The impact of household structure on disease-induced herd immunity.

The disease-induced herd immunity level [Formula: see text] is the fraction of the population that must be infected by an epidemic to ensure that a new epidemic among the remaining susceptible population is not supercritical. For a homogeneously mixing population [Formula: see text] equals the classical herd immunity level [Formula: see text], which is the fraction of the population that must be vaccinated in advance of an epidemic so that the epidemic is not supercritical. For most forms of heterogeneous mixing [Formula: see text], sometimes dramatically so. For an SEIR (susceptible [Formula: see text] exposed [Formula: see text] infective [Formula: see text] recovered) model of an epidemic among a population that is partitioned into households, in which individuals mix uniformly within households and, in addition, uniformly at a much lower rate in the population at large, we show that [Formula: see text] unless variability in the household size distribution is sufficiently large. Thus, introducing household structure into a model typically has the opposite effect on disease-induced herd immunity than most other forms of population heterogeneity. We reach this conclusion by considering an approximation [Formula: see text] of [Formula: see text], supported by numerical studies using real-world household size distributions. For [Formula: see text], we prove that [Formula: see text] when all households have size n, and conjecture that this inequality holds for any common household size n. We prove results comparing [Formula: see text] and [Formula: see text] for epidemics which are highly infectious within households, and also for epidemics which are weakly infectious within households.

An epidemic model with short-lived mixing groups.

Almost all epidemic models make the assumption that infection is driven by the interaction between pairs of individuals, one of whom is infectious and the other of whom is susceptible. However, in society individuals mix in groups of varying sizes, at varying times, allowing one or more infectives to be in close contact with one or more susceptible individuals at a given point in time. In this paper we study the effect of mixing groups beyond pairs on the transmission of an infectious disease in an SIR (susceptible [Formula: see text] infective [Formula: see text] recovered) model, both through a branching process approximation for the initial stages of an epidemic with few initial infectives and a functional central limit theorem for the trajectories of the numbers of infectives and susceptibles over time for epidemics with many initial infectives. We also derive central limit theorems for the final size of (i) an epidemic with many initial infectives and (ii) a major outbreak triggered by few initial infectives. We show that, for a given basic reproduction number [Formula: see text], the distribution of the size of mixing groups has a significant impact on the probability and final size of a major epidemic outbreak. Moreover, the standard pair-based homogeneously mixing epidemic model is shown to represent the worst case scenario, with both the highest probability and the largest final size of a major epidemic.

The time to extinction for a stochastic SIS-household-epidemic model.

We analyse a Markovian SIS epidemic amongst a finite population partitioned into households. Since the population is finite, the epidemic will eventually go extinct, i.e., have no more infectives in the population. We study the effects of population size and within household transmission upon the time to extinction. This is done through two approximations. The first approximation is suitable for all levels of within household transmission and is based upon an Ornstein-Uhlenbeck process approximation for the diseases fluctuations about an endemic level relying on a large population. The second approximation is suitable for high levels of within household transmission and approximates the number of infectious households by a simple homogeneously mixing SIS model with the households replaced by individuals. The analysis, supported by a simulation study, shows that the mean time to extinction is minimized by moderate levels of within household transmission.

The basic reproduction number, R0, in structured populations.

In this paper, we provide a straightforward approach to defining and deriving the key epidemiological quantity, the basic reproduction number, R0, for Markovian epidemics in structured populations. The methodology derived is applicable to, and demonstrated on, both SIR and SIS epidemics and allows for population as well as epidemic dynamics. The approach taken is to consider the epidemic process as a multitype process by identifying and classifying the different types of infectious units along with the infections from, and the transitions between, infectious units. For the household model, we show that our expression for R0 agrees with earlier work despite the alternative nature of the construction of the mean reproductive matrix, and hence, the basic reproduction number.

Systemic blastomycosis diagnosed by prostate needle biopsy.

A healthy 51-year-old man presented with a 1-month history of lower urinary tract irritative symptoms. Urinalysis was suggestive of infection, and the patient was treated with multiple antibiotics without relief of symptoms. A urological exam demonstrated abnormal induration of the prostate gland. Biopsy of the prostate gland revealed Blastomyces dermatitidis. In areas where Blastomyces dermatitidis is endemic, clinicians should be aware of the presence of this fungus and possible sites of infection.

Network epidemic models with two levels of mixing.

The study of epidemics on social networks has attracted considerable attention recently. In this paper, we consider a stochastic SIR (susceptible-->infective-->removed) model for the spread of an epidemic on a finite network, having an arbitrary but specified degree distribution, in which individuals also make casual contacts, i.e. with people chosen uniformly from the population. The behaviour of the model as the network size tends to infinity is investigated. In particular, the basic reproduction number R(0), that governs whether or not an epidemic with few initial infectives can become established is determined, as are the probability that an epidemic becomes established and the proportion of the population who are ultimately infected by such an epidemic. For the case when the infectious period is constant and all individuals in the network have the same degree, the asymptotic variance and a central limit theorem for the size of an epidemic that becomes established are obtained. Letting the rate at which individuals make casual contacts decrease to zero yields, heuristically, corresponding results for the model without casual contacts, i.e. for the standard SIR network epidemic model. A deterministic model that approximates the spread of an epidemic that becomes established in a large population is also derived. The theory is illustrated by numerical studies, which demonstrate that the asymptotic approximations work well, even for only moderately sized networks, and that the degree distribution and the inclusion of casual contacts can each have a major impact on the outcome of an epidemic.

A tutorial introduction to Bayesian inference for stochastic epidemic models using Approximate Bayesian Computation.

Likelihood-based inference for disease outbreak data can be very challenging due to the inherent dependence of the data and the fact that they are usually incomplete. In this paper we review recent Approximate Bayesian Computation (ABC) methods for the analysis of such data by fitting to them stochastic epidemic models without having to calculate the likelihood of the observed data. We consider both non-temporal and temporal-data and illustrate the methods with a number of examples featuring different models and datasets. In addition, we present extensions to existing algorithms which are easy to implement and provide an improvement to the existing methodology. Finally, R code to implement the algorithms presented in the paper is available on https://github.com/kypraios/epiABC.

Survey of intestinal parasitism in dogs in the Phoenix metropolitan area.

OBJECTIVE To determine the prevalence of selected intestinal parasites in pet dogs and recently apprehended free-roaming (AFR) shelter dogs in the Phoenix metropolitan area and compare those prevalences between the 2 groups. DESIGN Cross-sectional study. SAMPLE Convenience samples of fecal specimens from owned pet dogs from the Phoenix metropolitan area (n = 175) and free-roaming dogs apprehended and admitted to Maricopa County Animal Care and Control and Arizona Humane Society facilities from November 2014 through March 2015 (188). PROCEDURES Fresh fecal specimens were collected from all dogs; for AFR shelter dogs, specimens were collected within 72 hours after facility admission. Standard centrifugal flotation tests and an ELISA were performed to detect 5 common intestinal parasites (roundworms, hookworms, whipworms, Giardia spp, and Cystoisospora spp). Group comparisons were performed by means of the χ2 test and Rogan-Gladen prevalence estimate. RESULTS At least 1 of the 5 evaluated parasites was detected in 85 (45.2%) fecal specimens from AFR shelter dogs and 24 (13.7%) specimens from owned pet dogs. This prevalence differed significantly between the groups. Notably, the prevalence of Giardia spp in AFR shelter dogs (n = 76 [40.4%]) was higher than previously reported in the United States. CONCLUSIONS AND CLINICAL RELEVANCE The prevalence of the evaluated intestinal parasites, particularly of Giardia spp, in AFR shelter dogs was higher than expected. This information is important for veterinarians, animal shelter personnel, pet owners, human health-care providers, and public health officials to consider when devising effective interventions and risk communication efforts against potential zoonotic threats, particularly those relevant to the Phoenix metropolitan area.

A general model for stochastic SIR epidemics with two levels of mixing.

This paper is concerned with a general stochastic model for susceptible-->infective-->removed epidemics, among a closed finite population, in which during its infectious period a typical infective makes both local and global contacts. Each local contact of a given infective is with an individual chosen independently according to a contact distribution 'centred' on that infective, and each global contact is with an individual chosen independently and uniformly from the whole population. The asymptotic situation in which the local contact distribution remains fixed as the population becomes large is considered. The concepts of local infectious clump and local susceptibility set are used to develop a unified approach to the threshold behaviour of this class of epidemic models. In particular, a threshold parameter R(*) governing whether or not global epidemics can occur, the probability that a global epidemic occurs and the mean proportion of initial susceptibles ultimately infected by a global epidemic are all determined. The theory is specialised to (i) the households model, in which the population is partitioned into households and local contacts are chosen uniformly within an infective's household; (ii) the overlapping groups model, in which the population is partitioned in several ways, with local uniform mixing within the elements of the partitions; and (iii) the great circle model, in which individuals are equally spaced on a circle and local contacts are nearest-neighbour.

The efficacy of a toothbrush disinfectant spray--an in vitro study.

OBJECTIVES: Toothbrushes are contaminated by micro-organisms which may be sources of infection, re-infection or cross infection. The object of this research is to test the efficacy of a proprietary toothbrush spray disinfectant (Brushtox) against specific test bacteria and fungi and to consider its potential. METHODS: Three bacteria and two fungi representing a broad microbial spectrum with relevance to oral bacteria were used in four laboratory tests including an in vitro toothbrush disinfection test. RESULTS: Brushtox proved to be almost 100% effective in three tests and showed significant inhibitory action in the standard agar diffusion test. CONCLUSION: Brushtox is an effective disinfectant agent for bacteria and fungi on toothbrushes. The solution may be valuable in the control of a wide variety of oral infections and secondary infections, especially in frail or debilitated individuals or those on immuno-suppressive therapy, and also in healthy individuals.

Robust estimation of microbial diversity in theory and in practice.

Quantifying diversity is of central importance for the study of structure, function and evolution of microbial communities. The estimation of microbial diversity has received renewed attention with the advent of large-scale metagenomic studies. Here, we consider what the diversity observed in a sample tells us about the diversity of the community being sampled. First, we argue that one cannot reliably estimate the absolute and relative number of microbial species present in a community without making unsupported assumptions about species abundance distributions. The reason for this is that sample data do not contain information about the number of rare species in the tail of species abundance distributions. We illustrate the difficulty in comparing species richness estimates by applying Chao's estimator of species richness to a set of in silico communities: they are ranked incorrectly in the presence of large numbers of rare species. Next, we extend our analysis to a general family of diversity metrics ('Hill diversities'), and construct lower and upper estimates of diversity values consistent with the sample data. The theory generalizes Chao's estimator, which we retrieve as the lower estimate of species richness. We show that Shannon and Simpson diversity can be robustly estimated for the in silico communities. We analyze nine metagenomic data sets from a wide range of environments, and show that our findings are relevant for empirically-sampled communities. Hence, we recommend the use of Shannon and Simpson diversity rather than species richness in efforts to quantify and compare microbial diversity.

The basic reproduction number and the probability of extinction for a dynamic epidemic model.

We consider the spread of an epidemic through a population divided into n sub-populations, in which individuals move between populations according to a Markov transition matrix Σ and infectives can only make infectious contacts with members of their current population. Expressions for the basic reproduction number, R0, and the probability of extinction of the epidemic are derived. It is shown that in contrast to contact distribution models, the distribution of the infectious period effects both the basic reproduction number and the probability of extinction of the epidemic in the limit as the total population size N→∞. The interactions between the infectious period distribution and the transition matrix Σ mean that it is not possible to draw general conclusions about the effects on R0 and the probability of extinction. However, it is shown that for n=2, the basic reproduction number, R0, is maximised by a constant length infectious period and is decreasing in ς, the speed of movement between the two populations.

Schistosomiasis--an unusual cause of ureteral obstruction: a case history and perspective.

A male, 32 years of age, presented with dysuria and abdominal pain, but no gross hematuria. He emigrated three years earlier from Somalia, East Africa, and was currently employed as a poultry processor in a rural Wisconsin community. The patient denied any trauma, sexual activity, or family history of significant illness. Abdominal and genitourinary exams were normal with negative tests for gonococcus and chlamydia. Urinalysis demonstrated microhematuria. A urogram and retrograde pyelogram revealed a mildly dilated right ureter down to the ureterovesical junction. Cystoscopy showed punctate white lesions on the bladder urothelium. Ureteroscopy was used to biopsy abnormal tissue in the distal ureter and bladder. Biopsy tissue demonstrated deposits of Schistosoma haematobium eggs. No ova were seen in collected urine specimens. The patient was successfully treated with praziquantel and will be monitored for sequelae of the disease. Schistosomiasis (Bilharziasis) can be expected to be seen with increasing frequency in the United States with the continuing influx of immigrants and refugees, as well as the return of travelers and soldiers from endemic areas. While no intermediate snail host exists for the transmission of Schistosoma sp. in the United States, the continued importation of exotic animals including snails from Africa, as well as the ability of schistosomes to shift host species warrants concern. Additionally, increasing disease associated with non-human bird schistosomes of the same genus seen in the midwestern United States is occurring throughout Europe. One should be aware that praziquantel may not always be available or effective in the treatment of schistosomiasis. It behooves the practicing clinician to remain updated on the status of this widespread zoonosis.

Statistical inference and model selection for the 1861 Hagelloch measles epidemic.

A stochastic epidemic model is proposed which incorporates heterogeneity in the spread of a disease through a population. In particular, three factors are considered: the spatial location of an individual's home and the household and school class to which the individual belongs. The model is applied to an extremely informative measles data set and the model is compared with nested models, which incorporate some, but not all, of the aforementioned factors. A reversible jump Markov chain Monte Carlo algorithm is then introduced which assists in selecting the most appropriate model to fit the data.