, in without pattern formation regarding distribution species was relatively scattered, whereas it is intensive. other transitioned from unstable stable when parameter increased, aggregation degree higher than it. These findings highlight significant roles played by determining predator within system.</p>

Language: Английский

Citations

0
Hopf bifurcation and patterns in a modified SIR model DOI Creative Commons
Wenjie Yang, Qianqian Zheng, Jianwei Shen

et al.

Research Square (Research Square), Journal Year: 2023, Volume and Issue: unknown

Published: July 31, 2023

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

Language: Английский

Citations

0