Qualitative Dynamics and Pattern Formation of COVID-19 in the Modified SIR Model

Abstract SIR (susceptible-infective-recovery) model is a widely investigated model to explain the time evolution of infectious diseases. Outbreak of infectious diseases is affected by diffusion of infected, which is true especially in COVID-19 outbreak. Therefore, it is imperative to construct a diffusion network in the model for spatial consideration; However, the inclusion of a diffusion network is seldom considered for the studies. In this work, we first modified the SIR model for COVID-19 and then performed its stability and bifurcation analysis in qualitative research. Based on our analysis, we propose some of the advice to mitigate the spread of COVID-19. Then, a random diffusion network is constructed, which shows its vital role in the Turing instability and bifurcation. We noticed that the stability of network-organized SIR could be determined by the maximum of eigenvalues of the network matrix. The maximum of eigenvalues of the network matrix is proportional to network connection rate and infection rate of the network. Therefore, these two rates play a critical role in Turing instability. We perform the numerical simulations to verify the analytical results. We try to explain the spread mechanism of infectious diseases and provide some feasible strategies based on our analysis of these two models. Also, the reduced system method for a network-organized system is proposed, which is a novel approach to investigate the complex system.

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Delay-Induced Self-Organization Dynamics in a Prey-Predator Network with Diffusion

10.21203/rs.3.rs-1079664/v1 ◽

2021 ◽

Author(s):

Qing Hu ◽

Jianwei Shen

Keyword(s):

Time Delays ◽

Random Network ◽

Turing Instability ◽

Self Organization ◽

Network System ◽

Turing Pattern ◽

Network Connection ◽

Pattern Dynamics ◽

Connection Probability ◽

The Stability

Abstract Time delays can induce the loss of stability and degradation of performance. In this paper, the pattern dynamics of a prey-predator network with diffusion and delay are investigated, where the inhomogeneous distribution of species in space can be viewed as a random network, and delay can affect the stability of the network system. Our results show that time delay can induce the emergence of Hopf and Turing bifurcations, which are independent of the network, and the conditions of bifurcation are derived by linear stability analysis. Moreover, we find that the Turing pattern can be related to the network connection probability. The Turing instability region involving delay and network connection probability is obtained. Finally, the numerical simulation verifies our results.

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Turing instability in a diffusive SIS epidemiological model

International Journal of Biomathematics ◽

10.1142/s1793524515500060 ◽

2015 ◽

Vol 08 (01) ◽

pp. 1550006 ◽

Cited By ~ 1

Author(s):

Shaban Aly ◽

Houari B. Khenous ◽

Fatma Hussien

Keyword(s):

Infectious Diseases ◽

Modeling And Simulation ◽

Spatial Patterns ◽

Disease Model ◽

Turing Instability ◽

Nonlinear Incidence Rate ◽

Self Diffusion ◽

Cross Diffusion ◽

The Stability ◽

Theoretical Results

Modeling and simulation of infectious diseases help to predict the likely outcome of an epidemic. In this paper, a spatial susceptible-infective-susceptible (SIS) type of epidemiological disease model with self- and cross-diffusion are investigated. We study the effect of diffusion on the stability of the endemic equilibrium with disease-induced mortality and nonlinear incidence rate. In the absence of diffusion the stationary solution stays stable but becomes unstable with respect to diffusion and that Turing instability takes place. We show that a standard (self-diffusion) system may be either stable or unstable, cross-diffusion response can stabilize an unstable standard system or decrease a Turing space (the space which the emergence of spatial patterns is holding) compared to the Turing space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges. Numerical simulations are provided to illustrate and extend the theoretical results.

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Novel Approach of Improving Secondary Electron Detector in FIB System

10.31399/asm.cp.istfa2018p0206 ◽

2018 ◽

Author(s):

Steve Wang ◽

Jim McGinn ◽

Peter Tvarozek ◽

Amir Weiss

Keyword(s):

Integrated Circuit ◽

Secondary Electron ◽

Focused Ion Beam ◽

Ion Beam ◽

Vital Role ◽

Electron Detector ◽

System A ◽

Novel Approach

Abstract Secondary electron detector (SED) plays a vital role in a focused ion beam (FIB) system. A successful circuit edit requires a good effective detector. Novel approach is presented in this paper to improve the performance of such a detector, making circuit altering for the most advanced integrated circuit (IC) possible.

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Dynamical study of infochemical influences on tropic interaction of diffusive plankton system

SN Applied Sciences ◽

10.1007/s42452-021-04237-9 ◽

2021 ◽

Vol 3 (3) ◽

Author(s):

Satish Kumar Tiwari ◽

Ravikant Singh ◽

Nilesh Kumar Thakur

Keyword(s):

Dimethyl Sulfide ◽

Algal Bloom ◽

Turing Instability ◽

Model System ◽

Ode Model ◽

Estuarine Ecosystem ◽

Dynamical Study ◽

Oscillatory Dynamics ◽

The Stability ◽

Microzooplankton Grazing

AbstractWe propose a model for tropic interaction among the infochemical-producing phytoplankton and non-info chemical-producing phytoplankton and microzooplankton. Volatile information-conveying chemicals (infochemicals) released by phytoplankton play an important role in the food webs of marine ecosystems. Microzooplankton is an ecologically important grazer of phytoplankton for coexistence of a large number of phytoplankton species. Here, we discuss how information transferred by dimethyl sulfide shapes the interaction of phytoplankton. Phytoplankton deterrents may lead to propagation of IPP bloom. The interaction between IPP and microzooplankton follows the Beddington–DeAngelis-type functional response. Analytically, we discuss boundedness, stability and Turing instability of the model system. We perform numerical simulation for temporal (ODE model) as well as a spatial model system. Our numerical investigation shows that microzooplankton grazing refuse of IPP leads to oscillatory dynamics. Increasing diffusion coefficient of microzooplankton shows Turing instability. Time evolution also plays an important role in the stability of system dynamics. The results obtained in this paper are useful to understand the dominance of algal bloom in coastal and estuarine ecosystem.

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Quantum-mechanical hydration plays critical role in the stability of firefly oxyluciferin isomers: State-of-the-art calculations of the excited states

The Journal of Chemical Physics ◽

10.1063/5.0031356 ◽

2020 ◽

Vol 153 (20) ◽

pp. 201103

Author(s):

Yoshifumi Noguchi ◽

Miyabi Hiyama ◽

Motoyuki Shiga ◽

Hidefumi Akiyama ◽

Osamu Sugino

Keyword(s):

Excited States ◽

State Of The Art ◽

Critical Role ◽

Quantum Mechanical ◽

The Stability

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COVID-19 and emergency planning

British Journal of Healthcare Management ◽

10.12968/bjhc.2020.0016 ◽

2020 ◽

Vol 26 (4) ◽

pp. 1-3 ◽

Cited By ~ 2

Author(s):

George Winter

Keyword(s):

Infectious Diseases ◽

Vital Role ◽

Emergency Planning ◽

Global Society

As COVID-19 continues to spread worldwide, George Winter discusses emergency strategies, lessons from past epidemics and the vital role that healthcare managers can play in shaping responses to infectious diseases in today's global society.

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A Novel Approach to Fabricate Foam Ceramics from Steel Slag

Advances in Materials Science and Engineering ◽

10.1155/2020/4649082 ◽

2020 ◽

Vol 2020 ◽

pp. 1-7

Author(s):

Yu Zheng ◽

Xudong Luo ◽

Jinlong Yang ◽

Wenlong Huo ◽

Chi Kang

Keyword(s):

Compressive Strength ◽

Ph Value ◽

Steel Slag ◽

Raw Material ◽

Solid Loading ◽

Insulation Material ◽

Ceramic Foams ◽

Novel Approach ◽

The Stability ◽

First Time

A novel approach is used for fabricating steel slag foam ceramics based on the particle-stabilized foaming method. In this work, steel slag was used as the raw material and propyl gallate (PG) was used as the surface modifier. For the first time, steel slag ceramic foams were successfully fabricated based on particle-stabilized foams. The results show that the stability of the ceramic foams was closely related to the pH value and PG concentration. The porosity and compressive strength could be controlled by changing the solid loading of steel slag and sintering temperature. The porosity of steel slag foam ceramics ranged from 85.6% to 62.53%, and the compressive strength was from 1.74 MPa to 10.42 MPa. The thermal conductivity of steel slag foam ceramics was only 0.067 W (m·K)−1, which shows that it could be used as a thermal insulation material.

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DNA Genome Size Affects the Stability of the Adenovirus Virion

Journal of Virology ◽

10.1128/jvi.01644-08 ◽

2008 ◽

Vol 83 (4) ◽

pp. 2025-2028 ◽

Cited By ~ 23

Author(s):

Adam C. Smith ◽

Kathy L. Poulin ◽

Robin J. Parks

Keyword(s):

Genome Size ◽

Critical Role ◽

Heat Stability ◽

Helper Virus ◽

Heat Inactivation ◽

Similar Relationship ◽

Viral Dna ◽

A Genome ◽

The Stability ◽

Replication Defective Adenovirus

ABSTRACT Replication-defective adenovirus (Ad) vectors can vary considerably in genome length, but whether this affects virion stability has not been investigated. Helper-dependent Ad vectors with a genome size of ∼30 kb were 100-fold more sensitive to heat inactivation than their parental helper virus (>36 kb), and increasing the genome size of the vector significantly improved heat stability. A similar relationship between genome size and stability existed for Ad with early region 1 deleted. Loss of infectivity was due to release of vertex proteins, followed by disintegration of the capsid. Thus, not only does the viral DNA encode all of the heritable information essential for virus replication, it also plays a critical role in maintaining capsid strength and integrity.

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Analysis of Urban Effects in Oklahoma City using a Dense Surface Observing Network

Journal of Applied Meteorology and Climatology ◽

10.1175/jamc-d-15-0206.1 ◽

2016 ◽

Vol 55 (3) ◽

pp. 723-741 ◽

Cited By ~ 22

Author(s):

Xiao-Ming Hu ◽

Ming Xue ◽

Petra M. Klein ◽

Bradley G. Illston ◽

Sheng Chen

Keyword(s):

Metropolitan Area ◽

Land Surface ◽

Critical Role ◽

Central Business District ◽

Temperature Inversion ◽

Oklahoma City ◽

Near Surface ◽

Open Questions ◽

The Stability ◽

Business District

AbstractMany studies have investigated urban heat island (UHI) intensity for cities around the world, which is normally quantified as the temperature difference between urban location(s) and rural location(s). A few open questions still remain regarding the UHI, such as the spatial distribution of UHI intensity, temporal (including diurnal and seasonal) variation of UHI intensity, and the UHI formation mechanism. A dense network of atmospheric monitoring sites, known as the Oklahoma City (OKC) Micronet (OKCNET), was deployed in 2008 across the OKC metropolitan area. This study analyzes data from OKCNET in 2009 and 2010 to investigate OKC UHI at a subcity spatial scale for the first time. The UHI intensity exhibited large spatial variations over OKC. During both daytime and nighttime, the strongest UHI intensity is mostly confined around the central business district where land surface roughness is the highest in the OKC metropolitan area. These results do not support the roughness warming theory to explain the air temperature UHI in OKC. The UHI intensity of OKC increased prominently around the early evening transition (EET) and stayed at a fairly constant level throughout the night. The physical processes during the EET play a critical role in determining the nocturnal UHI intensity. The near-surface rural temperature inversion strength was a good indicator for nocturnal UHI intensity. As a consequence of the relatively weak near-surface rural inversion, the strongest nocturnal UHI in OKC was less likely to occur in summer. Other meteorological factors (e.g., wind speed and cloud) can affect the stability/depth of the nighttime boundary layer and can thus modulate nocturnal UHI intensity.

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