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The COVID-19 pandemic in Taiwan is part of the worldwide pandemic of coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2).As of 16 January 2022, 9,774,453 tests had been conducted in Taiwan, ...

- 848 (28 November 2021)
- Taiwan

COVID-19 is mainly transmitted when people breathe in air contaminated by droplets and small airborne particles containing the virus. Infected people exhale those particles as they breathe, talk, cough, sneeze, or sing. Transmission is more ...

- 5,192,695
- Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)

- 2–14 days (typically 5) from infection
- Symptomatic and supportive

- History
- Definitions in Specific Cases
- Estimation Methods
- Effective Reproduction Number
- Limitations of R0
- in Popular Culture

The roots of the basic

**reproduction**concept can be traced through the work of Ronald Ross, Alfred Lotka and others, but its first modern application in epidemiology was by George Macdonald in 1952, who constructed population models of the spread of malaria. In his work he called the quantity basic reproduction rate and denoted it by Z 0 {\\displaystyle Z_{0}} . "Rate" in this context means per person, which makes Z 0 {\\displaystyle Z_{0}} dimensionless as required. Because this can be misleading to anyone who understands "rate" only in the sense per unit of time, "number" or "ratio" is now preferred.[citation needed]Contact rate and infectious period

Suppose that infectious individuals make an average of β {\\displaystyle \\beta } infection-producing contacts per unit time, with a mean infectious period of τ {\\displaystyle \\tau } . Then the basic reproduction number is: 1. R 0 = c ¯ T τ , {\\displaystyle R_{0}={\\overline {c}}\\,T\\,\\tau ,} where c ¯ {\\displaystyle {\\overline {c}}} is the rate of contact between susceptible and infected individuals and T {\\displaystyle T} is the transmissibility, i.e, the probability of infection given a contac...

With varying latent periods

Latent period is the transition time between contagion event and disease manifestation. In cases of diseases with varying latent periods, the basic reproduction number can be calculated as the sum of the reproduction numbers for each transition time into the disease. An example of this is tuberculosis (TB). Blower and coauthors calculated from a simple model of TB the following reproduction number:

Heterogeneous populations

In populations that are not homogeneous, the definition of R 0 {\\displaystyle R_{0}} 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 fewe...

The basic reproduction number can be estimated through examining detailed transmission chains or through genomic sequencing. However, it is most frequently calculated using epidemiological models. During an epidemic, typically the number of diagnosed infections N ( t ) {\\displaystyle N(t)} over time t {\\displaystyle t} is known. In the early stages of an epidemic, growth is exponential, with a logarithmic growth rate In exponential growth, K {\\displaystyle K} is related to the doubling time T d {\\displaystyle T_{d}} as

In reality, varying proportions of the population are immune to any given disease at any given time. To account for this, the effective reproduction number R e {\\displaystyle R_{e}} is used, usually written as R t {\\displaystyle R_{t}} , or the average number of new infections caused by a single infected individual at time t in the partially susceptible population. It can be found by multiplying R 0 {\\displaystyle R_{0}} by the fraction S of the population that is susceptible. When the fraction of the population that is immune increases (i. e. the susceptible population S decreases) so much that R e {\\displaystyle R_{e}} drops below 1, "herd immunity" has been achieved and the number of cases occurring in the population will gradually decrease to zero.

Use of R 0 {\\displaystyle R_{0}} in the popular press has led to misunderstandings and distortions of its meaning. R 0 {\\displaystyle R_{0}} can be calculated from many different mathematical models. Each of these can give a different estimate of R 0 {\\displaystyle R_{0}} , which needs to be interpreted in the context of that model. Therefore, the contagiousness of different infectious agents cannot be compared without recalculating R 0 {\\displaystyle R_{0}} with invariant assumptions. R 0 {\\displaystyle R_{0}} values for past outbreaks might not be valid for current outbreaks of the same disease. Generally speaking, R 0 {\\displaystyle R_{0}} can be used as a threshold, even if calculated with different methods: if R 0 < 1 {\\displaystyle R_{0}<1} , the outbreak will die out, and if R 0 > 1 {\\displaystyle R_{0}>1} , the outbreak will expand. In some cases, for some models, values of R 0 < 1 {\\displaystyle R_{0}<1} can still lead to self-perpetuating outbreaks. This is particularly pr...

In the 2011 film Contagion, a fictional medical disaster thriller, a blogger's calculations for R 0 {\\displaystyle R_{0}} are presented to reflect the progression of a fatal viral infection from case studies to a pandemic. The methods depicted were faulty.