The quantification of disease occurrence is the cardinal feature of epidemiology. To accomplish this, the concept of rates was introduced, and rates have become the basic coinage of epidemiology (Fig. 12.1). Rates are fractions in which the numerator is the number of cases of disease and the denominator is a measure of the population. The incidence rate (also called the attack rate for acute infectious diseases) is used to quantify the number of new infections. A population and a time frame are defined, and the number of new cases in that population during that interval of time is counted. Note that the denominator includes both the size of population and time frame, and is often expressed as person-years (or any other standard interval of time; e.g., “thousand person-years” or “hundred person-weeks”). The incidence rate is then expressed as “cases per thousand person-years” or a similar term. Also note that the time element may be omitted in expressing incidence; the reader must then determine by context the time frame used.

Prevalence, technically not a rate but a ratio, refers to the total number of cases present within a specified time interval. Thus, the numerator in prevalence includes not just new cases but cases carried forward from the period prior to the specified time interval. When point prevalence is computed, a particular narrow time frame is selected, and the population recorded for that time frame constitutes the denominator. All cases “prevalent” on that date constitute the numerator. Prevalence is expressed as a ratio such as “cases per million”; note that there is no time parameter in this ratio.

Changes in incidence and prevalence may be divergent. A control program for human immunodeficiency virus (HIV) infection, for example, could decrease HIV incidence within a population through effective preventative measures but increase the prevalence of HIV infection through access to antiretroviral therapy and improved survival.

In epidemiology, consistency is a virtue. When cases and populations are counted prior to computing rates, care must be
taken to use the same definition for numerator and denominator. Persons counted in the denominator should be at risk to be a case in the numerator if infected. For instance, if incidence is computed for the population of Philadelphia for 2011, a case hospitalized in the city but resident outside the city would not be counted. A case with onset in December 2010 but still ill in 2011 would not be counted as an incident case but would be a prevalent case.

What distinguishes infectious disease epidemiology from chronic disease epidemiology is that the former accounts for dependent happenings, a term introduced by Ronald Ross,¹⁰² in which the incidence of a disease depends on its prevalence within a population.⁴⁵ Traditional epidemiologic and statistical methods that infer relationships between exposure and disease outcome assume that the outcome in one individual is independent of the outcome in other individuals, an assumption that is invalid for communicable viral infections.⁵⁴,⁸²

In practice, the accurate collection of data for the computation of rates is often a major undertaking, whereas the computations are relatively simple. Furthermore, the practicing epidemiologist must frequently work with incomplete and inaccurate information. In most developed countries, denominator (population) information is usually good, and numerator (case) information is the major problem. In resource-limited settings, accurate population data may be unavailable.

For infectious (viral) diseases, there are several sources of case data. Passive surveillance denotes the continuous reporting of disease by healthcare workers. By law, many viral diseases are designated as “reportable,” and in theory, the reporting of all cases is required. Cases are reported by practicing physicians, hospitals, or laboratories to local health jurisdictions, which in turn relay reports to a central state office whence they are transmitted to a national center (e.g., the U.S. Centers for Disease Control and Prevention). The weakest link is the initial report; in practice, only a small fraction of cases of many common viral diseases (such as 10%–15% of measles or hepatitis B cases) are reported to the national center (called the reporting efficiency). However, if the proportion of cases reported is consistent between geographic locales and between years, these reports may be used to monitor trends. Consistency is an important caveat, because the proportion of cases reported may increase if the absolute number of cases decreases. Changes in the case definition also may result in spurious changes in surveillance data. Reporting of certain rare or serious diseases, such as poliomyelitis or acquired immunodeficiency syndrome (AIDS), is often close to 100%; in such instances, reported cases can be used with much greater confidence for calculation of rates. Within increasing interest in the pandemic spread of respiratory viruses and the emergence of new zoonotic viral pathogens, global disease surveillance networks have been established to provide data on disease incidence and transmission in real time,¹⁴ including the Program for Monitoring Emerging Diseases (ProMED) and the World Health Organization’s Global Outbreak Alert and Response Network (GOARN).

Active case detection through epidemic investigation is the traditional approach to collecting information on outbreaks of disease. Such investigations are usually initiated by public health authorities but may be instigated by healthcare workers or patient families. The investigation is tailored to the situation and to the resources at hand, although experience has set certain guidelines, particularly for recurring outbreaks such as food-borne diseases. The purpose of such studies is several: (a) to classify the illness and determine the causative organism, (b) to assess the extent of the outbreak and its economic and health impact, (c) to abort the outbreak or prevent recurrent episodes, and (d) to inform or reassure the public. The first recognition of a new disease or isolation of a previously unknown virus has been accomplished as a result of an epidemic investigation. Examples are the identification of Lassa virus; Marburg virus; Sin Nombre virus (SNV), a hantavirus that is the cause of acute pulmonary syndrome; severe acute respiratory syndrome (SARS)-coronavirus; and the 2009 H1N1 influenza virus.

Serological surveys may be used to detect the footprints that a virus leaves in a population. Serosurveys are particularly useful for viruses because most viral infections leave an imprint on all infected individuals—that is, the presence of immunoglobulin G (IgG) antibody, which often is life long. Because many viruses cause asymptomatic infections or nondescript illnesses in addition to diagnosable diseases, serological surveys identify inapparent as well as apparent infections. Incident viral infection can be identified using assays for immunoglobulin M (IgM) antibody or antibody avidity, whereas IgG antibodies indicate prior infection or vaccination.

Modern epidemiology has made one outstanding contribution to the discipline—namely, the extension of hypothesis testing from the laboratory to populations. In general, the epidemiologist
attempts to test the hypothesis that one or more population variables influence the occurrence of a specified disease and, if so, to quantify this effect and estimate confidence limits. There are two general designs used for such studies: cohort and case-control studies. The essence of these designs is summarized next, and the reader is referred to appropriate texts for methodological exposition.³⁵

Many acute viral infections confer lifelong immunity. Upon re-exposure after initial infection, there is often reinfection but with minimal virus replication and an anamnestic immune response. Such reinfections are usually covert and almost never severe, resulting in minimal or no shedding of infectious virus. For certain viruses, such as poliovirus or rhinovirus, immunity is type specific and confers little protection against exposure to a different serotype. These simple facts have profound implications for viral epidemiology. For epidemiologic purposes, a population may be divided into three groups: susceptible, infected (and infectious), and immune. Persons infected at any time in the past may be considered immune (recovered) and are exempt from disease and unable to act as links in a transmission chain, whereas susceptible individuals can be infected, become infectious, and experience disease. This compartmentalization of the population is the basis for simple SIR (susceptible, infectious, recovered) models of virus transmission⁴ that can explain the periodicity in incidence as the outcome of the buildup and decline of susceptible individuals.

Susceptibility may not be present immediately after birth. IgG antibodies are actively transported across the placenta, conferring protective immunity to neonates and young infants. For such viral infections, individuals move from a protected state to a susceptible one in the first year of life. Immunity can then be conferred by vaccination or infection.

Persistent viral infections differ from acute infections because the infected individual may be capable of transmitting infection over many years and may develop disease at any time during virus persistence. In the instance of persistent viruses, the population may be divided into uninfected susceptibles and immune-but-infectious persons who carry serological markers of prior infection but who are still capable of acting as links in the chain of infection. Important examples are hepatitis B virus, HIV, and several herpesviruses (herpes simplex virus, varicella-zoster virus, and cytomegalovirus) that establish latent infection capable of reactivation.

For acute viral infections, the following three parameters determine incidence: the proportion of the population susceptible, the proportion of the population that is infectious, and the rate of contact between susceptible and infectious individuals, with contact defined as an encounter sufficient for transmission. The proportion of infected persons who become ill—the case infection ratio—determines the proportion of infected persons detected through case surveillance.

The course of infection in a single individual can be conveniently divided into several periods.²⁹ The interval from acquisition of infection to onset of illness is the incubation period. Note that “onset of illness” must be explicitly defined for each disease and is often measured by the first day on which pathognomonic signs or symptoms are reported. The interval from acquisition of infection to onset of infectiousness is the latent period. For most viral diseases, the latent period is shorter than the incubation period. Consequently, the infected individual begins to shed virus prior to the onset of illness (smallpox is a notable exception) and continues to shed during and sometimes after recovery from the acute illness. The effectiveness of quarantine measures is reduced when the latent period is significantly shorter than the incubation period as the infectious individual goes unrecognized. The period during which the infected person is potentially infectious for others is the infectious period.

Incubation periods for any viral disease vary around the mean, as illustrated in Figure 12.2. When a frequency distribution of individual incubation periods is plotted, it usually has a longer tail at the high end of the distribution (right skewed). If the frequency is plotted against the logarithm of time, the data often approximate a normal distribution.¹⁰⁴ This log-normal distribution is characteristic of the incubation periods of many viral infections.⁶⁰

The average period between infection of an individual and transmission to others is the generation time or transmission interval. From studies of selected outbreaks, the average interval between onsets of successive waves of cases (called the serial interval) has been determined, and the generation time is often assumed to be equal to this interval as the best approximation available. This is because it is often impossible to know the exact time of infection. These relationships are shown in Figure 12.3 for a typical acute viral infection.

Each virus has characteristic modes of host-to-host transmission: (a) direct person-to-person transmission through respiratory, fecal–oral, sexual, blood, or from mother to child, or (b) indirect transmission through fomites or vectors. Viruses that cause acute short-term infections require efficient transmission to subsequent hosts. Such infections are characterized by a relatively short infectious period and the excretion of high titers of infectious agent over a limited period of time, as in the instance of influenza, measles, and smallpox viruses. Viruses that cause persistent infections do not require such highly efficient modes of transmission, because they are excreted continuously or intermittently for many years and thus have a long infectious period to maintain virus
transmission. Horizontal transmission is often used to designate these modes of transmission from person to person.

Vertical transmission is used to denote transmission between parent and offspring. Such transmission may occur during gestation, by passage of virus across the placenta (e.g., rubella virus and HIV); perinatally during birth (e.g., herpes simplex or hepatitis B viruses); or from the mother via colostrum or milk (e.g., HIV). Germline transmission, another mode of vertical spread, is seen with certain animal retroviruses such as murine leukemia virus, which are transmitted as an integrated provirus that may be transcribed into infectious virus. Although retroviral sequences are carried in the human genome, there are presently no proven instances where these have been shown to function as infectious virions. Selected examples of horizontal and vertical transmission are listed in Table 12.5.

Arthropod-borne viruses (arboviruses) are usually maintained by continuously cycling between an insect host and a vertebrate host. In most instances, the virus replicates optimally in a single species or in a few closely related species of insects, which constitute the major, if not exclusive, vectors. Because most blood-feeding insects have a clear feeding preference for a few vertebrate species, this determines and limits the vertebrate species involved in the maintenance cycle. For some arboviruses, alternate maintenance cycles are limited to the insect host, with transovarial or sexual transmission from generation to generation of insects. These insect cycles may be critical to perpetuation of the virus during adverse conditions, such as overwintering, but otherwise play a minor role in viral dissemination.

There are only two arboviruses—dengue and urban yellow fever—of which humans are the major vertebrate host. In other instances, such as St. Louis encephalitis and La Crosse encephalitis, humans are accidentally infected when the vector mosquito happens to feed on humans as an alternate to the preferred vertebrate blood source, such as birds or woodland rodents.

A dead end or terminal host is one not involved in maintaining viral transmission. Humans are occasional terminal hosts for several viruses maintained in extrahuman cycles. These include arbovirus infections, with the exceptions of dengue and yellow fever viruses noted earlier. In addition, there are several zoonotic infections, most notably rabies, in which humans are terminal hosts. Transmission of rabies is often by bite, although for most other terminal infections in this group (such as Korean and Bolivian hemorrhagic fever viruses), environmental exposure to fomites is responsible. Table 12.4 lists examples of viral infections in which humans are terminal hosts.

The transmission of persistent viral infections differs from that of classic acute infections. Those persistent infections that can become latent, such as the herpesviruses, are transmissible intermittently during periods of activation. Thus, one individual may be infected in childhood and transmit infection 50 years later during a recrudescence. The ability for a single link in the infection chain to extend over such an interval has important implications for perpetuation and eradication of infection. Infections such as those caused by hepatitis B virus and HIV, which are transmissible over many years, are often transmitted very inefficiently. Thus, hepatitis B is transmitted to susceptible household contacts at a frequency of less than 1 per 100 person-years exposure, and HIV is transmitted to sexual contacts at a rate of approximately 1 transmission per 100 to 1,000 contact episodes, with the risk of transmission directly correlated with HIV viral load.³⁶ For such infections, transmission requires passage of body fluids or of viable infected cells. Despite inefficient transmission, the number of new infections initiated by each persistent infection may be high because of the long infectious period. An epidemic curve caused by such a virus may stretch over years rather than weeks, and the mathematical modeling of such persistent viral infections is profoundly different from acute infections because infectious individuals are not rapidly converted to noninfectious immunes but continue to accumulate.⁸

The transmissibility of viral infections may be quantified by the basic reproductive rate (R₀), defined as the average number of new infections initiated by a single infectious individual in a completely susceptible population over the course of that individual’s infectious period.⁴⁸ The reproductive rate of a pathogen is a function of pathogen characteristics as well as contact patterns within the community. Examples of R_o are 12 to 18 for measles virus, 5 to 7 for poliovirus and smallpox virus, and 1.5 to 2.0 for influenza viruses.⁴

R_o is determined by (a) the number of contacts between an infected individual and others, (b) the proportion of these contacts that are susceptible (assumed 100%), and (c) the probability of transmission per susceptible contact. The effective or net reproductive number (R) is the actual average number of secondary cases that occur and equals the product of R_o and the proportion of susceptible individuals in the population. R is smaller than R_o because not all individuals in real populations are susceptible, because of either prior infection or immunization. When R is greater than 1, the incidence of infection increases; when R is less than 1, the incidence wanes. When R equals 1, the number of infections is constant. Control programs aim to reduce R to below 1 to achieve disease elimination.

A simple mathematical expression that captures the three parameters for a directly transmitted pathogen is R = βXD, where β represents the transmission coefficient (a measure of the rate of contact between individuals and the likelihood of transmission during that contact per unit time), X is the proportion of susceptible individuals, and D is the duration of infectiousness. As can be seen from this simple formulation, elimination of a viral infection could be achieved by reducing effective contacts (e.g., quarantine), reducing the proportion of susceptible individuals (e.g., through vaccination), or reducing the infectious period (e.g., treatment to reduce viral load).

Mathematical models of viral dynamics with varying degrees of sophistication are widely used by infectious disease epidemiologists to understand temporal and spatial patterns of virus transmission within populations and to evaluate the potential impact of control strategies. Mathematical models help to quantify our understanding of infectious disease dynamics and can be used to assess interventions for which epidemiologic studies are not feasible or ethical (e.g., strategies to contain a smallpox outbreak as a result of bioterrorism).⁵⁴ The use of mathematical models in infectious disease epidemiology has a long history, with one of the earliest successful approaches being the model of malaria transmission dynamics developed by Sir Ronald Ross in the early 20th century.¹⁰³ Subsequent models of infectious disease dynamics were developed by Wade Hampton Frost and Lowell Reed (the Reed-Frost model), in which the incidence of newly infected persons was based on the probability of contact between susceptible and infectious hosts.² The models developed by W. O. Kermack and A. G. McKendrick were the first to divide the population into the three classes of individuals discussed earlier (susceptibles, infectious, and recovered; hence, SIR models) and estimated the number of new infections as a function of the number of susceptible and infectious individuals.⁵² These deterministic, compartmental models (based on difference or differential equations depending on whether time is treated as a discrete or continuous variable) were expanded and popularized by Roy Anderson and Robert May⁴ and became the basis for much infectious disease modeling. Variations on the basic SIR model include the addition of other compartments or classes of individuals (e.g., infected but not infectious or a period of maternally acquired protection), age-specific contact patterns, and stochastic processes. Useful models balance the goals of realism and simplicity, as more complex models require a greater number of underlying assumptions and parameter estimates. Useful models clarify our conceptual framework of viral transmission dynamics, suggest which variables are most important for transmission and require careful measurement, and generate new hypotheses. In addition, models can be used to estimate the likely size of an epidemic, its time course and periodicity, the reproductive number R, and the expected impact of various interventions. Finally, model validation against epidemiologic data is a critical component of model building and use.

Measles has long been a favored disease by infectious disease modelers because of the simple transmission dynamics and the long time series available as a result of the readily distinguishable clinical characteristics. Mathematical models of measles virus transmission allow for exploration of the impact of various vaccination strategies, including the optimum age at measles vaccination and the use of mass vaccination campaigns,⁵⁹,⁷⁴ that would otherwise be difficult to evaluate in epidemiologic studies. Model results suggest that the best age at which to vaccinate against measles depends critically on the age distribution of cases of infection prior to the introduction of control measures,⁷⁴ the introduction of mass vaccination will induce a temporary phase of low incidence of infection before the system settles to a new pattern of recurrent epidemics,⁷⁴ and that frequent, relatively low coverage mass vaccination campaigns are effective in reducing measles virus transmission.⁵⁹

In tabulating cases of viral infection, the epidemiologist looks for features that distinguish affected persons from the general population to identify risk factors for infection and disease. Clues may exist in demographic features and behavioral characteristics, such as age, sex, race, occupation, residence, or any aspect of personal conduct. Such variables are frequently the most important initial step in understanding an outbreak.

The first recognized outbreak of St. Louis encephalitis in 1933 involved a classical exercise in “shoe leather” epidemiology,⁶⁹ the finding of which led to the proposal that the disease was transmitted by an arthropod vector rather than by person-to-person contact. When this outbreak occurred, neither the disease nor the causal agent was known. Because it was an acute neurological disease, occurring in the summer, it was first thought to be a form of poliomyelitis or to be transmitted in the same manner through the fecal–oral route. The characteristic encephalitic manifestations made it relatively easy to identify many of the cases clinically. When these cases were assembled, and rates estimated, it became apparent that the incidence was greater in the suburbs of St. Louis than in the city proper. Furthermore, there was a striking concentration of cases among the inhabitants of one institution located in the suburbs; however, a comparison of several adjacent institutions revealed even more dramatic discrepancies, illustrated in Table 12.6. First, there were no cases in the personnel in an infectious disease hospital caring for many acute encephalitis cases—strong evidence against person-to-person transmission. Second, there were high rates in an almshouse but very low rates in two insane asylums. Investigation revealed that the almshouse lacked screens, whereas the other three institutions were screened. These observations were strongly reminiscent of the classic findings of the Reed commission investigating yellow fever in Havana⁹⁸ and suggested mosquito transmission. Finally, it was observed that the suburbs of St. Louis, although home to many affluent residents, lacked the system of storm
sewers present in the city. More sites with standing groundwater existed in the suburbs, and in the hot, dry summer of 1933, these sites were prime mosquito breeding sites. These observations suggested the mechanisms of transmission to the investigating epidemiologists.

The “Cutter incident” offers another example where descriptive epidemiology defined an unusual distribution of disease in a population, leading directly to the cause.⁸⁶ In mid-April 1955, newly approved inactivated poliomyelitis vaccine was distributed throughout the United States for immunization of children 5 to 9 years of age—the age group considered the highest risk and therefore given preference in the utilization of limited vaccine supplies. About 2 weeks later, at the end of April, reports were received of cases of acute paralytic poliomyelitis occurring in a small number of recently immunized children. Because this was close to the seasonal trough in poliomyelitis incidence, relatively few cases of poliomyelitis were occurring in the general population, thus a small number of vaccine-associated cases were particularly striking. Furthermore, vaccine-associated cases were confined to a few of the western states. It quickly became apparent that this geographic distribution was related to the manufacturer of vaccine. Vaccine had been produced by five manufacturers, and most cases were associated with vaccine produced by Cutter Laboratories, which produced the vaccine mainly used in western states. When rates were tabulated for different production pools of Cutter vaccine, the association focused on two high rate pools, as indicated in Table 12.7. Subsequent investigations showed that there were inadequacies in the inactivation and safety testing protocols recommended by the government, permitting the release of vaccine lots containing residual infectious virulent virus.