Читать книгу Principles of Virology, Volume 2 - Jane Flint, S. Jane Flint - Страница 39

Virus particles must spread from host to host to maintain a viable population. Spreading will occur if, on average, each infected 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.