Modeling epidemic spread with awareness and heterogeneous transmission rates in networks

During an epidemic outbreak in a human population, susceptibility to infection can be reduced by raising awareness of the disease. In this paper, we investigate the effects of three forms of awareness (i.e., contact, local, and global) on the spread of a disease in a random network. Connectivity-correlated transmission rates are assumed. By using the mean-field theory and numerical simulation, we show that both local and contact awareness can raise the epidemic thresholds while the global awareness cannot, which mirrors the recent results of Wu et al. The obtained results point out that individual behaviors in the presence of an infectious disease has a great influence on the epidemic dynamics. Our method enriches mean-field analysis in epidemic models.     

一起流行性脑脊髓膜炎疫情的调查及控制

目的对流行性脑脊髓膜炎疫情进行流行病学分析,以了解流行性脑脊髓膜炎(流脑)发生的特点,评价防控措施的效果。方法采用现场流行病学、血清学调查的方法对发生的流行性脑脊髓膜炎疫情进行调查分析。结果此疫情鉴定为一起C群脑膜炎奈瑟菌引起的聚集性病例,3例病人均已接种过A群流脑多糖疫苗3～4次,而未接种过A群C群流脑多糖疫苗,对C群脑膜炎奈瑟菌无免疫力;采取相应措施后疫情得到控制,没有引起流脑流行。结论对C群脑膜炎奈瑟菌所致疫情,采取以预防性服药、应急接种为主的综合控制措施能得到有效控制。     

Quantification of the effect of control strategies on classical swine fever epidemics

Emergency vaccination during an epidemic of classical swine fever virus (CSFV) has become a serious option because of the ethical problems of strategies with massive culling and the availability of a marker vaccine that reduces virus transmission. Here we present a model of between-herd CSFV transmission, which quantifies the effect of control strategies with and without vaccination. We estimate the model parameters from data of the Dutch CSFV epidemic of 1997/1998. With the model, a set of control strategies is compared, consisting of five control measures in several combinations. Consequently, the following general requirements of successful strategies can be formulated. First, to achieve extinction of a CSFV epidemic, transmission through transport should be prevented and the indirect virus transmission, i.e. all transmission not through animal contacts, should at least be halved, either by vaccination or by culling of the susceptible pig population. Second, to minimize the size and duration of an epidemic, the extinction requirements should be met quickly and indirect virus transmission should be reduced by far more than a half. Although the origin of the model parameters let the requirements in fact be only applicable for the south-eastern part of the Netherlands, it is argued that epidemics in other areas will not need stricter control strategies.     

The relationship between real-time and discrete-generation models of epidemic spread

Many important results in stochastic epidemic modelling are based on the Reed-Frost model or on other similar models that are characterised by unrealistic temporal dynamics. Nevertheless, they can be extended to many other more realistic models thanks to an argument first provided by Ludwig [Final size distributions for epidemics, Math. Biosci. 23 (1975) 33-46], that states that, for a disease leading to permanent immunity after recovery, under suitable conditions, a continuous-time infectious process has the same final size distribution as another more tractable discrete-generation contact process; in other words, the temporal dynamics of the epidemic can be neglected without affecting the final size distribution. Despite the importance of such an argument, its presence behind many results is often not clearly stated or hidden in references to previous results. In this paper, we reanalyse Ludwig’s result, highlighting some of the conditions under which it does not hold and providing a general framework to examine the differences between the continuous-time and the discrete-generation process.     

The effect of correlations on the population dynamics of lymphocytes

Recent studies of the population dynamics of a system of lymphocytes in an in vitro immune response have reported strong correlations in cell division times, both between parents and their progeny, and between those of sibling cells. The data also show a high level of correlation in the ultimate number of divisions achieved by cells within the same clone. Such correlations are often ignored in mathematical models of cell dynamics as they violate a standard assumption in the theory of branching processes, that of the statistical independence of cells. In this article we present a model in which these correlations can be incorporated, and have used this model to study the effect of these correlations on the population dynamics of a system of cells. We found that correlation in the division times between parents and their progeny can alter the mean population size of clones within the system, while all of the correlations can affect the variance in the sizes of different clones. The model was then applied to experimental data obtained from time-lapse video microscopy of a system of CpG stimulated B lymphocytes and it was found that inclusion of the correct correlation structure is necessary to accurately reproduce the observed population dynamics. We conclude that correlations in the dynamics of cells within an ensemble will affect the population dynamics of the system, and the effects will become more pronounced as the number of divisions increases.     

The probability of extinction in a bovine respiratory syncytial virus epidemic model

Backward bifurcation is a relatively recent yet well-studied phenomenon associated with deterministic epidemic models. It allows for the presence of multiple subcritical endemic equilibria, and is generally found only in models possessing a reasonable degree of complexity. One particular aspect of backward bifurcation that appears to have been virtually overlooked in the literature is the potential influence its presence might have on the behaviour of any analogous stochastic model. Indeed, the primary aim of this paper is to investigate this possibility. Our approach is to compare the theoretical probabilities of extinction, calculated via a particular stochastic formulation of a deterministic model exhibiting backward bifurcation, with those obtained from a series of stochastic simulations. We have found some interesting links in the behaviour between the deterministic and stochastic models, and are able to offer plausible explanations for our observations.     

具有年龄结构的接种流行病模型正平衡解的全局稳定性

研究一个具有年龄结构的接种SIS流行病模型正平衡解的稳定性,先利用等价积分方程给出了正平衡解存在的充分条件,再利用迭代方法及函数的单调性,得到了零平衡解与正平衡解全局稳定的充分条件。     

The Kermack-McKendrick epidemic model revisited

The Kermack-McKendrick epidemic model of 1927 is an age of infection model, that is, a model in which the infectivity of an individual depends on the time since the individual became infective. A special case, which is formulated as a two-dimensional system of ordinary differential ordinary differential equations, has often been called the Kermack-McKendrick model. One of the products of the SARS epidemic of 2002-2003 was a variety of epidemic models including general contact rates, quarantine, and isolation. These models can be viewed as age of infection epidemic models and analyzed using the approach of the full Kermack-McKendrick model. All these models share the basic properties that there is a threshold between disappearance of the disease and an epidemic outbreak, and that an epidemic will die out without infecting the entire population.     

西非防控埃博拉病毒病暴发和流行的分析

埃博拉出血热自1976年首次暴发以来,其高致死率引起了人们的高度重视。2014年的埃博拉病毒病疫情已造成6800多人死亡。其暴发流行既有病原学和流行病学因素,也与西非当地的政治、经济、文化、卫生现状及应对措施密切相关。因此,综合分析造成流行的因素,有利于尽快控制疫情的迅速蔓延。目前包括中国政府在内的国际社会给予了积极帮助,国际社会与西非本国防控力量的有效结合将在更短的时间内控制疫情,并为我国做好埃博拉病毒病疫情的相关防控提供新的思考。     

Estimation of the size of the vCJD epidemic

Estimates of the final size of the variant Creuzfeldt-Jakob Disease epidemic have been made by fitting theoretical curves of the incubation period distribution to the histogram of observed annual deaths to 2002, using various assumptions of the mean and standard deviation of this distribution, and also of the efficacy of the Specified Bovine Offals ban of 1989. Unless the mean incubation time is greater than 15 to 20 years the estimates lie in the low hundreds to about a thousand, and the most likely situation, of a mean between 11 and 15 years, gives estimates of about 150 to 500 deaths. Numbers above a few thousands would only occur if the mean incubation period is of the order of 25 to 30 years and reasons are adduced to indicate this is very unlikely. These numbers are not greatly increased if the ban was poorly observed. This method of analysis may be applicable to other situations where a cause that is limited in space and time is expected to have late effects.     

A Martingale Approach to the Investigation of the Duration of a Mild Epidemic

The present paper is an attempt to evolve a simple methodology to obtain the steady state solution of the duration of a mild epidemic (like conjunctivitis, for which the period of sickness is about a week and the period of immunity following recovery is comparatively large) and also the intensity of the epidemic measured by the number of infections during the complete spell of the epidemic. The methodology consists of constructing Martingales based on subcritical and supercritical forms of a Simple Branching Process; and obtaining the stopping time enabling to evaluate the expected duration of the epidemic and the sampling variance together with the intensity of the epidemic.     

Some properties of a simple stochastic epidemic model of SIR type

We investigate the properties of a simple discrete time stochastic epidemic model. The model is Markovian of the SIR type in which the total population is constant and individuals meet a random number of other individuals at each time step. Individuals remain infectious for R time units, after which they become removed or immune. Individual transition probabilities from susceptible to diseased states are given in terms of the binomial distribution. An expression is given for the probability that any individuals beyond those initially infected become diseased. In the model with a finite recovery time R, simulations reveal large variability in both the total number of infected individuals and in the total duration of the epidemic, even when the variability in number of contacts per day is small. In the case of no recovery, R=infinity, a formal diffusion approximation is obtained for the number infected. The mean for the diffusion process can be approximated by a logistic which is more accurate for larger contact rates or faster developing epidemics. For finite R we then proceed mainly by simulation and investigate in the mean the effects of varying the parameters p (the probability of transmission), R, and the number of contacts per day per individual. A scale invariant property is noted for the size of an outbreak in relation to the total population size. Most notable are the existence of maxima in the duration of an epidemic as a function of R and the extremely large differences in the sizes of outbreaks which can occur for small changes in R. These findings have practical applications in controlling the size and duration of epidemics and hence reducing their human and economic costs.     

On the effect of population heterogeneity on dynamics of epidemic diseases

The paper investigates a class of SIS models of the evolution of an infectious disease in a heterogeneous population. The heterogeneity reflects individual differences in the susceptibility or in the contact rates and leads to a distributed parameter system, requiring therefore, distributed initial data, which are often not available. It is shown that there exists a corresponding homogeneous (ODE) population model that gives the same aggregated results as the distributed one, at least in the expansion phase of the disease. However, this ODE model involves a nonlinear “prevalence-to-incidence” function which is not constructively defined. Based on several established properties of this function, a simple class of approximating function is proposed, depending on three free parameters that could be estimated from scarce data.How the behaviour of a population depends on the level of heterogeneity (all other parameters kept equal) – this is the second issue studied in the paper. It turns out that both for the short run and for the long run behaviour there exist threshold values, such that more heterogeneity is advantageous for the population if and only if the initial (weighted) prevalence is above the threshold.This research was partly supported by the Austrian Science Foundation under contract N0. 15618-OEK.     

Exploring landscape structure effect on termite territory size using a model approach

The foraging territory of the Formosan subterranean termite, Coptotermes formosanus Shiraki, was simulated by using a lattice model in order to study how landscape structure affects the foraging territory. Three kinds of landscape were generated on lattice space: ideal, random and fractal landscape. Each lattice cell had a value ranging from 0.0 to 1.0, interpreted as transition probability, P_trans, which represents spatially distributed property of the landscapes. The heterogeneity of the fractal landscape was characterized by a parameter, H, controlling aggregation of lattice cells with higher value of P_trans. Higher H values corresponded to higher aggregation levels. The model made use of minimized local rules based on empirical data that determines the development of the foraging territory. Additionally, seasonal cycle (summer and winter season), and obstacles which hinder the growth of the territory were incorporated in the model as environmental variables. Territory size was largest in the ideal landscape while it was larger in the random landscape than in the fractal landscape. As obstacle density increased, the territory size decreased. In the fractal landscape, the territory size increased, decreased, and increased again as H increased.     

The effect of gene drive on containment of transgenic mosquitoes

Mosquito-borne diseases such as malaria and dengue fever continue to be a major health problem through much of the world. Several new potential approaches to disease control utilize gene drive to spread anti-pathogen genes into the mosquito population. Prior to a release, these projects will require trials in outdoor cages from which transgenic mosquitoes may escape, albeit in small numbers. Most genes introduced in small numbers are very likely to be lost from the environment; however, gene drive mechanisms enhance the invasiveness of introduced genes. Consequently, introduced transgenes may be more likely to persist than ordinary genes following an accidental release. Here, we develop stochastic models to analyze the loss probabilities for several gene drive mechanisms, including homing endonuclease genes, transposable elements, Medea elements, the intracellular bacterium Wolbachia, engineered underdominance genes, and meiotic drive. We find that Medea and Wolbachia present the best compromise between invasiveness and containment for the six gene drive systems currently being considered for the control of mosquito-borne disease.     

2012年大连市流行性角结膜炎疫情的病原鉴定与基因特征分析

目的 鉴定一起大连市流行性角结膜炎疫情的病原体及型别.方法 采用荧光PCR方法针对30份眼拭标本进行检测,确定病原,并针对特定片段扩增产物测序进行分子定型.结果 21份标本荧光PCR检测结果为腺病毒阳性,核苷酸序列与人腺病毒15、29、56及其重组型高度同源,多重序列比对后构建的系统进化树上与人腺病毒56及其重组型位于同一分支.结论 本次疫情的致病病原为D亚属人腺病毒,疑为人腺病毒56型或其重组型.后续需要开展对五邻体(Penton)及纤突(Fi-ber)基因的全核苷酸序列测定及生物信息学分析最终确定型别.     

The effect of transmission route on plant virus epidemic development and disease control

A model for indirect vector transmission and epidemic development of plant viruses is extended to consider direct transmission through vector mating. A basic reproduction number is derived which is the sum of the R₀ values specific for three transmission routes. We analyse the model to determine the effect of direct transmission on plant disease control directed against indirect transmission. Increasing the rate of horizontal sexual transmission means that vector control rate or indirect transmission rate must be increased/decreased substantially to maintain R₀ at a value less than 1. By contrast, proportionately increasing the probability of transovarial transmission has little effect. Expressions are derived for the steady-state values of the viruliferous vector population. There is clear advantage for an insect virus in indirect transmission to plants, especially where the sexual and transovarial transmission rates are low; however information on virulence-transmissibility relationships is required to explain the evolution of a plant virus from an insect virus.