The emptiness formation probability correlation in homogeneous and dimerized XX chains

We review some known properties of the "emptiness formation probability" correlation which we have calculated numerically for spin-1/2 XX chains with constant (homogeneous) or alternating (dimerized) nearest-neighbor coupling and an external field (in $z$ direction) for arbitrary temperature. The long-distance asymptotic behavior of this correlation is known to be Gaussian at zero temperature and exponential at finite temperature for the homogeneous chain. By simple analytical arguments the exponential behavior at finite temperature extends to the dimerized system. Numerical results for the dimerized chain confirm the exponential decay at finite temperature and show Gaussian decay at zero temperature.Comment: Fixed some typos, added two references and remarks on finite-size effects. To be published in Cond. Mat. Phy

Mutation-selection models of sequence evolution in population genetics

The equilibrium properties of a number of deterministic mutation- selection models of sequence evolution are investigated. Both two- and four-state sequences are considered, the mutation model is a single-step mutation model. Two types of fitness functions are studied, namely permutation-invariant fitness functions, where the fitness of a sequence depends only on the number of mutations, not on their location within the sequence, and Hopfield-type fitness functions, where the fitness of a sequence is determined by its similarity to a number of predefined patterns. Maximum principles to determine the population mean fitness in equilibrium are derived, where the maximiser gives also the ancestral mean genotype. These maximum principles are used to investigate the error threshold phenomenon, i.e., the phenomenon that for certain fitness functions the population changes at a critical mutation rate from a well localised to a delocalised distribution in sequence space. The error threshold phenomenon is investigated for a four-state model with permutation-invariant fitness functions and for a two-state model with Hopfield-type fitness functions. Both models yield ordered and disordered as well as partially ordered phases

Estimating potential incidence of MERS-CoV associated with Hajj pilgrims to Saudi Arabia, 2014

Between March and June 2014 the Kingdom of Saudi Arabia (KSA) had a large outbreak of MERS-CoV, renewing fears of a major outbreak during the Hajj this October. Using KSA Ministry of Health data, the MERS-CoV Scenario and Modeling Working Group forecast incidence under three scenarios. In the expected incidence scenario, we estimate 6.2 (95% Prediction Interval [PI]: 1-17) pilgrims will develop MERS-CoV symptoms during the Hajj, and 4.0 (95% PI: 0-12) foreign pilgrims will be infected but return home before developing symptoms. In the most pessimistic scenario, 47.6 (95% PI: 32-66) cases will develop symptoms during the Hajj, and 29.0 (95% PI: 17-43) will be infected but return home asymptomatic. Large numbers of MERS-CoV cases are unlikely to occur during the 2014 Hajj even under pessimistic assumptions, but careful monitoring is still needed to detect possible mass infection events and minimize introductions into other countries

The Equity Impact Vaccines May Have On Averting Deaths And Medical Impoverishment In Developing Countries.

With social policies increasingly directed toward enhancing equity through health programs, it is important that methods for estimating the health and economic benefits of these programs by subpopulation be developed, to assess both equity concerns and the programs' total impact. We estimated the differential health impact (measured as the number of deaths averted) and household economic impact (measured as the number of cases of medical impoverishment averted) of ten antigens and their corresponding vaccines across income quintiles for forty-one low- and middle-income countries. Our analysis indicated that benefits across these vaccines would accrue predominantly in the lowest income quintiles. Policy makers should be informed about the large health and economic distributional impact that vaccines could have, and they should view vaccination policies as potentially important channels for improving health equity. Our results provide insight into the distribution of vaccine-preventable diseases and the health benefits associated with their prevention

Assessing the impact of preventive mass vaccination campaigns on yellow fever outbreaks in Africa: A population-level self-controlled case series study.

The Eliminate Yellow fever Epidemics (EYE) strategy was launched in 2017 in response to the resurgence of yellow fever in Africa and the Americas. The strategy relies on several vaccination activities, including preventive mass vaccination campaigns (PMVCs). However, to what extent PMVCs are associated with a decreased risk of outbreak has not yet been quantified. We used the self-controlled case series (SCCS) method to assess the association between the occurrence of yellow fever outbreaks and the implementation of PMVCs at the province level in the African endemic region. As all time-invariant confounders are implicitly controlled for in the SCCS method, this method is an alternative to classical cohort or case-control study designs when the risk of residual confounding is high, in particular confounding by indication. The locations and dates of outbreaks were identified from international epidemiological records, and information on PMVCs was provided by coordinators of vaccination activities and international funders. The study sample consisted of provinces that were both affected by an outbreak and targeted for a PMVC between 2005 and 2018. We compared the incidence of outbreaks before and after the implementation of a PMVC. The sensitivity of our estimates to a range of assumptions was explored, and the results of the SCCS method were compared to those obtained through a retrospective cohort study design. We further derived the number of yellow fever outbreaks that have been prevented by PMVCs. The study sample consisted of 33 provinces from 11 African countries. Among these, the first outbreak occurred during the pre-PMVC period in 26 (79%) provinces, and during the post-PMVC period in 7 (21%) provinces. At the province level, the post-PMVC period was associated with an 86% reduction (95% CI 66% to 94%, p < 0.001) in the risk of outbreak as compared to the pre-PMVC period. This negative association between exposure to PMVCs and outbreak was robustly observed across a range of sensitivity analyses, especially when using quantitative estimates of vaccination coverage as an alternative exposure measure, or when varying the observation period. In contrast, the results of the cohort-style analyses were highly sensitive to the choice of covariates included in the model. Based on the SCCS results, we estimated that PMVCs were associated with a 34% (95% CI 22% to 45%) reduction in the number of outbreaks in Africa from 2005 to 2018. A limitation of our study is the fact that it does not account for potential time-varying confounders, such as changing environmental drivers of yellow fever and possibly improved disease surveillance. In this study, we provide new empirical evidence of the high preventive impact of PMVCs on yellow fever outbreaks. This study illustrates that the SCCS method can be advantageously applied at the population level in order to evaluate a public health intervention

Uncertainty in the Tail of the Variant Creutzfeldt-Jakob Disease Epidemic in the UK

Despite low case numbers the variant Creutzfeldt-Jakob disease epidemic poses many challenges for public health planning due to remaining uncertainties in disease biology and transmission routes. We develop a stochastic model for variant CJD transmission, taking into account the known transmission routes (food and red-cell transfusion) to assess the remaining uncertainty in the epidemic. We use Bayesian methods to obtain scenarios consistent with current data. Our results show a potentially long but uncertain tail in the epidemic, with a peak annual incidence of around 11 cases, but the 95% credibility interval between 1 and 65 cases. These cases are predicted to be due to past food-borne transmissions occurring in previously mostly unaffected genotypes and to transmissions via blood transfusion in all genotypes. However, we also show that the latter are unlikely to be identifiable as transfusion-associated cases by case-linking. Regardless of the numbers of future cases, even in the absence of any further control measures, we do not find any self-sustaining epidemics

A simple approach to measure transmissibility and forecast incidence

Outbreaks of novel pathogens such as SARS, pandemic influenza and Ebola require substantial investments in reactive interventions, with consequent implementation plans sometimes revised on a weekly basis. Therefore, short-term forecasts of incidence are often of high priority. In light of the recent Ebola epidemic in West Africa, a forecasting exercise was convened by a network of infectious disease modellers. The challenge was to forecast unseen “future” simulated data for four different scenarios at five different time points. In a similar method to that used during the recent Ebola epidemic, we estimated current levels of transmissibility, over variable time-windows chosen in an ad hoc way. Current estimated transmissibility was then used to forecast near-future incidence. We performed well within the challenge and often produced accurate forecasts. A retrospective analysis showed that our subjective method for deciding on the window of time with which to estimate transmissibility often resulted in the optimal choice. However, when near-future trends deviated substantially from exponential patterns, the accuracy of our forecasts was reduced. This exercise highlights the urgent need for infectious disease modellers to develop more robust descriptions of processes – other than the widespread depletion of susceptible individuals – that produce non-exponential patterns of incidence

Potential Biases in Estimating Absolute and Relative Case-Fatality Risks during Outbreaks

Estimating the case-fatality risk (CFR)—the probability that a person dies from an infection given that they are a case—is a high priority in epidemiologic investigation of newly emerging infectious diseases and sometimes in new outbreaks of known infectious diseases. The data available to estimate the overall CFR are often gathered for other purposes (e.g., surveillance) in challenging circumstances. We describe two forms of bias that may affect the estimation of the overall CFR—preferential ascertainment of severe cases and bias from reporting delays—and review solutions that have been proposed and implemented in past epidemics. Also of interest is the estimation of the causal impact of specific interventions (e.g., hospitalization, or hospitalization at a particular hospital) on survival, which can be estimated as a relative CFR for two or more groups. When observational data are used for this purpose, three more sources of bias may arise: confounding, survivorship bias, and selection due to preferential inclusion in surveillance datasets of those who are hospitalized and/or die. We illustrate these biases and caution against causal interpretation of differential CFR among those receiving different interventions in observational datasets. Again, we discuss ways to reduce these biases, particularly by estimating outcomes in smaller but more systematically defined cohorts ascertained before the onset of symptoms, such as those identified by forward contact tracing. Finally, we discuss the circumstances in which these biases may affect non-causal interpretation of risk factors for death among cases

How can the public health impact of vaccination be estimated?

BACKGROUND: Deaths due to vaccine preventable diseases cause a notable proportion of mortality worldwide. To quantify the importance of vaccination, it is necessary to estimate the burden averted through vaccination. The Vaccine Impact Modelling Consortium (VIMC) was established to estimate the health impact of vaccination. METHODS: We describe the methods implemented by the VIMC to estimate impact by calendar year, birth year and year of vaccination (YoV). The calendar and birth year methods estimate impact in a particular year and over the lifetime of a particular birth cohort, respectively. The YoV method estimates the impact of a particular year's vaccination activities through the use of impact ratios which have no stratification and stratification by activity type and/or birth cohort. Furthermore, we detail an impact extrapolation (IE) method for use between coverage scenarios. We compare the methods, focusing on YoV for hepatitis B, measles and yellow fever. RESULTS: We find that the YoV methods estimate similar impact with routine vaccinations but have greater yearly variation when campaigns occur with the birth cohort stratification. The IE performs well for the YoV methods, providing a time-efficient mechanism for updates to impact estimates. CONCLUSIONS: These methods provide a robust set of approaches to quantify vaccination impact; however it is vital that the area of impact estimation continues to develop in order to capture the full effect of immunisation