Location of emergency rescue center based on SIR epidemiological model

In view of the pressure time of emergency rescue against the infectious diseases,a mathematical model to optimize the location of emergency rescue centers is proposed.The model takes full account of the spread function of infectious diseases,the cycle of pulse vaccination,the distance between the demand area and the emergency rescue centers,as well as the building and maintenance cost for the emergency rescue center,and so on.At the same time,the model integrates the traditional location selection models which are the biggest cover model,the p-center model and the p-median model,and it embodies the principles of fairness and efficiency for the emergency center location.Finally,a computation of an example arising from practice provides satisfactory results.

基于SIR模型的无线网络安全威胁态势量化评估算法

为确保网络安全,及时掌控安全状况,以易感者、感染者和免疫者(SIR:Susceptible Infected Recovered)模型为基础,面向无线网络提出安全威胁态势量化评估算法。选取资产价值性,系统脆弱性与威胁性作为量化评估指标,分别根据信息资产的安全属性与主机劣势的Agent检测值,得到价值性量化值与脆弱性量化值。基于病毒的传播特性,改进SIR模型,分析病毒传播特征,获得威胁性量化值。结合3个指标量化值,建立无线网络安全威胁态势的量化评估算法,用所得态势值评估网络安全状况。测试结果表明,该方法评估出的主机与整个无线网络的安全威胁态势值均与期望值高度拟合,且评估时间更短。所提算法具备良好的评估准确性与实时性,能为网络安全状况分析提供有效的数据依据,及时给予管理员可靠的决策支持。

基于SIR模型重构医院保障设备监控预警系统

医院智能楼宇的建设离不开精细化的管理。后勤系统众多,对各系统运行状态进行实时监控,保障医疗秩序的安全稳定开展,需要楼宇自控系统合理分配监控点位。点位分布的过多,会造成成本增加;分布过少,起不到全面监控的效果。借助管理工具查找预警信息规律,找出系统运行风险的阈值和极值,实现点位重构,并对不同风险程度的点位采取不同的管理措施,从而达到降低成本、降低风险、优化运维的最终目标。

GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.

GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION

In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].

GLOBAL STABILITY OF SIRS EPIDEMIC MODELS WITH A CLASS OF NONLINEAR INCIDENCE RATES AND DISTRIBUTED DELAYS

In this article, we establish the global asymptotic stability of a disease-free equilibrium and an endemic equilibrium of an SIRS epidemic model with a class of nonlin- ear incidence rates and distributed delays. By using strict monotonicity of the incidence function and constructing a Lyapunov functional, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. When the nonlinear inci- dence rate is a saturated incidence rate, our result provides a new global stability condition for a small rate of immunity loss.

Epidemic Propagation: An Automaton Model as the Continuous SIR Model

The use of the SIR model to predict the time evolution of an epidemic is very frequent and has spatial information about its propagation which may be very useful to contrast its spread. In this paper we take a particular cellular automaton model that well reproduces the time evolution of the disease given by the SIR model;setting the automaton is generally an annoying problem because we need to run a lot of simulations, compare them to the solution of the SIR model and, finally, decide the parameters to use. In order to make this procedure easier, we will show a fast method that, in input, requires the parameters of the SIR continuous model that we want to reproduce, whereas, in output, it yields the parameters to use in the cellular automaton model. The problem of computing the most suitable parameters for the reticular model is reduced to the problem of finding the roots of a polynomial Equation.

STOCHASTIC SIRS MODEL DRIVEN BY LVY NOISE

The paper establishes two stochastic SIRS models with jumps to describe the spread of network virus by cyber war, terrorism and others. First, adding random perturbations proportionally to each variable, we get the dynamic properties around the positive equilibrium of the deterministic model and the conditions for persistence and extinction. Second, giving a random disturbance to endemic equilibrium, we get a stochastic system with jumps. By modifying the existing Lyapunov function, we prove the positive solution of the system is stochastically stable.

Asymptotic Behavior of a Stochastic SIRS Model with Non-linear Incidence and Levy Jumps

A stochastic susceptible-infective-recovered-susceptible( SIRS) model with non-linear incidence and Levy jumps was considered. Under certain conditions, the SIRS had a global positive solution. The stochastically ultimate boundedness of the solution of the model was obtained by using the method of Lyapunov function and the generalized Ito's formula. At last,asymptotic behaviors of the solution were discussed according to the value of R0. If R0< 1,the solution of the model oscillates around a steady state, which is the diseases free equilibrium of the corresponding deterministic model,and if R0> 1,it fluctuates around the endemic equilibrium of the deterministic model.

SIR Model of Spread of Zika Virus Infections: ZIKV Linked to Microcephaly Simulations

An SIR model of Zika virus (ZIKV) spread is formulated that includes ZIKV infections to newborns. Analytically, the model has one disease free and one endemic equilibrium point. The free one is stable for some conditions when R0 and unstable when R0>1. In Brazil, when R0≈2>1 ZIKV infections expand and for R0 = 0.875R0) of the model. There are parameters for human-mosquito transmission and some for sexual-transmission factor. It appears that controlling spread of ZIKV infections by human-mosquito transmission may greatly reduce the value of R0.

Delayed Dynamics of SIR Model for COVID-19

This paper presents a new modified SIR model which incorporates appropriate delay parameters leading to a more precise prediction of COVID-19 real time data. The efficacy of the newly developed SIR model is proven by comparing its predictions to real data obtained from four counties namely Germany, Italy, Kuwait, and Oman. Two included delay periods for incubation and recovery within the SIR model produce a sensible and more accurate representation of the real time data. In the absence of the two-delay period () the dynamical behavior of the model will not correspond to today’s picture and lag the detection of the epidemic peak. The reproductive number R0 is defined for the model for values of recovery time delay of the infective case. The effect of recovery time may produce second wave, and/or an oscillation which could destabilize the behavior of the system and a periodic oscillation can arise due to Hopf bifurcation phenomenon.

一类具有饱和恢复率的随机SIR传染病模型的持久性

在确定型模型的基础上,考虑随机因素,得到了一类具有饱和发生率的随机SIR模型。首先给出随机模型的正不变集,进而介绍持久性含义,利用Ito公式及强大数定律得到了疾病流行的充分性条件。结果表明,当白噪声强度满足一定的参数条件时,染病类群体不会消失,这对于控制疾病的蔓延是不利的。

Analysis of a Delayed SIR Model with Exponential Birth and Saturated Incidence Rate

In this paper, a delayed SIR model with exponential demographic structure and the saturated incidence rate is formulated. The stability of the equilibria is analyzed with delay: the endemic equilibrium is locally stable without delay;and the endemic equilibrium is stable if the delay is under some condition. Moreover the dynamical behaviors from stability to instability will change with an appropriate?critical value. At last, some numerical simulations of the model are given to illustrate the main theoretical results.

A Restricted SIR Model with Vaccination Effect for the Epidemic Outbreaks Concerning COVID-19

This paper presents a restricted SIRmathematicalmodel to analyze the evolution of a contagious infectious disease outbreak(COVID-19)using available data.The new model focuses on two main concepts:first,it can present multiple waves of the disease,and second,it analyzes how far an infection can be eradicated with the help of vaccination.The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability.The basic reproduction number is calculated,and the positivity of the solutions is established.Numerical simulations are performed to determine if it is multipeak and evaluate vaccination’s effects.In addition,the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.

DYNAMICS FOR AN SIR EPIDEMIC MODEL WITH NONLOCAL DIFFUSION AND FREE BOUNDARIES

This paper is concerned with the spatial propagation of an SIR epidemic model with nonlocal diffusion and free boundaries describing the evolution of a disease.This model can be viewed as a nonlocal version of the free boundary problem studied by Kim et al.(An SIR epidemic model with free boundary.Nonlinear Anal RWA,2013,14:1992-2001).We first prove that this problem has a unique solution defined for all time,and then we give sufficient conditions for the disease vanishing and spreading.Our result shows that the disease will not spread if the basic reproduction number R_(0)<1,or the initial infected area h_(0),expanding ability μ and the initial datum S_(0) are all small enough when 1<R_(0)<1+d/μ_(2)+α.Furthermore,we show that if 1<R_(0)<1+d/μ_(2)+α,the disease will spread when h_(0) is large enough or h_(0) is small but μ is large enough.It is expected that the disease will always spread when R_(0)≥1+d/μ_(2)+α which is different from the local model.

Dynamics of a Nonautonomous SIR Model with Time-Varying Impulsive Release and General Nonlinear Incidence Rate in a Polluted Environment

In a polluted environment, considering the biological population infected with a kind of disease and hunted by human beings, we formulate a nonautonomous SIR population-epidemic model with time-varying impulsive release and general nonlinear incidence rate and investigate dynamical behaviors of the model. Under the reasonable assumptions, the sufficient conditions which guarantee the globally attractive of the disease-free periodic solution and the permanence of the infected fish are established, that is, the infected fish dies out if , whereas the disease persists if . To substantiate our theoretical results, extensive numerical simulations are performed for a hypothetical set of parameter values.

Study on the Dynamics of an SIR Epidemic Model with Saturated Growth Rate

In this paper, we investigate the dynamic properties of an SIR epidemic model with saturated growth rate. Under the conditions of an arbitrary initial value, we prove that the system exists unique positive solution, and give the sufficient conditions caused by random environmental factors leading to the extinction of infectious diseases. Moreover, we verify the conditions for the persistence of infectious diseases in the mean sense. Finally, we provide the biology interpretation and some strategies to control the infectious diseases.

Hopf Bifurcation Analysis for a Delayed SIRS Epidemic Model with a Nonlinear Incidence Rate

This paper is concerned with a delayed SIRS epidemic model with a nonlinear incidence rate. The main results are given in terms of local stability and Hopf bifurcation. Sufficient conditions for the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained by regarding the time delay as the bifurcation parameter. Further,the properties of Hopf bifurcation such as the direction and stability are investigated by using the normal form theory and center manifold argument. Finally,some numerical simulations are presented to verify the theoretical analysis.

Extinction and Stationary Distribution of a Stochastic SIR Epidemic Model with Jumps

A stochastic susceptible-infective-recovered(SIR)epidemic model with jumps was considered.The contributions of this paper are as follows.(1) The stochastic differential equation(SDE)associated with the model has a unique global positive solution;(2) the results reveal that the solution of this epidemic model will be stochastically ultimately bounded,and the non-linear SDE admits a unique stationary distribution under certain parametric conditions;(3) the coefficients play an important role in the extinction of the diseases.

Asymptotic Behavior and Stability of Stochastic SIR Model with Variable Diffusion Rates

In this paper, we propose random fluctuation on contact and recovery rates in deterministic SIR model with disease deaths in nonparametric manner and derive a new stochastic SIR model with distributed time delay and general diffusion coefficients. By analysis of the introduced model, we obtain the sufficient conditions for the regularity, existence and uniqueness of a global solution by means of Lyapunov function. Moreover, we also investigate the stochastic asymptotic stability of disease free equilibria and endemic equilibria of this model. Finally, we illustrate our general results by applications.