scholarly journals A Node-Based SIRS Epidemic Model with Infective Media on Complex Networks

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Leyi Zheng ◽  
Longkun Tang
Keyword(s):  
Epidemic Model ◽  
Small World ◽  
Spreading Rate ◽  
Node Degree ◽  
Strong Positive Correlation ◽  
Globally Asymptotically Stable ◽  
Sirs Epidemic Model ◽  
Theoretical Investigations ◽  
Fully Connected ◽  
The Impact

We focus on the node-based epidemic modeling for networks, introduce the propagation medium, and propose a node-based Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model with infective media. Theoretical investigations show that the endemic equilibrium is globally asymptotically stable. Numerical examples of three typical network structures also verify the theoretical results. Furthermore, comparison between network node degree and its infected percents implies that there is a strong positive correlation between both; namely, the node with bigger degree is infected with more percents. Finally, we discuss the impact of the epidemic spreading rate of media as well as the effective recovered rate on the network average infected state. Theoretical and numerical results show that (1) network average infected percents go up (down) with the increase of the infected rate of media (the effective recovered rate); (2) the infected rate of media has almost no influence on network average infected percents for the fully connected network and NW small-world network; (3) network average infected percents decrease exponentially with the increase of the effective recovered rate, implying that the percents can be controlled at low level by an appropriate large effective recovered rate.

scholarly journals An SIRS Epidemic Model Supervised by a Control System for Vaccination and Treatment Actions Which Involve First-Order Dynamics and Vaccination of Newborns

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 36
Author(s):  
Santiago Alonso-Quesada ◽  
Manuel De la Sen ◽  
Raúl Nistal
Keyword(s):  
Control System ◽  
Equilibrium Point ◽  
Epidemic Model ◽  
Equilibrium Points ◽  
Threshold Value ◽  
Design Parameters ◽  
Globally Asymptotically Stable ◽  
Sirs Epidemic Model ◽  
Existence And Stability ◽  
Disease Free

This paper analyses an SIRS epidemic model with the vaccination of susceptible individuals and treatment of infectious ones. Both actions are governed by a designed control system whose inputs are the subpopulations of the epidemic model. In addition, the vaccination of a proportion of newborns is considered. The control reproduction number Rc of the controlled epidemic model is calculated, and its influence in the existence and stability of equilibrium points is studied. If such a number is smaller than a threshold value Rc, then the model has a unique equilibrium point: the so-called disease-free equilibrium point at which there are not infectious individuals. Furthermore, such an equilibrium point is locally and globally asymptotically stable. On the contrary, if Rc>Rc, then the model has two equilibrium points: the referred disease-free one, which is unstable, and an endemic one at which there are infectious individuals. The proposed control strategy provides several free-design parameters that influence both values Rc and Rc. Then, such parameters can be appropriately adjusted for guaranteeing the non-existence of the endemic equilibrium point and, in this way, eradicating the persistence of the infectious disease.

scholarly journals Modeling Public Opinion Polarization in Group Behavior by Integrating SIRS-Based Information Diffusion Process

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-20 ◽  
Author(s):  
Tinggui Chen ◽  
Jiawen Shi ◽  
Jianjun Yang ◽  
Guodong Cong ◽  
Gongfa Li
Keyword(s):  
Epidemic Model ◽  
Social Transformation ◽  
Information Diffusion ◽  
Small World ◽  
Group Behavior ◽  
Experimental Simulation ◽  
Group Polarization ◽  
Polarization Model ◽  
Relationship Strength ◽  
Sirs Epidemic Model

Currently, China is in the period of social transformation. Such transformation continuously results in high group polarization behaviors, which attracts many attentions. In order to explore the evolutionary mechanism and formation process of group polarization behavior, this paper proposes a group polarization model which is integrated into the Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model. In this paper, firstly, the SIRS epidemic model and the factors of relationship strength are introduced based on the J-A model (proposed by Jager and Amblard) to enhance the information transmission and interaction among individuals. In addition, the BA network (proposed by Barabasi and Albert) model is used as the agent adjacency model due to its closeness to the real social network structure. After that, the Monte Carlo method is applied to conduct experimental simulation. Subsequently, this paper analyzes the simulation results in threefold: (1) comparison of polarization processes with and without integration of the SIRS epidemic model; (2) adjusting the immune recovery parameter γ and the relationship strength z to explore the role of these two parameters in the polarization process; and (3) comparing the polarization effects of different network structures. Through the experiments, we find that BA network is more polarized than small-world network in the same scale. Finally, corresponding measures are proposed to prevent and mitigate the occurrence of group polarization.

THE DYNAMICS AND THERAPEUTIC STRATEGIES OF A SEIS EPIDEMIC MODEL

2013 ◽  
Vol 06 (05) ◽  
pp. 1350029 ◽  
Author(s):  
XINZHU MENG ◽  
ZHITAO WU ◽  
TONGQIAN ZHANG
Keyword(s):  
Basic Reproduction Number ◽  
Epidemic Model ◽  
Therapeutic Strategy ◽  
Reproduction Number ◽  
Asymptotically Stable ◽  
Epidemic Disease ◽  
Globally Asymptotically Stable ◽  
Effective Therapeutic Strategy ◽  
The Impact ◽  
The Basic Reproduction Number

Based on an epidemic model which Manvendra and Vinay [Mathematical model to simulate infections disease, VSRD-TNTJ3(2) (2012) 60–68] have proposed, we consider the dynamics and therapeutic strategy of a SEIS epidemic model with latent patients and active patients. First, the basic reproduction number is established by applying the method of the next generation matrix. By means of appropriate Lyapunov functions, it is proven that while the basic reproduction number 0 < R0 < 1, the disease-free equilibrium is globally asymptotically stable and the disease eliminates; and if the basic reproduction number R0 > 1, the endemic equilibrium is globally asymptotically stable and therefore the disease becomes endemic. Numerical investigations of their basin of attraction indicate that the locally stable equilibria are global attractors. Second, we consider the impact of treatment on epidemic disease and analytically determine the most effective therapeutic strategy. We conclude that the most effective therapeutic strategy consists of treating both the exposed and the infectious, while treating only the exposed is the least effective therapeutic strategy. Finally, numerical simulations are given to illustrate the effectiveness of the proposed results.

THRESHOLD AND STABILITY RESULTS FOR AN SIRS EPIDEMIC MODEL WITH A GENERAL PERIODIC VACCINATION STRATEGY

2005 ◽  
Vol 13 (02) ◽  
pp. 131-150 ◽  
Author(s):  
I. A. MONEIM ◽  
D. GREENHALGH
Keyword(s):  
Epidemic Model ◽  
Vaccination Strategy ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Contact Rate ◽  
Globally Asymptotically Stable ◽  
Epidemic Dynamics ◽  
Sirs Epidemic Model ◽  
Sirs Model ◽  
Periodic Disease

An SIRS epidemic model with general periodic vaccination strategy is analyzed. This periodic vaccination strategy is discussed first for an SIRS model with seasonal variation in the contact rate of period T = 1 year. We start with the case where the vaccination strategy and the contact rate have the same period and then discuss the case where the period of the vaccination strategy is LT, where L is an integer. We investigate whether a periodic vaccination strategy may force the epidemic dynamics to have periodic behavior. We prove that our SIRS model has a unique periodic disease free solution (DFS) whose period is the same as that of the vaccination strategy, which is globally asymptotically stable when the basic reproductive number R0 is less than or equal to one in value. When R0 > 1, we prove that there exists a non-trivial periodic solution of period the same as that of the vaccination strategy. Some persistence results are also discussed. Threshold conditions for these periodic vaccination strategies to ensure that R0 ≤ 1 are derived.

STABILITY ANALYSIS OF A DELAYED SIRS EPIDEMIC MODEL WITH VACCINATION AND NONLINEAR INCIDENCE

2012 ◽  
Vol 05 (06) ◽  
pp. 1250050 ◽  
Author(s):  
XIAOHONG TIAN
Keyword(s):  
Epidemic Model ◽  
Local Stability ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Threshold Value ◽  
Iteration Scheme ◽  
Endemic Equilibrium ◽  
Globally Asymptotically Stable ◽  
Sirs Epidemic Model ◽  
Disease Free

In this paper, an SIRS epidemic model with time delay and vaccination is investigated. By analyzing the corresponding characteristic equation, the local stability of disease-free equilibrium of the model is established. By constructing Lyapunov functional, sufficient conditions are established for the local stability of an endemic equilibrium of the model. Further, a threshold value is obtained. By using comparison arguments, it is proved when the threshold value is less than unity, the disease-free equilibrium is globally asymptotically stable. When the threshold value is greater than unity, by using an iteration scheme and by constructing appropriate Lyapunov functional, respectively, sufficient conditions are derived for the global stability of the endemic equilibrium of the model. Numerical simulations are carried out to illustrate the theoretical results.

scholarly journals Global Dynamics of a Generalized SIRS Epidemic Model with Constant Immigration

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Qianqian Cui ◽  
Qinghui Du ◽  
Li Wang
Keyword(s):  
Epidemic Model ◽  
Reproduction Number ◽  
Direct Method ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Lyapunov Direct Method ◽  
Globally Asymptotically Stable ◽  
Sirs Epidemic Model ◽  
Dynamical Behaviors ◽  
Disease Case

In this paper, we discuss the global dynamics of a general susceptible-infected-recovered-susceptible (SIRS) epidemic model. By using LaSalle’s invariance principle and Lyapunov direct method, the global stability of equilibria is completely established. If there is no input of infectious individuals, the dynamical behaviors completely depend on the basic reproduction number. If there exists input of infectious individuals, the unique equilibrium of model is endemic equilibrium and is globally asymptotically stable. Once one place has imported a disease case, then it may become outbreak after that. Numerical simulations are presented to expound and complement our theoretical conclusions.

Dynamics of a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination and nonlinear incidence under regime switching and Lévy jumps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Junna Hu ◽  
Buyu Wen ◽  
Ting Zeng ◽  
Zhidong Teng
Keyword(s):  
Epidemic Model ◽  
Regime Switching ◽  
Markov Switching ◽  
Threshold Value ◽  
Open Problems ◽  
Nonlinear Incidence ◽  
Sirs Epidemic Model ◽  
Stochastic Epidemic ◽  
Lévy Jumps ◽  
White Noises

Abstract In this paper, a stochastic susceptible-infective-recovered (SIRS) epidemic model with vaccination, nonlinear incidence and white noises under regime switching and Lévy jumps is investigated. A new threshold value is determined. Some basic assumptions with regard to nonlinear incidence, white noises, Markov switching and Lévy jumps are introduced. The threshold conditions to guarantee the extinction and permanence in the mean of the disease with probability one and the existence of unique ergodic stationary distribution for the model are established. Some new techniques to deal with the Markov switching, Lévy jumps, nonlinear incidence and vaccination for the stochastic epidemic models are proposed. Lastly, the numerical simulations not only illustrate the main results given in this paper, but also suggest some interesting open problems.

scholarly journals Splanchnic Vein Thrombosis in Acute Pancreatitis and Its Consequences

2021 ◽  
Vol 27 ◽  
pp. 107602962110102
Author(s):  
Łukasz Nawacki ◽  
Jarosław Matykiewicz ◽  
Ewa Stochmal ◽  
Stanisław Głuszek
Keyword(s):  
Acute Pancreatitis ◽  
Severe Disease ◽  
Vascular Complication ◽  
Strong Positive Correlation ◽  
Splanchnic Vein Thrombosis ◽  
Vein Thrombosis ◽  
Computed Tomography Scans ◽  
Negative Effect ◽  
Medical Histories ◽  
The Impact

Splanchnic vein thrombosis (SVT) is a serious vascular complication that can occur in patients with acute pancreatitis. We assessed the incidence of SVT and its relationship with acute pancreatitis (AP) and associated complications. We carried out a retrospective analysis of medical histories from patients hospitalized with AP in a single surgical center. Histories were acquired from patients with abdominal and pelvic computed tomography scans performed between the 2nd and 3rd day of hospitalization. We assessed the impact and extent of thrombosis over the disease course. We found a strong positive correlation (Cramer’s V coefficient = 0.34) between SVT and disease severity. Mortality in the study group was 7.2% (8 patients) of which 5 patients (62.5%) were diagnosed with SVT. We observed an increased incidence of death among patients with thrombosis, with results approaching significance ( P = 0.056). In our study, we found that SVT has a negative effect on the course of AP and is associated with more severe disease and increased mortality.

scholarly journals Threshold Dynamics in a Model for Zika Virus Disease with Seasonality

2021 ◽  
Vol 83 (4) ◽  
Author(s):  
Mahmoud A. Ibrahim ◽  
Attila Dénes
Keyword(s):  
Zika Virus ◽  
Reproduction Number ◽  
Virus Disease ◽  
Threshold Dynamics ◽  
Global Dynamics ◽  
Threshold Parameter ◽  
Globally Asymptotically Stable ◽  
Linear Integral ◽  
The Impact ◽  
Disease Free

AbstractWe present a compartmental population model for the spread of Zika virus disease including sexual and vectorial transmission as well as asymptomatic carriers. We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number $${\mathscr {R}}_{0}$$ R 0 as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If $${\mathscr {R}}_0 < 1,$$ R 0 < 1 , then the disease-free periodic solution is globally asymptotically stable, while if $${\mathscr {R}}_0 > 1,$$ R 0 > 1 , then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.

scholarly journals The mathematics of multiple lockdowns

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Antonio Scala
Keyword(s):  
Beneficial Effect ◽  
Epidemic Model ◽  
Final Size ◽  
Optimal Response ◽  
Support Strategy ◽  
The Impact ◽  
New Strategies

AbstractWhile vaccination is the optimal response to an epidemic, recent events have obliged us to explore new strategies for containing worldwide epidemics, like lockdown strategies, where the contacts among the population are strongly reduced in order to slow down the propagation of the infection. By analyzing a classical epidemic model, we explore the impact of lockdown strategies on the evolution of an epidemic. We show that repeated lockdowns have a beneficial effect, reducing the final size of the infection, and that they represent a possible support strategy to vaccination policies.

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