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Author: Admin | 2025-04-28
There is some correlation between people's immunization (e.g., vaccination) status, then the formula may underestimate the herd immunity threshold.[9]Graph of herd immunity threshold vs basic reproduction number with selected diseasesThe basic reproduction number is affected by several factors, including the duration of infectivity of affected people, the contagiousness of the microorganism, and the number of susceptible people in the population that the infected people contact.[10]The roots of the basic reproduction concept can be traced through the work of Ronald Ross, Alfred Lotka and others,[11] but its first modern application in epidemiology was by George Macdonald in 1952,[12] who constructed population models of the spread of malaria. In his work he called the quantity basic reproduction rate and denoted it by . Overview of estimation methods[edit]Compartmental models[edit]Compartmental models are a general modeling technique often applied to the mathematical modeling of infectious diseases. In these models, population members are assigned to 'compartments' with labels – for example, S, I, or R, (Susceptible, Infectious, or Recovered). These models can be used to estimate .Epidemic models on networks[edit]Epidemics can be modeled as diseases spreading over networks of contact and disease transmission between people.[13] Nodes in these networks represent individuals and links (edges) between nodes represent the contact or disease transmission between them. If such a network is a locally tree-like network, then the basic reproduction can be written in terms of the average excess degree of the transmission network such that:where is the mean-degree (average degree) of the network and is the second moment of the transmission network degree distribution.Heterogeneous populations[edit]In populations that are not homogeneous, the definition of is more subtle. The definition must account for the fact that a typical infected individual may not be an average individual. As an extreme example, consider a population in which a small portion of the individuals mix fully with one another while the remaining individuals are all isolated. A disease may be able to spread in the fully mixed portion even though a randomly selected individual would lead to fewer than one secondary case. This is because the typical infected individual is in the fully mixed portion and thus is able to successfully cause infections. In general, if the individuals infected early in an epidemic are on average either more likely or less likely to transmit the infection than individuals infected late in the epidemic, then the computation of must account for this difference. An appropriate definition for in this case is "the expected number of secondary cases produced, in a completely susceptible population, produced by a typical infected individual".[14]The basic reproduction number can be computed as a ratio of known rates over time: if a contagious individual contacts other people per unit time, if all of those people are assumed to contract the disease, and if the disease has a mean infectious period of , then the basic reproduction number is just . Some diseases have multiple possible latency periods, in which case the reproduction number for the disease overall is the sum of
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