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The interval between successive cases of an infectious disease is determined by the time from infection to infectiousness, the duration of infectiousness, the time from infection to disease onset (incubation period), the duration of any extra-human phase of the infectious agent, and the proportion clinically affected among infected individuals. The interval is important in the interpretation of infectious disease surveillance and trend data, in the identification of outbreaks, and in the optimization of quarantine and contact tracing. This paper discusses the properties of these intervals, as measured between transmission events or between clinical onsets of successive infected individuals, noting the determinants of their ranges and frequency distributions, the circumstances under which secondary cases may arise before primaries, and under which the infection transmission interval will be different from the interval between clinical onsets of successive cases. It discusses the derivation of interval distribution statistics from descriptive data given in standard textbooks, with illustrations from published data on outbreaks, households, and epidemiologic tracing. Finally, it discusses the implications of such measures for studies of secondary attack rates, for the persistence of infection in human communities, for outbreak response, and for elimination or eradication programs.

Several social and medical attributes are associated with both avoidance or delay of vaccination and an increased risk of adverse events such as sudden infant death syndrome or childhood encephalopathy. Studies that fail to control adequately for such confounding factors are likely to underestimate the risks of adverse events attributable to vaccination. This paper reviews the literature on studies of severe adverse events after the administration of pertussis antigen-containing vaccines, with particular attention to the measures taken by different investigators to avoid this problem. Most published studies have reported a deficit of sudden infant death syndrome among vaccinees, which may reflect confounding in their study designs. An expression is derived to explore the extent of underestimation that may be introduced in such studies, under different sets of conditions. Confounding of this sort is a general problem for studies of adverse reactions to prophylactic interventions, as they may be withheld from some individuals precisely because they are already at high risk of the adverse event.

The lifetime risk of developing disease, the incubation period, and the time period between infection and transmission (the serial interval) are three important measures for interpreting trends in tuberculous infection and disease but are complicated by strong age dependencies regarding disease risk and by the potential for reinfection to occur. By using a model of the epidemiology of tuberculosis in England and Wales, the authors demonstrated that all three measures changed dramatically during the 20th century largely as a result of declines in the risk of infection. The estimated lifetime risk was highest following infection in early adulthood and declined with year of infection; the age-weighted average was approximately 12% during the last 50 years. Incubation period distributions depend on whether they are viewed prospectively (from infection to disease onset) or retrospectively (since infection for cases with disease onset at a particular time). As children rarely develop infectious forms of tuberculosis, infections acquired in childhood are associated with considerably longer serial intervals than those acquired in adulthood. These unusual properties are probably shared by other infections with long intervals between infection and disease. The results are important for interpreting data on transmission patterns, as are now being derived from molecular epidemiologic studies.

The global poliomyelitis eradication initiative has been a tremendous success, with current evidence suggesting that wild poliovirus will cease to circulate anywhere in the world soon after the year 2000. As the goal of wild poliovirus eradication is approached, concern has been raised about the potential for persistent transmission of oral polio vaccine (OPV) viruses, as these viruses are known to revert toward wild-type neurovirulence. This paper has been extracted from a document prepared for the World Health Organization on the implications of OPV transmissibility for the strategy of stopping OPV vaccination after global eradication of wild polioviruses. The authors review the empirical evidence on OPV transmissibility available from household and community transmission studies and from mass-vaccination experiences. They then consider theoretical measures of transmissibility and persistence for wild and OPV viruses (secondary attack rate, basic reproduction number, and critical populations' size), to assess whether transmissibility of OPV viruses is sufficient to allow persistence of these viruses after cessation of vaccination. The findings indicate that OPV viruses could persist under various plausible circumstances, and that this potential should be a major consideration when planning the cessation of OPV vaccination.In view of the growing concern over the potential for persistent transmission of oral polio vaccine (OPV) viruses, this paper examines a document on the implications of OPV transmissibility for the strategy of stopping OPV vaccination after global eradication of wild polio viruses. It reviews the empirical evidence on OPV transmissibility gathered from household and community transmission studies and from mass-vaccination experiences. It assesses whether transmissibility of OPV viruses are sufficient to allow persistence of these viruses after cessation of vaccination by considering theoretical measures of transmissibility and persistence for wild and OPV viruses. This review concludes that there is a risk that OPV viruses will persist and that such persistence could occur in a variety of ways. Further research is needed to assess the implications for OPV virus persistence, especially on issues concerning the long-term excretion by immunodeficient individuals; the ability for OPV viruses to spread and persist in communities with low seroprevalence; the risk of reversion to wild-type transmissibility; environmental survival and potential reservoirs of OPV virus; duration of mucosal immunity; and the prevalence of viable poliovirus in stored samples.

Data on household and dwelling contact with known leprosy cases were available on more than 80,000 initially disease-free individuals followed up during the 1980s in a rural district of northern Malawi. A total of 331 new cases of leprosy were diagnosed among them. Individuals recorded as living in household or dwelling contact with multibacillary patients at the start of follow-up were at approximately five- to eightfold increased risk of leprosy, respectively, compared with individuals not living in such households or dwellings. Individuals living in household or dwelling contact with paucibacillary cases were both at approximately twofold increased risk. The higher risk associated with multibacillary contact and the fact that dwelling contact entailed a greater risk than household contact if the association was with multibacillary, but not with paucibacillary, disease suggest that paucibacillary cases may not themselves be sources of transmission, but rather just markers that a household has had contact with some (outside) source of infection. When household contact was considered alone, the risks of disease were appreciably higher for younger than for older contacts and for male compared with female contacts. Despite the elevated risk of leprosy associated with household or dwelling contact, only 15% of all incidence cases arose among recognized household contacts. Given the dynamic nature of household membership and consequent misclassification of contact status, the true contribution to overall incidence of contact within household or dwelling settings is likely to be much higher than this, perhaps 30% or higher. Considering the predilection of males for infectious multibacillary forms of the disease, the transmission of Mycobacterium leprae at an early age, in particular to males, may be of particular importance for the persistence of leprosy in endemic communities. Although residential contact with a multibacillary case is the strongest known determinant of leprosy risk, the vast majority of such contacts never manifest disease, which indicates a crucial role for genetic and/or environmental factors in the transmission of M. leprae infection and/or the pathogenesis of clinical leprosy.

Most of the factors associated with the failure of a vaccination to provide protective immunity are not distributed uniformly or randomly within populations. This paper explores the extent to which a nonrandom distribution of vaccination failures and the selection of exceptional situations for investigation may influence estimates of vaccine performance. The authors show that outbreak investigations will tend to underestimate vaccination efficacy, and that the extent of underestimation will be related directly to the size of the epidemic triggering an investigation, the vaccination coverage in the community, and the extent of clustering of vaccination failures in the population; it will be related inversely to the size of and contact intensity within the investigated community. These potential sources of bias are not the only problems that arise in estimating vaccine efficacy, but they should be taken into consideration when analyzing and interpreting outbreak situations. The fact that outbreak investigations carried out within the United States during the past decade have provided estimates of measles vaccination efficacy on the order of 95% is consistent with a somewhat higher overall "true" efficacy of current vaccines and procedures in the total population. It is important to understand better the frequency, distribution, and risk factors for vaccination failures in populations.

Recent years have witnessed a considerable increase in the development and use of mathematical and computer-based models in infectious disease epidemiology. As a measure of this increase, Bailey (1) finds that the literature in this field has grown at a greater-than-exponential rate over the past two decades/ilthough one may suspect that some of the published models have greater value as exercises in mathematics than as contributions to "real disease" epidemiology, this is certainly not true of all of them; and many examples can be cited of major contributions of mathematical models in revealing relationships underlying complex epidemiologic phenomena, in hypothesis testing, and in the

There is a tendency for governments to decide whether or not to offer routine vaccination on the basis of arguments of financial cost, whereas individuals decide whether or not to accept vaccination on the basis of their perception of the risks involved. Furthermore, some vaccines impart, or appear to impart, a degree of indirect protection to nonvaccinated individuals in the community. For both of these reasons, public motives concerning vaccination differ from those of the individual. The quantitative implications of these differences are explored in this paper. It is found that, under a broad range of conditions, rational informed individuals would "choose" a lower vaccine uptake than would the community if it acted as a whole. The result is applied to the pertussis situation in England over the past 30 years and provides a measure of a public's changing perception of the risks associated with that vaccine.