The contribution of neighbours to an individual's risk of typhoid outcome.

An individual's risk of infection from an infectious agent can depend on both the individual's own risk and protective factors and those of individuals in the same community. We hypothesize that an individual's exposure to an infectious agent is associated with the risks of infection of those living nearby, whether their risks are modified by pharmaceutical interventions or by other factors, because of the potential for transmission from them. For example, unvaccinated individuals living in a highly vaccinated community can benefit from indirect protection, or living near more children in a typhoid-endemic region (where children are at highest risk) might result in more exposure to typhoid. We tested this hypothesis using data from a cluster-randomized typhoid vaccine trial. We first estimated each individual's relative risk of confirmed typhoid outcome using their vaccination status and age. We defined a new covariate, potential exposure, to be the sum of the relative risks of all who live within 100 m of each person. We found that potential exposure was significantly associated with an individual's typhoid outcome, and adjusting for potential exposure affected estimates of vaccine efficacy. We suggest that it is useful and feasible to adjust for spatially heterogeneous distributions of individual-level risk factors, but further work is required to develop and test such approaches.

Household transmissibility of avian influenza A (H7N9) virus, China, February to May 2013 and October 2013 to March 2014.

To study human-to-human transmissibility of the avian influenza A (H7N9) virus in China, household contact information was collected for 125 index cases during the spring wave (February to May 2013), and for 187 index cases during the winter wave (October 2013 to March 2014). Using a statistical model, we found evidence for human-to-human transmission, but such transmission is not sustainable. Under plausible assumptions about the natural history of disease and the relative transmission frequencies in settings other than household, we estimate the household secondary attack rate (SAR) among humans to be 1.4% (95% CI: 0.8 to 2.3), and the basic reproductive number R0 to be 0.08 (95% CI: 0.05 to 0.13). The estimates range from 1.3% to 2.2% for SAR and from 0.07 to 0.12 for R0 with reasonable changes in the assumptions. There was no significant change in the human-to-human transmissibility of the virus between the two waves, although a minor increase was observed in the winter wave. No sex or age difference in the risk of infection from a human source was found. Human-to-human transmissibility of H7N9 continues to be limited, but it needs to be closely monitored for potential increase via genetic reassortment or mutation.

Assessing the impact of travel restrictions on international spread of the 2014 West African Ebola epidemic.

The quick spread of an Ebola outbreak in West Africa has led a number of countries and airline companies to issue travel bans to the affected areas. Considering data up to 31 Aug 2014, we assess the impact of the resulting traffic reductions with detailed numerical simulations of the international spread of the epidemic. Traffic reductions are shown to delay by only a few weeks the risk that the outbreak extends to new countries.

El Tor cholera with severe disease: a new threat to Asia and beyond.

During epidemics of cholera in two rural sites (Bakerganj and Mathbaria), a much higher proportion of patients came for treatment with severe dehydration than was seen in previous years. V. cholerae O1 isolated from these patients was found to be El Tor in its phenotype, but its cholera toxin (CT) was determined to be that of classical biotype. Whether the observed higher proportion of severe dehydration produced by the El Tor biotype was due to a shift from El Tor to classical CT or due to other factors is not clear. However, if cholera due to strains with increased severity spread to other areas where treatment facilities are limited, there are likely to be many more cholera deaths.

Use of immunological markers and continuous-time Markov models to estimate progression of HIV infection in homosexual men.

OBJECTIVES: We used continuous-time Markov models based on CD4 cell counts and anti-CD3 reactivity (i.e., measure for T-cell quality) to study the progression of HIV infection in a cohort study of homosexual men in Amsterdam. We also compared the effectiveness of anti-CD3 reactivity as a marker for disease progression with that of CD4 cell counts. METHODS: We used data from 467 men (6905 visits) with visits at 3-month intervals between October 1984 and March 1993. To account for measurement error and short time-scale variability, the immunological stage at each visit was determined using a kernel smoother on log-transformed data from each individual. The Markov model had six marker-defined stages and a seventh stage for clinical AIDS. The initial stage-occupation probabilities for seroconverters were used to estimate the incubation time from infection to AIDS. Confidence intervals were calculated using the bootstrap method to account for the effect of smoothing on the variability of our estimates. RESULTS: The CD4 staging scheme estimated the median time from seroconversion to AIDS at 8.3 years [95% confidence interval (CI), 8.1-8.6], and a similar estimate was obtained with the anti-CD3 staging model. The CD4 model predicts that 10.2% (95% CI, 9.9-13.1) will remain AIDS-free 15 years after seroconversion. The mean number of stages visited before AIDS is lower with the CD4 model (7.4; 95% CI, 7.2-7.7) than with the anti-CD3 model (11.3; 95% CI, 10.8-12.0), implying that anti-CD3 predicts progression less well than CD4 cell count. CONCLUSIONS: CD4 lymphocyte counts and anti-CD3 reactivity are each associated with an increased hazard for progression to AIDS. Therefore, men in different CD4-stages (anti-CD3 stages) follow different incubation period distributions to AIDS. However, anti-CD3 predicts progression less well than CD4 cell count. Staged time-continuous Markov models are useful to study immunological markers for HIV disease progression.

The dynamics of CD4+ T-lymphocyte decline in HIV-infected individuals: a Markov modeling approach.

We modeled the decline of CD4+ T-lymphocytes (T4 cells) in HIV-infected individuals with a continuous-time Markov process. The model partitions the HIV infection period into six progressive T4-cell count intervals (states), followed by a seventh state: a definitive HIV-infection end point, i.e., AIDS diagnosis or Walter Reed stage 6 (opportunistic infections). The Markov model was used to estimate the state-specific progression rates from data as functions of important progression cofactors. We applied the model to data on 1,796 HIV-positive individuals in the U.S. Army. The estimated mean waiting time from seroconversion to when the T4-cell count persistently drops below 500/mm3, but is greater than 349/mm3, is 4.1 years, and the waiting time to a T4-cell count of less than 200/mm3 is estimated at 8.0 years. The estimated rate of T4-cell decline was higher for HIV-infected individuals with initially high numbers of T4 cells, but the estimated rate of decline remains relatively uniform when the T4-cell count dropped persistently below 500/mm3. The opportunistic infection incubation period, i.e., the time from seroconversion to opportunistic infection diagnosis, is estimated at 9.6 years. Age is found to be an important cofactor. The estimated mean opportunistic infection incubation periods are 11.1, 10.0, and 8.9 years for the youngest (less than or equal to 25 years old), the middle (26-30 years old), and the oldest (greater than 30 years old) age groups, respectively.(ABSTRACT TRUNCATED AT 250 WORDS)

Role of the primary infection in epidemics of HIV infection in gay cohorts.

A review of the data on infectivity per contact for transmission of the HIV suggests that the infectivity may be on the order of 0.1-0.3 per anal intercourse in the period of the initial infection, 10(-4) to 10(-3) in the long asymptomatic period, and 10(-3) to 10(-2) in the period leading into AIDS. The pattern of high contagiousness during the primary infection followed by a large drop in infectiousness may explain the pattern of epidemic spread seen in male homosexual cohorts in the early years of the epidemic. Simulations of cohorts of homosexual males, using that range of parameter values, indicate the following: (a) The initial fast rise and then more or less rapid flattening of the incidence curve of seropositives is primarily due to rapid initial spread, yielding a group of infecteds all of whom pass into the low infectivity asymptomatic period at close to the same time. All this occurs only if the basic reproduction number for the primary infection is > 1. (b) The behavioral changes that have been reported all started after the incidence of new infections began to fall, too late to have a major effect on the initial rise. The behavioral changes had a major effect in slowing down the subsequent rise in the number of seropositives. (c) High activity groups play an important role in the early rapid rise of the epidemic. However, it is not likely that the rapid decrease in rate of growth of seropositives is solely due to saturation of these very high activity groups. Although the evidence for this interpretation of the role of the primary infection is not conclusive, its implications for prevention and for vaccine trials are so markedly different from those of other interpretations that we consider it to be an important hypothesis for further testing.

Measures of the effects of vaccination in a randomly mixing population.

Vaccine efficacy in the field is often derived from the relative attack rates in the vaccinated and unvaccinated after an outbreak. In this paper, vaccine efficacy is defined in terms of the probability that the infectious agent is transmitted from an infected to a susceptible person, and a method for estimating it from the usual attack rate data is given. We explore two mechanisms of vaccine action defined by Smith et al, but include an underlying dynamic epidemic model of an acute directly transmitted disease. We show analytically that under the model in which the vaccine mechanism reduces the probability of infection given a certain exposure, vaccine efficacy based on the relative attack rates underestimates the protective effect of the vaccine based on the relative transmission probabilities. Under the other model in which the vaccine mechanism offers complete protection to a certain proportion of those vaccinated, and no protection to the other vaccinated proportion, the vaccine efficacy based on the relative attack rates will equal that based on the transmission probabilities. Parameters for the effectiveness of a vaccination programme are defined in terms of the direct and indirect benefit to a single person as well as the total and average benefit to the entire population, and derived from the dynamic model for an outbreak of an acute directly transmitted disease. These effects can also be estimated without an actual separate unvaccinated population, independent of assumptions about the vaccine mechanism. The variation of these measures as functions of the fraction of vaccinated people in the population is explored numerically.

Simulation of mechanisms of viral interference in influenza.

Biological interference among viral agents might have significant implications for disease prevention and therapy. Field data for influenza yield conflicting evidence concerning the independence of infection rates, or disease severity, for two co-circulating viruses. To examine the effects of several assumed modes of interference for influenza, simulations of a Monte Carlo micropopulation model of influenza epidemics have been performed. Model parameters were selected so that the simulated attack rates for each of two different viral strains matched actual field data. Rates of infection were compared for single agents and for two viruses with only behavioural interference. Other simulations included temporary immunity to the other virus for the duration of the infection, and/or reduced shedding of viral particles for dual infections. Simulated viral competition had little impact on epidemic severity, duration, or size distribution. Under the conditions studied, viral interference in natural populations would be difficult to infer from field observations of attack rates. Other simulations extended a partial immunity and/or reduced viral shedding during an infection with a second virus. These indicated that interference might be suggested by field data, but it could not be demonstrated conclusively. Still other simulations showed that for epidemics with much higher attack rates for both viruses, it would be relatively easy to demonstrate interference. However, in order to observe interference between influenza strains, it would be necessary to monitor on an almost daily basis, using a method of viral detection which would have to be both highly specific and also very sensitive.

Statistical procedures for estimating the community probability of illness in family studies: rhinovirus and influenza.

A statistical method is presented for determining acquisition rates of illness from community sources of infection and for distinguishing among viruses which are associated with different epidemic seasons. The new method consists of a computationally simple procedure for estimating the community transmission parameter and the standard error of the estimator. This method, as well as a previously developed maximum likelihood procedure, is applied to illness data as a means for distinguishing among broad patterns of illness acquisition. The periods evaluated are the rhinovirus, influenza A and influenza B seasons in Tecumseh, Michigan, for the years 1976-1980. Tecumseh households are stratified into exposure groups depending on age-group composition. Estimates are found for the risk differences of illness acquired from the community for households with different age-group distributions. Analysis of the Tecumseh data reveals that members of households with children are more apt than members of households without children to acquire illness associated with rhinovirus, influenza A and influenza B from the community. Members of households with just preschool children (and adults) are more apt than members of households with just school children (and adults) to acquire illness associated with rhinovirus and influenza B from the community. In contrast, members of households with just preschool children (and adults) are just as likely as members of households with just school children (and adults) to acquire illnesses associated with influenza A from the community.

Simulation studies of influenza epidemics: assessment of parameter estimation and sensitivity.

The influenza simulation model of Elveback et al is used to evaluate the accuracy of the maximum likelihood procedure of Longini et al for estimating the secondary attack rate in households. The sample population from the Tecumseh Respiratory Illness Study is mapped into the simulation model and simulations are carried out over a range of parameter values and conditions, some of which were derived from influenza seasons in Tecumseh and from the Seattle Flu Study for the years 1975-1980. The estimation procedure is found to be quite robust for parameter values preset within appropriate limits for influenza. However, a significant difference is found between the preset and estimated household contact parameter for epidemics of medium and high intensity when the preset value is zero. Incremental increases in the household contact parameter are shown to produce marked increases in the overall infection attack rate demonstrating that household spread is an important link in maintaining infection in other mixing groups such as schools, preschool groups and neighbourhood clusters of households.

Estimation of vaccine efficacy from epidemics of acute infectious agents under vaccine-related heterogeneity.

A stochastic epidemic model is formulated for the study of the protective effects of vaccination in a population that is stratified by vaccine-related factors. The epidemic model is transformed into a counting process, and then martingale-based methods are used to provide estimators of vaccine efficacy and their variances. Following an example, various extensions of the model are discussed.

A simulation model of AIDS in San Francisco: I. Model formulation and parameter estimation.

A model is formulated for the spread of the human immunodeficiency virus (HIV) and the subsequent development of acquired immunodeficiency syndrome (AIDS) in the population of homosexual men in San Francisco. The dynamic simulation model includes sexually very active and active subpopulations, migration, and a staged progression of HIV-infected persons to AIDS and death. Numerous data sources are used to estimate parameter values in the model. In a companion paper, simulations using the model and parameter estimates are found that are consistent with HIV and AIDS incidence data.

[Procedures for estimating transmission parameters from influenza epidemics: use of serological data]. / Otsenka parametrov, kharakterizuiushchikh rasprostranenie grippa v period épidemii na osnove serologicheskikh dannykh.

A maximum likelihood procedure is given for estimating household and community transmission parameters from observed influenza infection data. The mathematical model used does not require the specification of infection onset times and, therefore, can be used with serological data which detect asymptomatic infections. Infection data was derived by serology and virus isolation from the Tecumseh Respiratory Illness Study and the Seattle Flu Study for the years 1975-1979. Influenza A (H1N1), A (H3N2), and B viruses were found to be in descending order both in terms of ease of spread in the household and intensity of the epidemic in the community except when two strains co-circulate. Children are found to be the main introducers of influenza into households.

Models of epidemics and endemicity in genetically variable host populations.

A discrete time genetics model is developed for populations that are undergoing selection due to infectious disease. It is assumed that the generation time of the host and infectious agent are not-synchronous and that only the host population is evolving. Two classes of epidemic processes are considered. The first class is for infectious agents that confer immunity following infection, while the second class is for those that do not confer immunity. The necessary and sufficient conditions are found in order for the disease to persist in a stable polymorphic host population. These conditions are shown to depend on the density of susceptibles, the selection coefficients, and the severity and class of the disease process.

Estimation of incidence of HIV infection using cross-sectional marker surveys.

Methods of estimating the probability density function of infection times for a population, using serial cross-sectional measurements of a marker of disease progression, are presented. The infection time distribution may be calculated back to the beginning of the epidemic, if it is possible to sample individuals who were infected at the beginning of the epidemic; otherwise, under a Markov assumption, the infection time distribution may be calculated conditional on infection after sampling has begun. In either case, the proportion of prevalent cases infected in an arbitrary time interval between the onset and termination of sampling may be measured. Data from the San Francisco Men's Health Study are analyzed; the infection time distribution compares well with that estimated by Bacchetti (1990, Journal of the American Statistical Association 85, 1002-1008) using stored sera from several San Francisco cohort studies.

The ecological effects of individual exposures and nonlinear disease dynamics in populations.

To describe causally predictive relationships, model parameters and the data used to estimate them must correspond to the social context of causal actions. Causes may act directly upon the individual, during a contact between individuals, or upon a group dynamic. Assuming that outcomes in different individuals are independent puts the causal action directly upon individuals. Analyses making this assumption are thus inappropriate for infectious diseases, for which risk factors alter the outcome of contacts between individuals. Transmission during contact generates nonlinear infection dynamics. These dynamics can so attenuate exposure-infection relationships at the individual level that even risk factors causing the vast majority of infections can be missed by individual-level analyses. On the other hand, these dynamics amplify causal associations between exposure and infection at the ecological level. The amplification and attenuation derive from chains of transmission initiated by exposed individuals but involving unexposed individuals. A study of household exposure to the only vector of dengue in Mexico illustrates the phenomenon. An individual-level analysis demonstrated almost no association between exposure and infection. Ecological analysis, in contrast, demonstrated a strong association. Transmission models that are devoid of any sources of the ecological fallacy are used to illustrate how nonlinear dynamics generate such results.