A cellular automata model of epidemics of a heterogeneous susceptibility

In this paper we present a model with spatial heterogeneity based on cellular automata (CA). In the model we consider the relevant heterogeneity of host (susceptible) mixing and the natural birth rate. We divide the susceptible population into three groups according to the immunity of each individual based on the classical susceptible--infected--removed (SIR) epidemic models, and consider the spread of an infectious disease transmitted by direct contact among humans and vectors that have not an incubation period to become infectious. We test the local stability and instability of the disease-free equilibrium by the spectrum radii of Jacobian. The simulation shows that the structure of the nearest neighbour size of the cell (or the degree of the scale-free networks) plays a very important role in the spread properties of infectious disease. The positive equilibrium of the infections versus the neighbour size follows the third power law if an endemic equilibrium point exists. Finally, we analyse the feature of the infection waves for the homogeneity and heterogeneous cases respectively.     

Immunization of susceptible-infected model on scale-free networks

In this paper, we investigate two major immunization strategies, random immunization and targeted immunization, of the susceptible-infected (SI) model on the Barabási-Albert (BA) networks. For the heterogeneous structure, the random strategy is quite ineffective if the vaccinated proportion is small, while the targeted one which prefers to vaccinate the individuals with the largest degree can sharply depress the epidemic spreading even only a tiny fraction of population are vaccinated. The analytical solution is also obtained, which can capture the trend of velocity change vs. the amount of vaccinated population.     

一类SEIRS型流行病的细胞自动机模型

本文通过分析SEIRS类流行病，建立了该类疾病的二维概率细胞自动机模型。在二维中，每个细胞的状态代表易感者，潜伏者，患者，恢复者（或免疫者）和死亡者五个部分个体之一。我们研究了两种情况下，即对潜伏者和患者隔离与不隔离将对疾病转播的影响。经研究我们发现，如果不隔离疾病将持续流行，而及时的隔离则将会减缓疾病的流行。本模型给出了对具体疾病利用细胞自动进行仿真的算法。我们发现当恢复者的失去免疫力大于时，疾病潜伏者和患者的密度序列将在正平衡点附近振荡。最后，我们用计算机对模型进行了仿真。     

Imperfect targeted immunization in scale-free networks

Scale-free networks are prone to epidemic spreading. To provide cost-effective protection for such networks, targeted immunization was proposed to selectively immunize the hub nodes. In many real-life applications, however, the targeted immunization may not be perfect, either because some hub nodes are hidden and consequently not immunized, or because the vaccination simply cannot provide perfect protection. We investigate the effects of imperfect targeted immunization in scale-free networks. Analysis and simulation results show that there exists a linear relationship between the inverse of the epidemic threshold and the effectiveness of targeted immunization. Therefore, the probability of epidemic outbreak cannot be significantly lowered unless the protection is reasonably strong. On the other hand, even a relatively weak protection over the hub nodes significantly decreases the number of network nodes ever getting infected and therefore enhances network robustness against virus. We show that the above conclusions remain valid where there exists a negative correlation between nodal degree and infectiousness.     

Effects of City-Size Heterogeneity on Epidemic Spreading in a Metapopulation: A Reaction-Diffusion Approach

We review and introduce a generalized reaction-diffusion approach to epidemic spreading in a metapopulation modeled as a complex network. The metapopulation consists of susceptible and infected individuals that are grouped in subpopulations symbolizing cities and villages that are coupled by human travel in a transportation network. By analytic methods and numerical simulations we calculate the fraction of infected people in the metapopulation in the long time limit, as well as the relevant parameters characterizing the epidemic threshold that separates an epidemic from a non-epidemic phase. Within this model, we investigate the effect of a heterogeneous network topology and a heterogeneous subpopulation size distribution. Such a system is suited for epidemic modeling where small villages and big cities exist simultaneously in the metapopulation. We find that the heterogeneous conditions cause the epidemic threshold to be a non-trivial function of the reaction rates (local parameters), the network’s topology (global parameters) and the cross-over population size that separates “village dynamics” from “city dynamics”.     

自适应网络中病毒传播的稳定性和分岔行为研究

自适应复杂网络是以节点状态与拓扑结构之间存在反馈回路为特征的网络. 针对自适应网络病毒传播模型, 利用非线性微分动力学系统研究病毒传播行为; 通过分析非线性系统对应雅可比矩阵的特征方程, 研究其平衡点的局部稳定性和分岔行为, 并推导出各种分岔点的计算公式. 研究表明, 当病毒传播阈值小于病毒存在阈值, 即R₀0^c时, 网络中病毒逐渐消除, 系统的无病毒平衡点是局部渐近稳定的; R₀^c0<1时, 网络出现滞后分岔, 产生双稳态现象, 系统存在稳定的无病毒平衡点、较大稳定的地方病平衡点和较小不稳定的地方病平衡点; R₀>1时, 网络中病毒持续存在, 系统唯一的地方病平衡点是局部渐近稳定的. 研究发现, 系统先后出现了鞍结分岔、跨临界分岔、霍普夫分岔等分岔行为. 最后通过数值仿真验证所得结论的正确性. 关键词： 自适应网络 稳定性 分岔 基本再生数     

Optimal vaccination and treatment of an epidemic network model

In this Letter, we firstly propose an epidemic network model incorporating two controls which are vaccination and treatment. For the constant controls, by using Lyapunov function, global stability of the disease-free equilibrium and the endemic equilibrium of the model is investigated. For the non-constant controls, by using the optimal control strategy, we discuss an optimal strategy to minimize the total number of the infected and the cost associated with vaccination and treatment. Table 1 and Figs. 1–5 are presented to show the global stability and the efficiency of this optimal control.     

Analysis of epidemic models with demographics in metapopulation networks

In this paper, two susceptible–infected–susceptible (SIS) epidemic models are presented and analyzed by reaction–diffusion processes with demographics in metapopulation networks. Firstly, an SIS model with constant-inputting is discussed. The model has a disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number is less than unity, otherwise it is unstable. It has an endemic equilibrium, which is globally asymptotically stable. Secondly, in another SIS model, the birth rate is the form of Logistic. Similarly, the stability of disease-free equilibrium and endemic equilibrium is also proved. Finally, numerical simulations are performed to illustrate the analytical results.     

Effects of Vaccination Efficacy on Wealth Distribution in Kinetic Epidemic Models

The spread of the COVID-19 pandemic has highlighted the close link between economics and health in the context of emergency management. A widespread vaccination campaign is considered the main tool to contain the economic consequences. This paper will focus, at the level of wealth distribution modeling, on the economic improvements induced by the vaccination campaign in terms of its effectiveness rate. The economic trend during the pandemic is evaluated, resorting to a mathematical model joining a classical compartmental model including vaccinated individuals with a kinetic model of wealth distribution based on binary wealth exchanges. The interplay between wealth exchanges and the progress of the infectious disease is realized by assuming, on the one hand, that individuals in different compartments act differently in the economic process and, on the other hand, that the epidemic affects risk in economic transactions. Using the mathematical tools of kinetic theory, it is possible to identify the equilibrium states of the system and the formation of inequalities due to the pandemic in the wealth distribution of the population. Numerical experiments highlight the importance of the vaccination campaign and its positive effects in reducing economic inequalities in the multi-agent society.     

考虑网络流量的无标度网络病毒免疫策略研究

考虑网络交通流量对病毒传播行为的影响,基于平均场理论研究无标度网络上的病毒免疫策略,提出一种改进的熟人免疫机理.理论分析表明,在考虑网络交通流量影响的情况下,当免疫节点密度较小时,随机免疫几乎不能降低病毒的传播速率,而对网络实施目标免疫则能够有效抑制病毒的传播,并且选择度最大的节点进行免疫与选择介数最大的节点进行免疫的效果基本相同.研究还发现,对于网络全局信息未知的情况,与经典熟人免疫策略相比,所提出的免疫策略能够获得更好的免疫效果.通过数值仿真对理论分析进行了验证. 关键词： 无标度网络 病毒传播 交通流量 免疫策略     

Quadratic corrections to three‐point functions

Following the recent progress on the calculation of three‐point correlators with two “heavy” (with large quantum numbers) and one “light” states at strong coupling, we compute the logarithmic divergent terms of leading bosonic quantum corrections to correlation functions with “heavy” operators corresponding to simple string solutions in AdS₅ × S⁵. The “light” operator is chosen to be the dilaton. An important relation connecting the corrections to both the dimensions of “heavy” states, and the structure constants is recovered.     

Effects of disease characteristics and population distribution on dynamics of epidemic spreading among residential sites

We investigate the spreading processes of epidemic diseases among many residential sites for different disease characteristics and different population distributions by constructing and solving a set of integrodifferential equations for the evolutions of position-dependent infected and infective rates, taking into account the infection processes both within a single site and among different sites. In a spreading process the states of an individual include susceptible (S), incubative (I), active (A) and recovered (R) states. Although the transition from S to I mainly depends on the active rate, the susceptible rate and the connectivity among individuals, the transitions from I to A and from A to R are determined by intrinsic characteristics of disease development in individuals. We adopt incubation and infection periods to describe the intrinsic features of the disease. By numerically solving the equations we find that the asymptotic behavior of the spreading crucially depends on the infection period and the population under affection of an active individual. Other factors, such as the structure of network and the popular distribution, play less important roles. The study may provide useful information for analyzing the key parameters affecting the dynamics and the asymptotic behavior.     

Epidemic spreading on networks with vaccination

In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.     

The impact of human activity patterns on asymptomatic infectious processes in complex networks

The study of the impact of human activity patterns on network dynamics has attracted a lot of attention in recent years. However, individuals’ knowledge of their own physical states has rarely been incorporated into modeling processes. In real life, for certain infectious processes, infected agents may not have any visible or physical signs and symptoms; therefore, they may believe that they are uninfected even when they have been infected asymptomatically. This infection awareness factor is covered neither in the classical epidemic models such as SIS nor in network propagation studies. In this article, we propose a novel infectious process model that differentiates between the infection awareness states and the physical states of individuals and extend the SIS model to deal with both asymptomatic infection characteristics and human activity patterns. With regards to the latter, we focus particularly on individuals’ testing action, which is to determine whether an individual is infected by an epidemic. The simulation results show that less effort is required in controlling the disease when the transmission probability is either very small or large enough and that Poisson activity patterns are more effective than heavy-tailed patterns in controlling and eliminating asymptomatic infectious diseases due to the long-tail characteristic.     

Effects of delayed recovery and nonuniform transmission on the spreading of diseases in complex networks

We investigate the effects of delaying the time to recovery (delayed recovery) and of nonuniform transmission on the propagation of diseases on structured populations. Through a mean-field approximation and large-scale numerical simulations, we find that postponing the transition from the infectious to the recovered states can largely reduce the epidemic threshold, therefore promoting the outbreak of epidemics. On the other hand, if we consider nonuniform transmission among individuals, the epidemic threshold increases, thus inhibiting the spreading process. When both mechanisms are at work, the latter might prevail, hence resulting in an increase of the epidemic threshold with respect to the standard case, in which both ingredients are absent. Our findings are of interest for a better understanding of how diseases propagate on structured populations and to a further design of efficient immunization strategies.     

Superradiance with Incoherent Nonradiative Decay

We describe superradiance of a few emitters in a dissipative environment with nonradiative decay in the Schrödinger approach, which is simpler than the density matrix formalism. We find that superradiance increases the quantum efficiency of the radiation if the baths, responsible for dissipation, do not come to equilibrium. The reason is that decoherence destroys Dicke “dark” states, lets emitters radiate, and does not affect the fast radiation from “bright” Dicke states.     

Epidemic spreading on a scale-free network with awareness

This paper presents a modified susceptible-infected-recovered(SIR) model with the effects of awareness and vaccination to study the epidemic spreading on scale-free networks based on the mean-field theory.In this model,when susceptible individuals receive awareness from their infected neighbor nodes,they will take vaccination measures.The theoretical analysis and the numerical simulations show that the existence of awareness and vaccination can significantly improve the epidemic threshold and reduce the risk of virus outbreaks.In addition,regardless of the existence of vaccination,the awareness can increase the spreading threshold and slow the spreading speed effectively.For a given awareness and a certain spreading rate,the total number of infections reduces with the increasing vaccination rate.     

Global analysis of multiple routes of disease transmission on heterogeneous networks

In this paper, we propose and study an SIS epidemic model with multiple transmission routes on heterogeneous networks. We focus on the dynamical evolution of the prevalence. Through mathematical analysis, we obtain the basic reproduction number _R0$R_0$ by investigating the local stability of the disease-free equilibrium and also investigate the effects of various immunization schemes on disease spread. We further obtain that the disease will die out independent of the initial infections if the basic reproduction number is less than one, otherwise if the basic reproduction number is larger than one, the system converges to a unique endemic equilibrium, which is globally stable and thus the disease persists in the population. Our theoretical results are conformed by a series of numerical simulations and suggest a promising way for the control of infectious diseases with multiple routes.     

Variations of the epidemic distribution with some characteristic parameters

Considering the epidemic spread among a population of mobile agents which can get infected and maintain the infection for a period, we investigate the variation of the homogeneity of the epidemic distribution with the remaining time of infection τ, the velocity modulus of the agent v, and the infection rate α. We find that the distribution of the infected cluster size is always exponential. By analyzing the variation of the characteristic infected cluster size coefficient, we show that, the inhomogeneity of the epidemic distribution increases with the increase of τ for very low v, while decreases with the increase of τ for moderate v. And the epidemic distribution tends to a homogeneous state as both v and α increase.     

Variations in epidemic distribution with some characteristic parameters

Considering the spread of an epidemic among a population of mobile agents that can get infected and maintain the infection for a period, we investigate the variation in the homogeneity of the distribution of the epidemic with the remaining time of infection τ, the velocity modulus of the agent v, and the infection rate α. We find that the distribution of the infected cluster size is always exponential. By analyzing the variation of the characteristic infected cluster size coefficient, we show that the inhomogeneity of epidemic distribution increases with an increase in τ for very low v, while it decreases with an increase in τ for moderate v. The epidemic distribution also tends to a homogeneous state as both v and α increase.