host passes the agent to more than one new host before the original host dies or clears the infection. The probability of such transmission is related to the size of the host population: infections can spread only if population density exceeds a minimal value. These concepts have been incorporated into a comprehensive theory of host-parasite interactions that is well known in ecological circles, but not always appreciated. This theory describes the parameters of viral infection in quantitative terms. The basic reproductive number for a virus population, R0 (pronounced “R-naught”), is de fined as the number of secondary infections that can arise in a large population of susceptible hosts from a single infected individual during its life span. If R0 is <1, it is impossible to sustain an epidemic; in fact, it may be possible to eradicate the pathogen, especially if the species of hosts that it infects is limited. If R0 is >1, an epidemic is possible, but random fluctuations in the number of transmissions in the early stages of infection in a susceptible population can lead to either extinction or explosion of the infection. If R0 is much greater than 1, an epidemic (or perhaps a pandemic) is almost certain (Table 1.1). The proportion of the susceptible population that must be vaccinated to prevent virus spread is calculated as 1—1/R0. In the simplest model, R0 = tau × c × d, where tau is the probability of infection, given contact between an infected and uninfected host; c is the average duration of contact between them; and d is the duration of infectivity. Consequently, the longer the exposure among individuals and the length of the infectious period, the higher R0 will be.
The original host-parasite theory assumed well-mixed, homogeneous host populations in which each individual host has the same probability of becoming infected. Although the general concepts remain valid, additional parameters and constraints have been added to the mathematical models as more has been learned about population diversity and the dynamics of viral infections (Chapter 10). For example, immune-resistant viral mutants with differences in virulence and transmissibility can be selected, and some individuals (called super transmitters) can pass infection to others much more readily than the majority. We also now know that virus populations are more diverse than first imagined, and the constellation of possible host populations affects their evolution in ways not easily captured by mathematical equations. Consequently, although the calculations are useful indications of the thresholds that govern the spread of a virus in a population (that is, they help to determine if a disease is likely to die out[R0 is <1] or become endemic [R0 is >1]), they cannot be used to compare possible outcomes in particular cases or for different diseases.
Table 1.1 Reproductive numbers for selected viruses
| Virus | R 0 a |
|---|---|
| Measles | 12–18 |
| Smallpox | 5–7 |
| Polio | ∼7 |
| SARS–CoV–2 | 2–3 |
| Influenza | |
| 2009 (H1N1) | 1.47 |
| 1957, 1968 pandemics | 1.8 |
| 1918 pandemic | 2.4–5.4 |
| Ebola | 1.3–1.8b |
aValues from Centers for Disease Control and Prevention website.
bSource: Chowell G et al. 2004. J Theoret Biol 229:199–126.
While mathematical formulas and statistics are crucial to all studies in virology, they are of particular value in viral epidemiology. An understanding of some essential principles concerning the use of statistics in virology is provided in Box 1.6.
Methods Used by Epidemiologists
We have considered some of the terms that epidemiologists use, but how do these scientists monitor and develop strategies to control the spread of viruses in populations? An investigation begins at the site of an outbreak, where as much descriptive data as possible about the infected individuals and the environment are gathered. In cases of viral infections in humans, information on recent travel, lifestyle, and preexisting health conditions is considered, along with the medical records of infected individuals to generate a testable hypothesis about the origin of the outbreak. The word “descriptive” can have a negative connotation in virology, often used to imply the opposite of “mechanistic.” However, in epidemiology, descriptive studies are essential to establish or exclude particular hypotheses about the origins of an outbreak. Indeed, descriptive epidemiology was the cornerstone for the discovery of human immunodeficiency virus during the AIDS epidemic in the 1980s (Box 1.7).
Following the descriptive phase, analytical epidemiological methods are used to test hypotheses using control populations in either retrospectively or prospectively focused studies. Clinical epidemiology focuses on the collection of biospecimens, such as blood, sputum, urine, and feces, to search for viral agents or other pathogens and to help determine the potential route of transmission. Once specimens are collected, nucleic acid sequencing is often performed on the samples to deter mine the nature of the infectious agent, or to define how genetic variants may have spread within a population. Studies may also include serological analyses, in which antibodies in the blood that implicate previous infection are identified.
Surveillance
The establishment of vigilant surveillance procedures that can shorten the period between the beginning of an epidemic and its detection is crucial to mitigating the impact of an outbreak. One could argue that the development of worldwide surveil lance programs and information sharing have had as profound an impact on limiting viral infections as antiviral medications and vaccines. The U.S. Centers for Disease Control and Prevention (CDC) was established in 1946 after World War II, with a primary mission to prevent malaria from spreading across the country. The scope of the CDC quickly expanded, and this institution is now a central repository for information and biospecimens available to epidemiologists; it also offers educational tools to foster awareness and ensure public safety. The World Health Organization (WHO), founded in 1948 as an international agency of the United Nations, is charged with establishing priorities and guidelines for the worldwide eradication of viral agents. The WHO provides support to countries that may not have the resources to combat infectious diseases, and coordinates results from a global network of participating laboratories. While the WHO provides coordination, the experimental work is performed in hundreds of laboratories throughout the world, often in remote locations, which process samples and relay information back to the WHO. These WHO-certified laboratories adhere to stringent standards to ensure consistency of methods and interpretations. The laboratories conduct field surveillance using wild and sentinel animals, and perform periodic blood screening for signs of infection or immunity (Box 1.8). The chief successes of such global-surveillance efforts to date include the eradications of smallpox virus and rinderpest virus, the latter of which causes disease in agricultural animals, such as cattle and sheep.
