A note on epidemics in heterogeneous populations.

Recent analysis has shown the importance of heterogeneity for understanding the course of epidemics. However, the results generally rely on computer models or the assumption that the population consists of internally homogeneous subgroups. This note presents some analytic results for the more general case, in which any distribution can characterize population heterogeneity in susceptibility under proportionate mixing. At any moment, epidemics in such a situation resemble classic epidemics, with rate of spread governed by the average susceptibility of those not yet infected. But, over time, this average susceptibility falls at a rate proportional to the dispersion of susceptibility among those not yet infected. The author concludes by noting some implications of heterogeneity for understanding epidemics.     

Dynamics of stochastic epidemics on heterogeneous networks

Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a heterogeneous network. Using this, we consider analytically the early asymptotic exponential growth phase of such epidemics, showing how the higher order moments of the network degree distribution enter into the stochastic behaviour of the epidemic. We find that the first three moments of the network degree distribution are needed to specify the variance in disease prevalence fully, meaning that the skewness of the degree distribution affects the variance of the prevalence of infection. We compare these asymptotic results to simulation and find a close agreement for city-sized populations.     

Emergent heterogeneity in declining tuberculosis epidemics

Tuberculosis is a disease of global importance: over 2 million deaths are attributed to this infectious disease each year. Even in areas where tuberculosis is in decline, there are sporadic outbreaks which are often attributed either to increased host susceptibility or increased strain transmissibility and virulence. Using two mathematical models, we explore the role of the contact structure of the population, and find that in declining epidemics, localized outbreaks may occur as a result of contact heterogeneity even in the absence of host or strain variability. We discuss the implications of this finding for tuberculosis control in low incidence settings.     

The size of epidemics in populations with heterogeneous susceptibility

We formulate and study a general epidemic model allowing for an arbitrary distribution of susceptibility in the population. We derive the final-size equation which determines the attack rate of the epidemic, somewhat generalizing previous work. Our main aim is to use this equation to investigate how properties of the susceptibility distribution affect the attack rate. Defining an ordering among susceptibility distributions in terms of their Laplace transforms, we show that a susceptibility distribution dominates another in this ordering if and only if the corresponding attack rates are ordered for every value of the reproductive number R0. This result is used to prove a sharp universal upper bound for the attack rate valid for any susceptibility distribution, in terms of R0 alone, and a sharp lower bound in terms of R0 and the coefficient of variation of the susceptibility distribution. We apply some of these results to study two issues of epidemiological interest in a population with heterogeneous susceptibility: (1) the effect of vaccination of a fraction of the population with a partially effective vaccine, (2) the effect of an epidemic of a pathogen inducing partial immunity on the possibility and size of a future epidemic. In the latter case, we prove a surprising '50% law': if infection by a pathogen induces a partial immunity reducing susceptibility by less than 50%, then, whatever the value of R0>1 before the first epidemic, a second epidemic will occur, while if susceptibility is reduced by more than 50%, then a second epidemic will only occur if R0 is larger than a certain critical value greater than 1.     

Modeling epidemics dynamics on heterogenous networks

The dynamics of the SIS process on heterogenous networks, where different local communities are connected by airlines, is studied. We suggest a new modeling technique for travelers movement, in which the movement does not affect the demographic parameters characterizing the metapopulation. A solution to the deterministic reaction-diffusion equations that emerges from this model on a general network is presented. A typical example of a heterogenous network, the star structure, is studied in detail both analytically and using agent-based simulations. The interplay between demographic stochasticity, spatial heterogeneity and the infection dynamics is shown to produce some counterintuitive effects. In particular it was found that, while movement always increases the chance of an outbreak, it may decrease the steady-state fraction of sick individuals. The importance of the modeling technique in estimating the outcomes of a vaccination campaign is demonstrated.     

Percolation on heterogeneous networks as a model for epidemics

We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong heterogeneity, i.e. a wide range of variation of susceptibility, patchiness in the spread of the epidemic is very likely, and the criterion for epidemic outbreak depends strongly on the heterogeneity. These results are qualitatively different from those of standard models in epidemiology, but correspond to real effects. We suggest that heterogeneity in the epidemic will affect the phylogenetic distance distribution of the disease-causing organisms. We also investigate small world lattices, and show that the effects mentioned above are even stronger.     

On the spread of epidemics in a closed heterogeneous population

Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptible-infective-removed) model is formulated and analyzed when susceptibility to or infectivity of a particular disease is distributed. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from the model with distributed susceptibility and infectivity with the initial gamma-distribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which is believed to mimic reality with high accuracy, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution of susceptibility is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual moment-closure methods can lead to erroneous conclusions if applied for the study of the long-term behavior of the models.     

Modeling the Potential Impact of Host Population Survival on the Evolution of M. tuberculosis Latency

Tuberculosis (TB) is an infectious disease with a peculiar feature: Upon infection with the causative agent, Mycobacterium Tuberculosis (MTB), most hosts enter a latent state during which no transmission of MTB to new hosts occurs. Only a fraction of latently infected hosts develop TB disease and can potentially infect new hosts. At first glance, this seems like a waste of transmission potential and therefore an evolutionary suboptimal strategy for MTB. It might be that the human immune response keeps MTB in check in most hosts, thereby preventing it from achieving its evolutionary optimum. Another possible explanation is that long latency and progression to disease in only a fraction of hosts are evolutionary beneficial to MTB by allowing it to persist better in small host populations. Given that MTB has co-evolved with human hosts for millenia or longer, it likely encountered small host populations for a large share of its evolutionary history and had to evolve strategies of persistence. Here, we use a mathematical model to show that indeed, MTB persistence is optimal for an intermediate duration of latency and level of activation. The predicted optimal level of activation is above the observed value, suggesting that human co-evolution has lead to host immunity, which keeps MTB below its evolutionary optimum.     

耐多药结核病的分子机制及其检测方法

结核病发现已有 1 0 0多年历史 ,人们曾乐观地预言 2 0世纪末即将消灭结核病。然而不合理的联合用药、管理不善、药物供应不足质量不佳以及间断用药等 ,使结核分支杆菌不能及时被杀死 ,产生耐药性。当前耐药性结核病已成为结核病疫情上升和难以控制的一个重要原因。目前约有 50 0 0万人感染了耐药结核分支杆菌。耐多药结核病是耐药结核病中后果最严重的一种 ,给结核病的防治带来很大困难。1　耐多药结核病的定义及其分类有关耐多药结核病 (ｍｕｌｔｉｄｒｕｇ -ｒｅｓｉｓｔａｎｔｔｕｂｅｒｃｕｌｏｓｉｓ ,ＭＤＲ-ＴＢ)的定义 ,国际上目前…     

Occurrence of heterogeneous R-plasmids during two concurrent epidemics due to multidrug-resistantSalmonella oranienburg

During two different epidemics that started in August–September, 1980, 140 and 6 multidrug-resistant strains ofSalmonella oranienburg were isolated from a Children's Hospital in New Delhi (epidemic 1) and H.N. Das Hospital in Bombay (epidemic 2) respectively. Out of 140, 123 strains showed high levels of resistance to ampicillin, kanamycin, streptomycin, sulfamethoxazole, tetracycline, and trimethoprim. All six strains of epidemic 2 and two strains of epidemic 1 were also found resistant to chloramphenicol in addition to the above antibiotics. The genetic characterization of conjugative R-plasmids harbored by these strains revealed that, while strains of epidemic 1 carry a fi^–, 96 megadalton, an unclassified plasmid, the strains isolated during epidemic 2 contain a fi^–, 62 megadalton plasmid of incompatibility group I₁. All the six strains of epidemic 2 were found to produce bacteriocin of Col Ib group. Plasmid transfer studies revealed that the genes for antibiotic resistance and bacteriocin production were coded on a single plasmid of 62 megadalton. The data show the significance of detailed genetic analysis while dealing with the clonal outbreaks due to same resistant serotypes.     

On treatment of tuberculosis in heterogeneous populations

Global eradication of tuberculosis (TB) is an international agenda. Thus understanding effects of treatment of TB in different settings is crucial. In previous work, we introduced the framework for a mathematical model of epidemic TB in demographically distinct, heterogeneous populations. Simulations showed the importance of genetic susceptibility in determining endemic prevalence levels. In the work presented here, we include treatment and investigate different strategies for treatment of latent and active TB disease in heterogeneous populations. We illustrate how the presence of a genetically susceptible subpopulation dramatically alters effects of treatment in the same way a core population does in the setting of sexually transmitted diseases. In addition, we evaluate treatment strategies that focus specifically on this subpopulation, and our results indicate that genetically susceptible subpopulations should be accounted for when designing treatment strategies to achieve the greatest reduction in disease prevalence.     

用PCR方法定向突变结核分枝杆菌glmU基因

目的:结核分枝杆茵glmU基因是分枝杆菌生长必需基因,其编码产物具有乙酰基转移酶活性和尿嘧啶转移酶活性,参与细胞壁前体物UDP-乙酰葡糖胺(UDP-GlcNAc)的生物合成,研究其空间结构可以定向设计酶抑制剂.方法:利用PCR方法定向突变结核分枝杆菌glmO基因,并用大肠杆菌BL21(DE3)高表达m-GlmU蛋白.结果:获得了定向突变的结核分枝杆菌glmU基因,m-glmU.纯化的m-GlmU蛋白仍具有乙酰基转移酶活性和尿嘧啶核苷转移酶活性.结论:纯化的m-GlmU蛋白为进一步研究其稳定性、测定其空间结构提供了物质基础.     

Test for differentiation of M. tuberculosis and M. bovis from other mycobacteria.

A test is described for selective inhibition of Mycobacterium tuberculosis and M. bovis isolates in fluid medium. The method employs rho-nitro-alpha-acetyl-amino-beta-hydroxy-propiophenone (NAP) as an inhibitory agent for differentiation of mammalian tuberculosis strains from other Mycobacteria.