The effect of waning immunity on long-term behaviour of stochastic models for the spread of infection

In stochastic modelling of infectious spread, it is often assumed that infection confers permanent immunity, a susceptible-infective-removed (SIR) model. We show how results concerning long-term (endemic) behaviour may be extended to a susceptible-infective-removed-susceptible (SIRS) model, in which immunity is temporary. Since the full SIRS model with demography is rather intractable, we also consider two simpler models: the susceptible-infective-susceptible (SIS) model with demography, in which there is no immunity; and the SIRS model in a closed population. For each model, we first analyse a deterministic model, then approximate the quasi-stationary distribution (equilibrium distribution conditional upon non-extinction of infection) using a moment closure technique. We look in particular at the effect of the immune period upon infection prevalence and upon time to fade-out of infection. Our main findings are that a shorter average immune period leads to higher infection prevalence in quasi-stationarity, and to longer persistence of infection in the population.     

The Effect of Loss of Immunity on Noise-Induced Sustained Oscillations in Epidemics

The effect of loss of immunity on sustained population oscillations about an endemic equilibrium is studied via a multiple scales analysis of a SIRS model. The analysis captures the key elements supporting the nearly regular oscillations of the infected and susceptible populations, namely, the interaction of the deterministic and stochastic dynamics together with the separation of time scales of the damping and the period of these oscillations. The derivation of a nonlinear stochastic amplitude equation describing the envelope of the oscillations yields two criteria providing explicit parameter ranges where they can be observed. These conditions are similar to those found for other applications in the context of coherence resonance, in which noise drives nearly regular oscillations in a system that is quiescent without noise. In this context the criteria indicate how loss of immunity and other factors can lead to a significant increase in the parameter range for prevalence of the sustained oscillations, without any external driving forces. Comparison of the power spectral densities of the full model and the approximation confirms that the multiple scales analysis captures nonlinear features of the oscillations.     

Impact of vaccination and birth rate on the epidemiology of pertussis: a comparative study in 64 countries

Bordetella pertussis infection remains an important public health problem worldwide despite decades of routine vaccination. A key indicator of the impact of vaccination programmes is the inter-epidemic period, which is expected to increase with vaccine uptake if there is significant herd immunity. Based on empirical data from 64 countries across the five continents over the past 30–70 years, we document the observed relationship between the average inter-epidemic period, birth rate and vaccine coverage. We then use a mathematical model to explore the range of scenarios for duration of immunity and transmission resulting from repeat infections that are consistent with empirical evidence. Estimates of pertussis periodicity ranged between 2 and 4.6 years, with a strong association with susceptible recruitment rate, defined as birth rate × (1 − vaccine coverage). Periodicity increased by 1.27 years on average after the introduction of national vaccination programmes (95% CI: 1.13, 1.41 years), indicative of increased herd immunity. Mathematical models suggest that the observed patterns of pertussis periodicity are equally consistent with loss of immunity that is not as rapid as currently thought, or with negligible transmission generated by repeat infections. We conclude that both vaccine coverage and birth rate drive pertussis periodicity globally and that vaccination induces strong herd immunity effects. A better understanding of the role of repeat infections in pertussis transmission is critical to refine existing control strategies.     

The loss of immunity in directly transmitted infections modeling: Effects on the epidemiological parameters

When directly transmitted infectious diseases are modeled assuming an everlasting induced immunity (and constant contact rate), there are well-established formulas to deal with, which is not true if we include the loss of induced immunity. In general, the immunity induced by the disease is everlasting. We propose a model considering the loss of immunity and present methods for the estimation of two epidemiological parameters: the force of infection and the basic reproduction ratio. We also analyze the effects of the loss of immunity on these parameters. Based on these results, we conclude that reinfection can play an important role in highly vaccinated populations.     

Modeling epidemics caused by respiratory syncytial virus (RSV)

Respiratory syncytial virus (RSV) is the most common cause of acute lower respiratory tract infection in children. In this paper we use models of RSV transmission to interpret the pattern of seasonal epidemics of RSV disease observed in different countries, and to estimate epidemic and eradication thresholds for RSV infection. We compare the standard SIRS model with a more realistic model of RSV transmission in which individuals acquire immunity gradually after repeated exposure to infection. The models are fitted to series of monthly hospital case reports of RSV disease from developed and developing countries. The models can explain many of the observed patterns: regular yearly outbreaks in some countries, and in other countries cycles of alternating larger and smaller annual epidemics, with shifted maxima in alternate years. Previously these patterns have been attributed to the transmission of different strains of RSV. In some countries the timing of epidemics is not consistent with increased social contact among school children during term time being the major driving mechanism. Climatic factors appear to be more important. Qualitatively different models gave equally good fits to the data series, but estimates of the transmission parameter were different by a factor of 4. Estimates of the basic reproduction number (R(0)) ranged from 1.2 to 2.1 with the SIRS model, and from 5.4 to 7.1 with the model with gradual acquisition of partial immunity.     

Vaccination based control of infections in SIRS models with reinfection: special reference to pertussis

The aim of this paper is to study the impact of introducing a partially protective vaccine on the dynamics of infection in SIRS models where primary and secondary infections are distinguished. We investigate whether a public health strategy based solely on vaccinating a proportion of newborns can lead to an effective control of the disease. In addition to carrying out the qualitative analysis, the findings are further explained by numerical simulations. The model exhibits backward bifurcation for certain values of the parameters. In these cases the standard basic reproduction number (obtained by inspection of the uninfected state) is not significant. The key threshold is the reinfection level which depends on the relative transmissibility (susceptibility) of secondary, with respect to primary, infected (susceptible) individuals and the relative loss of immunity of vaccinated, with respect to recovered, individuals. If one or all of these ratios decrease, then the threshold increases which increases the possibility to contain the infection by vaccination. The analysis shows further that symptomatic infections can be eliminated by vaccination solely.     

Inference of Type-Specific HPV Transmissibility,Progression and Clearance Rates: A Mathematical Modelling Approach

Quantifying rates governing the clearance of Human Papillomavirus (HPV) and its progression to clinical disease, together with viral transmissibility and the duration of naturally-acquired immunity, is essential in estimating the impact of vaccination programmes and screening or testing regimes. However, the complex natural history of HPV makes this difficult. We infer the viral transmissibility, rate of waning natural immunity and rates of progression and clearance of infection of 13 high-risk and 2 non-oncogenic HPV types, making use of a number of rich datasets from Sweden. Estimates of viral transmissibility, clearance of initial infection and waning immunity were derived in a Bayesian framework by fitting a susceptible-infectious-recovered-susceptible (SIRS) transmission model to age- and type-specific HPV prevalence data from both a cross-sectional study and a randomised controlled trial (RCT) of primary HPV screening. The models fitted well, but over-estimated the prevalence of four high-risk types with respect to the data. Three of these types (HPV-33, -35 and -58) are among the most closely related phylogenetically to the most prevalent HPV-16. The fourth (HPV-45) is the most closely related to HPV-18; the second most prevalent type. We suggest that this may be an indicator of cross-immunity. Rates of progression and clearance of clinical lesions were additionally estimated from longitudinal data gathered as part of the same RCT. Our estimates of progression and clearance rates are consistent with the findings of survival analysis studies and we extend the literature by estimating progression and clearance rates for non-16 and non-18 high-risk types. We anticipate that such type-specific estimates will be useful in the parameterisation of further models and in developing our understanding of HPV natural history.     

Anti-inflammatory response of IL-4, IL-10 and TGF-beta in patients with systemic inflammatory response syndrome

The systemic inflammatory response syndrome (SIRS) is an inflammatory process seen in association with a large number of clinical infective and non-infective conditions. The aim of this study was to investigate the role of anti-inflammatory cytokines such as interleukin-4 (IL-4), interleukin-10 (IL-10), and transforming growth factor-beta (TGF-beta). Serum levels of IL-4, IL-10 and TGF-beta were determined in 45 patients with SIRS: 38 patients had SIRS of infectious origin, whereas seven patients had non-infectious SIRS. Twenty healthy subjects were used as controls. Serum levels of IL-4, IL-10 and TGF-beta were determined by an immunoenzyme assay. A significant increase of IL-4 was observed in these patients at the time of diagnosis and 5 days later. In contrast, serum levels of IL-10 were not increased at the time of diagnosis, but a slight decrease was noted after 5 days. Serum levels of TGF-beta were not increased at time of diagnosis, and a slight increase was observed after 5 days. Serum levels of IL-4 were significantly higher in patients with infectious SIRS at the time of diagnosis, whereas no significant difference between infectious and non-infectious SIRS was noted for serum levels of IL-10 and TGF-beta at the time of diagnosis and 5 days later. During SIRS, serum levels of IL-4 were significantly increased with a significant correlation between IL-4 and mortality, and only levels of IL-4 were significantly increased in the SIRS caused by infectious stimuli.     

Oscillations in a patchy environment disease model

For a single patch SIRS model with a period of immunity of fixed length, recruitment-death demographics, disease related deaths and mass action incidence, the basic reproduction number R(0) is identified. It is shown that the disease-free equilibrium is globally asymptotically stable if R(0)<1. For R(0)>1, local stability of the endemic equilibrium and Hopf bifurcation analysis about this equilibrium are carried out. Moreover, a practical numerical approach to locate the bifurcation values for a characteristic equation with delay-dependent coefficients is provided. For a two patch SIRS model with travel, it is shown that there are several threshold quantities determining its dynamic behavior and that travel can reduce oscillations in both patches; travel may enhance oscillations in both patches; or travel can switch oscillations from one patch to another.     

SIRS评分预测急诊科抢救室病人预后的临床研究

目的探讨全身炎症反应综合征（SIRS）评分对预测急诊科抢救室危重病人预后的意义。方法对急诊科抢救室救治的596例病人进行SIRS评分,分析不同SIRS评分病人的住院率、病死率,评价SIRS评分与病人住院率、病死率的相关性。结果随着SIRS分值的增加,病人住院率与病死率亦增加;SIRS评分≥2分时,病人住院率和病死率均明显增加,差异有统计学意义（P〈0.01）。结论 SIRS评分系统作为一种简单的评分系统,能够初步预测急诊科抢救室危重病人的预后,具有一定的临床应用价值。     

小儿脓毒症休克相关基因的筛选及网络构建

为探究脓毒症休克与SIRS的差异表达基因及网络的构建,筛选潜在的核心基因,从GEO数据库下载相关基因表达谱GSE26378,数据分为脓毒症休克与SIRS各29个样本,通过在线软件GCBI对其进行标准化及差异基因筛选;对差异基因进行GO分析;基于KEGG进行功能通路分析以及基因信号网络分析;差异基因共表达网络分析。结果表明:两组中总共有1 456个基因被识别为差异基因(P0.05),与SIRS组相比,脓毒症休克组中有条859条下调基因,597条上调基因。GO功能富集分析显示差异基因主要参与了细胞周期、细胞免疫、细胞代谢。KEGG功能通路分析显示差异基因主要参与了MAPK信号通路、P53信号通路、wnt信号通路、细胞凋亡信号通路,细胞周期受体信号通路等。共表达分析发现基因CCNB1、NUSAP1、OIP5、SHCBP1、ZWINT、TOP2A、DLGAP5等位于网络中央部位,而基因信号网络分析发现基因PLCB1、PIK3CA、STAT3、CAMK2D、PRKCB、CREB1位于网络核心。基因芯片分析有助于发现脓毒症休克与SIRS患儿外周血单核细胞在转录组学上的改变,而生物信息学网络分析有助于发现潜在的靶点。     

Different age distribution patterns of human, nematode, and Arabidopsis duplicate genes

We studied the age distribution of duplicate genes in each of four eukaryotic genomes: human, Arabidopsis thaliana, Caenorhabditis elegans, and Drosophila melanogaster. The four distributions differ greatly from each other, contrary to the previous proposal of a universal L-shaped distribution in all eukaryotic genomes studied. Indeed, only the distribution in humans is L-shaped. The distribution in Arabidopsis is consistent with the hypothesis of an ancient genome duplication with no recent burst of duplication events, while the distribution in C. elegans is nearly uniform. We also applied a nonparametric method to the human distribution to show that the rate of loss of duplicate genes decreases over time, contrary to the proposal of an exponential decay. One possible explanation of the decreasing rate of loss of duplicate genes over time could be rapid functional divergence between duplicate genes, providing an advantage for the retention of both duplicates.     

Identification of Predictive Early Biomarkers for Sterile-SIRS after Cardiovascular Surgery

Systemic inflammatory response syndrome (SIRS) is a common complication after cardiovascular surgery that in severe cases can lead to multiple organ dysfunction syndrome and even death. We therefore set out to identify reliable early biomarkers for SIRS in a prospective small patient study for timely intervention. 21 Patients scheduled for planned cardiovascular surgery were recruited in the study, monitored for signs of SIRS and blood samples were taken to investigate biomarkers at pre-assigned time points: day of admission, start of surgery, end of surgery, days 1, 2, 3, 5 and 8 post surgery. Stored plasma and cryopreserved blood samples were analyzed for cytokine expression (IL1β, IL2, IL6, IL8, IL10, TNFα, IFNγ), other pro-inflammatory markers (sCD163, sTREM-1, ESM-1) and response to endotoxin. Acute phase proteins CRP, PCT and pro-inflammatory cytokines IL6 and IL8 were significantly increased (p<0.001) at the end of surgery in all patients but could not distinguish between groups. Normalization of samples revealed significant increases in IL1β changes (p<0.05) and decreased responses to endotoxin (p<0.01) in the SIRS group at the end of surgery. Soluble TREM-1 plasma concentrations were significantly increased in patients with SIRS (p<0.01). This small scale patient study could show that common sepsis markers PCT, CRP, IL6 and TNFα had low predictive value for early diagnosis of SIRS after cardiovascular surgery. A combination of normalized IL1β plasma levels, responses to endotoxin and soluble TREM-1 plasma concentrations at the end of surgery are predictive markers of SIRS development in this small scale study and could act as an indicator for starting early therapeutic interventions.     

肾盂灌注冲洗并发全身炎症反应综合征猪模型的建立

目的:建立一种肾镜下肾盂灌注冲洗并发全身炎症反应综合征(SIRS)的猪模型。方法:家猪10头,随机分为假手术组和模型组,每组按时间点分为基础状态(Basic)、术后0h、术后6h、术后12h和术后24h 5个亚组。猪肾穿刺造瘘,利用自体盲肠内容物加入肾盂冲洗液中,模拟经皮肾镜取石术(PCNL)持续肾盂灌注冲洗1h。每个时间点观测肛温(T)、呼吸(RR)、心率(HR);采血行血细胞计数分析(WBC、RBC、PLT)、肾功能(Cr、BUN、β2-MG)测定、血清IL-6、IL-10、TNF-α含量测定;用光镜和电镜观察肾脏组织病理变化。结果:模型组在术后6 h-24 h各项指标与假手术组相比变化明显,差异有统计学意义(P<0.05或<0.01)。模型组肾脏组织光镜和电镜下观察病理切片均较假手术组有明显的形态学改变。结论:本模型较好地模拟了临床病人PCNL并发SIRS的病理生理过程,为进一步研究其发病机制和预防治疗具有重要意义。     

Abundance of early functional HIV-specific CD8+ T cells does not predict AIDS-free survival time

Background

T-cell immunity is thought to play an important role in controlling HIV infection, and is a main target for HIV vaccine development. HIV-specific central memory CD8⁺ and CD4⁺ T cells producing IFNγ and IL-2 have been associated with control of viremia and are therefore hypothesized to be truly protective and determine subsequent clinical outcome. However, the cause-effect relationship between HIV-specific cellular immunity and disease progression is unknown. We investigated in a large prospective cohort study involving 96 individuals of the Amsterdam Cohort Studies with a known date of seroconversion whether the presence of cytokine-producing HIV-specific CD8⁺ T cells early in infection was associated with AIDS-free survival time.

Methods and Findings

The number and percentage of IFNγ and IL-2 producing CD8⁺ T cells was measured after in vitro stimulation with an overlapping Gag-peptide pool in T cells sampled approximately one year after seroconversion. Kaplan-Meier survival analysis and Cox proportional hazard models showed that frequencies of cytokine-producing Gag-specific CD8⁺ T cells (IFNγ, IL-2 or both) shortly after seroconversion were neither associated with time to AIDS nor with the rate of CD4⁺ T-cell decline.

Conclusions

These data show that high numbers of functional HIV-specific CD8⁺ T cells can be found early in HIV infection, irrespective of subsequent clinical outcome. The fact that both progressors and long-term non-progressors have abundant T cell immunity of the specificity associated with low viral load shortly after seroconversion suggests that the more rapid loss of T cell immunity observed in progressors may be a consequence rather than a cause of disease progression.     

Effects of a disease affecting a predator on the dynamics of a predator-prey system

We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We consider two time scales, a fast one for the disease and a comparatively slow one for predator-prey interactions and for predator mortality. We use the classical “aggregation method” in order to obtain a reduced equivalent model. We show that there are two possible asymptotic behaviors: either the predator population dies out and the prey tends to its carrying capacity, or the predator and prey coexist. In this latter case, the predator population tends either to a “disease-free” or to a “disease-endemic” state. Moreover, the total predator density in the disease-endemic state is greater than the predator density in the “disease-free” equilibrium (DFE).     

胰十二指肠切除术后肠黏膜屏障损伤与肠道细菌移位的临床研究（英文）

目的：探讨胰十二指肠切除手术后肠道细菌移位（BT）与术后全身炎症反应综合征（SIRS）关系。方法：40例择期行胰十二指肠切除手术患者,于术前和术后1、3、5天采集外周血,进行血浆D-乳酸,全血细菌DNA检测.全血DNA提取后进行PCR扩增,采用靶基因为大肠杆菌特异性β半乳糖苷酶基因和16SrRNA基因。观察患者术后10天以监测SIRS情况。结果：术前PCR检测全血细菌DNA均为阴性,术后共有13例阳性。术后出现全身炎症反应综合征（SIRS）的患者PCR阳性率为85.7%（12/14）,无SIRS组为3.8%（1/26（）P〈0.01）。PCR阳性组SIRS发生率为93.2%（12/13）,阴性组为7.4%（2/27）（P〈0.01）.PCR阳性的患者外周血血浆D-乳酸浓度较PCR阴性者明显升高（P〈0.01）,有SIRS的患者外周血血浆D-乳酸浓度较无SIRS患者明显升高（P〈0.01）。结论：胰十二指肠切除术后肠黏膜屏障损伤与BT关系密切,术后SIRS和与BT密切相关。PCR技术对术后SIRS有较好的早期预警价值。     

Recovery of an Antiviral Antibody Response following Attrition Caused by Unrelated Infection

The homeostatic mechanisms that regulate the maintenance of immunological memory to the multiple pathogen encounters over time are unknown. We found that a single malaria episode caused significant dysregulation of pre-established Influenza A virus-specific long-lived plasma cells (LLPCs) resulting in the loss of Influenza A virus-specific Abs and increased susceptibility to Influenza A virus re-infection. This loss of LLPCs involved an FcγRIIB-dependent mechanism, leading to their apoptosis. However, given enough time following malaria, the LLPC pool and humoral immunity to Influenza A virus were eventually restored. Supporting a role for continuous conversion of Influenza A virus-specific B into LLPCs in the restoration of Influenza A virus immunity, B cell depletion experiments also demonstrated a similar requirement for the long-term maintenance of serum Influenza A virus-specific Abs in an intact LLPC compartment. These findings show that, in addition to their established role in the anamnestic response to reinfection, the B cell pool continues to be a major contributor to the maintenance of long-term humoral immunity following primary Influenza A virus infection, and to the recovery from attrition following heterologous infection. These data have implications for understanding the longevity of protective efficacy of vaccinations in countries where continuous infections are endemic.     

胰十二指肠切除术后肠黏膜屏障损伤与肠道细菌移位的临床研究

目的:探讨胰十二指肠切除手术后肠道细菌移位(BT)与术后全身炎症反应综合征(SIRS)关系。方法:40例择期行胰十二指肠切除手术患者,于术前和术后1、3、5天采集外周血,进行血浆D-乳酸,全血细菌DNA检测.全血DNA提取后进行PCR扩增,采用靶基因为大肠杆菌特异性β半乳糖苷酶基因和16SrRNA基因。观察患者术后10天以监测SIRS情况。结果:术前PCR检测全血细菌DNA均为阴性,术后共有13例阳性。术后出现全身炎症反应综合征(SIRS)的患者PCR阳性率为85.7%(12/14),无SIRS组为3.8%(1/26()P<0.01)。PCR阳性组SIRS发生率为93.2%(12/13),阴性组为7.4%(2/27)(P<0.01).PCR阳性的患者外周血血浆D-乳酸浓度较PCR阴性者明显升高(P<0.01),有SIRS的患者外周血血浆D-乳酸浓度较无SIRS患者明显升高(P<0.01)。结论:胰十二指肠切除术后肠黏膜屏障损伤与BT关系密切,术后SIRS和与BT密切相关。PCR技术对术后SIRS有较好的早期预警价值。