Non-exponential tolerance to infection in epidemic systems--modeling, inference, and assessment.

The transmission dynamics of infectious diseases have been traditionally described through a time-inhomogeneous Poisson process, thus assuming exponentially distributed levels of disease tolerance following the Sellke construction. Here we focus on a generalization using Weibull individual tolerance thresholds under the susceptible-exposed-infectious-removed class of models which is widely employed in epidemics. Applications with experimental foot-and-mouth disease and historical smallpox data are discussed, and simulation results are presented. Inference is carried out using Markov chain Monte Carlo methods following a Bayesian approach. Model evaluation is performed, where the adequacy of the models is assessed using methodology based on the properties of Bayesian latent residuals, and comparison between 2 candidate models is also considered using a latent likelihood ratio-type test that avoids problems encountered with relevant methods based on Bayes factors.

Social contact networks and disease eradicability under voluntary vaccination.

Certain theories suggest that it should be difficult or impossible to eradicate a vaccine-preventable disease under voluntary vaccination: Herd immunity implies that the individual incentive to vaccinate disappears at high coverage levels. Historically, there have been examples of declining coverage for vaccines, such as MMR vaccine and whole-cell pertussis vaccine, that are consistent with this theory. On the other hand, smallpox was globally eradicated by 1980 despite voluntary vaccination policies in many jurisdictions. Previous modeling studies of the interplay between disease dynamics and individual vaccinating behavior have assumed that infection is transmitted in a homogeneously mixing population. By comparison, here we simulate transmission of a vaccine-preventable SEIR infection through a random, static contact network. Individuals choose whether to vaccinate based on infection risks from neighbors, and based on vaccine risks. When neighborhood size is small, rational vaccinating behavior results in rapid containment of the infection through voluntary ring vaccination. As neighborhood size increases (while the average force of infection is held constant), a threshold is reached beyond which the infection can break through partially vaccinated rings, percolating through the whole population and resulting in considerable epidemic final sizes and a large number vaccinated. The former outcome represents convergence between individually and socially optimal outcomes, whereas the latter represents their divergence, as observed in most models of individual vaccinating behavior that assume homogeneous mixing. Similar effects are observed in an extended model using smallpox-specific natural history and transmissibility assumptions. This work illustrates the significant qualitative differences between behavior-infection dynamics in discrete contact-structured populations versus continuous unstructured populations. This work also shows how disease eradicability in populations where voluntary vaccination is the primary control mechanism may depend partly on whether the disease is transmissible only to a few close social contacts or to a larger subset of the population.

Smallpox transmission and control: spatial dynamics in Great Britain.

Contingency planning for the possible deliberate reintroduction of smallpox has become a priority for many national public health organizations in recent years. We used an individual-based spatial model of smallpox transmission in Great Britain and census-derived journey-to-work data to accurately describe the spatiotemporal dynamics of an outbreak of smallpox in the community. A Markov chain Monte-Carlo algorithm was developed to generate sociospatial contact networks that were consistent with demographic and commuting data. We tested the sensitivity of model predictions to key epidemiological parameters before choosing three representative scenarios from within the range explored. We examined the spatiotemporal dynamics for these illustrative scenarios and assessed the efficacy of symptomatic case isolation, contact tracing with vaccination, and reactive regional mass vaccination as policy options for control. We conclude that case isolation and contact tracing with vaccination would be sufficient to halt ongoing transmission rapidly, unless policy effectiveness was compromised by resource or other constraints. A slight reduction in the expected size and duration of an outbreak could be achieved with regional mass vaccination, but these benefits are small and do not justify the high numbers of vaccine doses required and their associated negative side effects.

The effect of social mixing controls on the spread of smallpox--a two-level model.

Responding to a possible bioterror attack of Smallpox has become a major concern to governments, local public officials and health authorities. This concern has been reflected in numerous studies that model and evaluate possible response strategies. Many of these studies consider only vaccination policies and assume homogeneous mixing, where all instances of contacts in the population are equally likely. Such a mixing pattern is rather unlikely to represent population interaction in a modern urban setting, which typically is separated into households on the one hand, and into daily meeting sites such as schools and offices, on the other hand. In this paper we develop a two-level social interaction model where an individual moves back and forth between home and a daily meeting site, possibly passing through a general meeting site such as mass transit system or other crowded areas. Based on the model, we evaluate the effect of social mixing controls, situational awareness of the public health system and mass vaccination on the spread of smallpox. It is shown that mixing controls and alertness of the response system may have a significant impact on the spread of the epidemic. Some policy recommendations are discussed.

A population survey of smallpox knowledge, perceptions, and healthcare-seeking behavior surrounding the Iraq invasion--Connecticut 2002-03.

BACKGROUND: Knowledge and perceptions about smallpox would probably influence public behavior following an intentional smallpox release. We assessed public knowledge, perceptions, and related healthcare-seeking behavior in Connecticut during the period of heightened interest in smallpox preparedness surrounding the Iraq invasion. METHODS: Smallpox-related questions were added to Connecticut's Behavioral Risk Factor Surveillance System survey, an ongoing statewide adult population-based survey during December 2002-July 2003 and November-December 2003. RESULTS: Among 4,074 respondents, when asked about a hypothetical febrile illness, 72% would first contact their primary care provider (PCP) on weekdays. During nights and weekends, respondents would depend nearly equally on PCPs and emergency departments (37% versus 36%). Most knew smallpox is transmissible from person to person (72%) but not that the majority infected with smallpox survive (38%) or that smallpox is most contagious after the appearance of rash (11%). Knowledge regarding transmissibility and mortality improved during the study period (p < 0.001). Only 31% recognized that vaccinia vaccine is riskier than routine vaccines; 41% would choose vaccination if available. Concern about smallpox's potential use as a weapon was high but decreased after President Bush declared "mission accomplished" in Iraq in May 2003 (p < 0.001). CONCLUSIONS: Despite national coverage of smallpox by the media, most respondents lacked basic knowledge regarding the disease. Incorrect perceptions regarding vaccinia vaccine's risks could increase inappropriate vaccine demand among nonexposed people with vaccine contraindications during a mass vaccination campaign. Current perceptions should inform future smallpox preparedness planning. In addition, both PCPs and emergency medicine clinicians should be targeted for education regarding smallpox diagnosis.

Analyzing bioterror response logistics: the case of smallpox.

To evaluate existing and alternative proposals for emergency response to a deliberate smallpox attack, we embed the key operational features of such interventions into a smallpox disease transmission model. We use probabilistic reasoning within an otherwise deterministic epidemic framework to model the 'race to trace', i.e., attempting to trace (via the infector) and vaccinate an infected person while (s)he is still vaccine-sensitive. Our model explicitly incorporates a tracing/vaccination queue, and hence can be used as a capacity planning tool. An approximate analysis of this large (16 ODE) system yields closed-form estimates for the total number of deaths and the maximum queue length. The former estimate delineates the efficacy (i.e., accuracy) and efficiency (i.e., speed) of contact tracing, while the latter estimate reveals how congestion makes the race to trace more difficult to win, thereby causing more deaths. A probabilistic analysis is also used to find an approximate closed-form expression for the total number of deaths under mass vaccination, in terms of both the basic reproductive ratio and the vaccination capacity. We also derive approximate thresholds for initially controlling the epidemic for more general interventions that include imperfect vaccination and quarantine.

Biological warfare and infection control.

Though many agents have been proposed as potential biological weapons, the feasibility of biological warfare is largely a matter of conjecture. The unpredictable and indiscriminate devastation caused by natural epidemics during wartime should warn us of the dangers of employing microbes as weapons.

Temporal-spatial-social parameters in the spread of contagious disease.

A conceptual theoretical model was built on the basis of prominent concepts of the generally accepted knowledge on the spread of contagious disease. Subsequently, the model was applied to a real epidemic of variola minor (the mild form of smallpox) and four phases of the epidemic were disclosed. The phases discriminated themselves through their relationships to invasion of certain city subdivisions and rural districts and particularly, through the type of social units involved and the type of persons introducing the disease into these units. Introduction of variola minor into day schools with further spread in classes passed across a threshold which led to a boosting of the number of households affected and of the area involved in the epidemic. The phase of maximal spread corresponded to this operation of day schools as diffusion agencies. The temporal-spatial-social correspondence suggests that phases of the epidemic did occur as a result of periodic variation of the mechanism of spread.