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| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Herd immunity | 3/4 | https://en.wikipedia.org/wiki/Herd_immunity | reference | science, encyclopedia | 2026-05-05T07:29:16.564067+00:00 | kb-cron |
With p being by itself on the left side of the equation, it can be renamed as pc, representing the critical proportion of the population needed to be immune to stop the transmission of disease, which is the same as the HIT. R0 functions as a measure of contagiousness, so low R0 values are associated with lower HITs, whereas higher R0s result in higher HITs. For example, the HIT for a disease with an R0 of 2 is theoretically only 50%, whereas a disease with an R0 of 10, the theoretical HIT is 90%. When the effective reproduction number Re of a contagious disease is reduced to and sustained below 1 new individual per infection, the number of cases occurring in the population gradually decreases until the disease has been eliminated. If a population is immune to a disease in excess of that disease's HIT, the number of cases reduces at a faster rate, outbreaks are even less likely to happen, and outbreaks that occur are smaller than they would be otherwise. If the population immunity falls below the herd immunity threshold, where the effective reproduction number increases to above 1, the population is said to have an "immunity gap", and then the disease is neither in a steady state nor decreasing in incidence, but is actively spreading through the population and infecting a larger number of people than usual. An assumption in these calculations is that populations are homogeneous, or well-mixed, meaning that every individual is equally likely to come into contact with any other individual, when in reality, populations are better described as social networks as individuals tend to cluster together, remaining in relatively close contact with a limited number of other individuals. In these networks, transmission only occurs between those who are geographically or physically close to one another. The shape and size of a network is likely to alter a disease's HIT, making incidence either more or less common. Mathematical models can use contact matrices to estimate the likelihood of encounters and thus transmission. In heterogeneous populations, R0 is considered to be a measure of the number of cases generated by a "typical" contagious person, which depends on how individuals within a network interact with each other. Interactions within networks are more common than between networks, in which case the most highly connected networks transmit disease more easily, resulting in a higher R0 and a higher HIT than would be required in a less connected network. In networks that either opt not to become immune or are not immunized sufficiently, diseases may persist despite not existing in better-immunized networks.
=== Overshoot === The cumulative proportion of individuals who get infected during the course of a disease outbreak can exceed the HIT, because the HIT does not represent the point at which the disease stops spreading, but rather the point at which each infected person infects fewer than one additional person on average. When the HIT is reached, the number of additional infections does not immediately drop to zero. The excess of the cumulative proportion of infected individuals over the theoretical HIT is known as the overshoot.
== Boosts ==
=== Vaccination ===
The primary way to boost levels of immunity in a population is through vaccination. Vaccination is originally based on the observation that milkmaids exposed to cowpox were immune to smallpox, so the practice of inoculating people with the cowpox virus began as a way to prevent smallpox. Well-developed vaccines provide protection in a far safer way than natural infections, as vaccines generally do not cause the diseases they protect against, and severe adverse effects are significantly less common than complications from natural infections. The immune system does not distinguish between natural infections and vaccines, forming an active response to both, so immunity induced by vaccination is similar to what would have occurred from contracting and recovering from the disease. To achieve herd immunity through vaccination, vaccine manufacturers aim to produce vaccines with low failure rates, and policy makers aim to encourage their use. After the successful introduction and widespread use of a vaccine, sharp declines in the incidence of diseases it protects against can be observed, which decreases the number of hospitalizations and deaths caused by such diseases. Assuming a vaccine is 100% effective, then the equation used for calculating the herd immunity threshold can be used for calculating the vaccination level needed to eliminate a disease, written as Vc. Vaccines are usually imperfect, however, so the effectiveness, E, of a vaccine must be accounted for:
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{\displaystyle V_{c}={\frac {1-{\frac {1}{R_{0}}}}{E}}.}
From this equation, it can be observed that if E is less than (1 − 1/R0), then eliminating a disease is impossible, even if the entire population is vaccinated. Similarly, waning vaccine-induced immunity, as occurs with acellular pertussis vaccines, requires higher levels of booster vaccination to sustain herd immunity. If a disease has ceased to be endemic to a population, then natural infections no longer contribute to a reduction in the fraction of the population that is susceptible. Only vaccination contributes to this reduction. The relationship between vaccine coverage and effectiveness and disease incidence can be shown by subtracting the product of the effectiveness of a vaccine and the proportion of the population that is vaccinated, pv, from the herd immunity threshold equation as follows:
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{\displaystyle \left(1-{\frac {1}{R_{0}}}\right)-(E\times p_{v}).}