In
epidemiology
Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and determinants of health and disease conditions in a defined population.
It is a cornerstone of public health, and shapes policy decisions and evide ...
, the basic reproduction number, or basic reproductive number (sometimes called basic reproduction ratio or basic reproductive rate), denoted
(pronounced ''R nought'' or ''R zero''), of an
infection
An infection is the invasion of tissues by pathogens, their multiplication, and the reaction of host tissues to the infectious agent and the toxins they produce. An infectious disease, also known as a transmissible disease or communicable dis ...
is the
expected number
In probability theory, the expected value (also called expectation, expectancy, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a ...
of cases directly generated by one case in a population where all individuals are
susceptible
Susceptibility may refer to:
Physics and engineering
In physics the susceptibility is a quantification for the change of an extensive property under variation of an intensive property. The word may refer to:
* In physics, the susceptibility of ...
to infection.
The definition assumes that no other individuals are infected or
immunized (naturally or through
vaccination
Vaccination is the administration of a vaccine to help the immune system develop immunity from a disease. Vaccines contain a microorganism or virus in a weakened, live or killed state, or proteins or toxins from the organism. In stimulating ...
). Some definitions, such as that of the
Australian Department of Health
The Department of Health and Aged Care (DHAC), formerly the Department of Health, is a department of the Australian Government responsible for health research, funding, promotion and regulation in Australia. Primary health care and aged care ...
, add the absence of "any deliberate intervention in disease transmission".
The basic reproduction number is not necessarily the same as the
effective reproduction number
In epidemiology, the basic reproduction number, or basic reproductive number (sometimes called basic reproduction ratio or basic reproductive rate), denoted R_0 (pronounced ''R nought'' or ''R zero''), of an infection is the expected number of ...
(usually written
't'' for time sometimes
), which is the number of cases generated in the current state of a population, which does not have to be the uninfected state.
is a
dimensionless number
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
(persons infected per person infecting) and not a time rate, which would have units of time
−1, or units of time like
doubling time.
is not a biological constant for a pathogen as it is also affected by other factors such as environmental conditions and the behaviour of the infected population.
values are usually estimated from mathematical models, and the estimated values are dependent on the model used and values of other parameters. Thus values given in the literature only make sense in the given context and it is recommended not to use obsolete values or compare values based on different models.
does not by itself give an estimate of how fast an infection spreads in the population.
The most important uses of
are determining if an emerging
infectious disease
An infection is the invasion of tissues by pathogens, their multiplication, and the reaction of host tissues to the infectious agent and the toxins they produce. An infectious disease, also known as a transmissible disease or communicable di ...
can spread in a population and determining what proportion of the population should be immunized through vaccination to eradicate a disease. In commonly used
infection models, when
the infection will be able to start spreading in a population, but not if
. Generally, the larger the value of
, the harder it is to control the epidemic. For simple models, the proportion of the population that needs to be effectively immunized (meaning not susceptible to infection) to prevent sustained spread of the infection has to be larger than
. This is the so-called ''
Herd immunity
Herd immunity (also called herd effect, community immunity, population immunity, or mass immunity) is a form of indirect protection that applies only to contagious diseases. It occurs when a sufficient percentage of a population has become im ...
'' ''threshold'' or ''herd immunity level''. Here, herd immunity means that the disease cannot spread in the population because each infected person, on average, can only transmit the infection to less than one other contact.
Conversely, the proportion of the population that remains susceptible to infection in the
endemic equilibrium is
. However, this threshold is based on simple models that assume a fully mixed population with no
structured relations between the individuals. For example, if there is some correlation between people's immunization (e.g., vaccination) status, then the formula
may underestimate the herd immunity threshold.
The basic reproduction number is affected by several factors, including the duration of
infectivity
In epidemiology, infectivity is the ability of a pathogen to establish an infection. More specifically, infectivity is a pathogen's capacity for horizontal transmission — that is, how frequently it spreads among hosts that are not in a parent ...
of affected people, the infectiousness of the
microorganism
A microorganism, or microbe,, ''mikros'', "small") and ''organism'' from the el, ὀργανισμός, ''organismós'', "organism"). It is usually written as a single word but is sometimes hyphenated (''micro-organism''), especially in olde ...
, and the number of susceptible people in the population that the infected people contact.
History
The roots of the basic reproduction concept can be traced through the work of
Ronald Ross
Sir Ronald Ross (13 May 1857 – 16 September 1932) was a British medical doctor who received the Nobel Prize for Physiology or Medicine in 1902 for his work on the transmission of malaria, becoming the first British Nobel laureate, and the ...
,
Alfred Lotka and others, but its first modern application in epidemiology was by
George Macdonald
George MacDonald (10 December 1824 – 18 September 1905) was a Scottish author, poet and Christian Congregational church, Congregational Minister (Christianity), minister. He was a pioneering figure in the field of modern fantasy literature a ...
in 1952, who constructed population models of the spread of
malaria
Malaria is a mosquito-borne infectious disease that affects humans and other animals. Malaria causes symptoms that typically include fever, tiredness, vomiting, and headaches. In severe cases, it can cause jaundice, seizures, coma, or death. S ...
. In his work he called the quantity basic reproduction rate and denoted it by
. "Rate" in this context means per person, which makes
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.
Definitions in specific cases
Contact rate and infectious period
![R Naught Ebola and Flu Diagram](https://upload.wikimedia.org/wikipedia/commons/f/f4/R_Naught_Ebola_and_Flu_Diagram.svg)
Suppose that infectious individuals make an average of
infection-producing contacts per unit time, with a mean infectious period of
. Then the basic reproduction number is:
This simple formula suggests different ways of reducing
and ultimately infection propagation. It is possible to decrease the number of infection-producing contacts per unit time
by reducing the number of contacts per unit time (for example staying at home if the infection requires contact with others to propagate) or the proportion of contacts that produces infection (for example wearing some sort of protective equipment). Hence, it can also be written as
[J.H. Jones]
Notes on R0
Stanford University (2007).
:
where
is the rate of contact between susceptible and infected individuals and
is the transmissibility, i.e, the probability of infection given a contact. It is also possible to decrease the infectious period
by finding and then isolating, treating or eliminating (as is often the case with animals) infectious individuals as soon as possible.
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:
In their model, it is assumed that the infected individuals can develop active TB by either direct progression (the disease develops immediately after infection) considered above as FAST tuberculosis or
endogenous reactivation
Endogenous substances and processes are those that originate from within a living system such as an organism, tissue, or cell.
In contrast, exogenous substances and processes are those that originate from outside of an organism.
For example, ...
(the disease develops years after the infection) considered above as SLOW tuberculosis.
Heterogeneous populations
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".
The basic reproduction number can be computed as a ratio of known rates over time: if an infectious 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 the reproduction number for each transition time into the disease.
Epidemic Models on Networks
In reality, diseases spread over
networks
Network, networking and networked may refer to:
Science and technology
* Network theory, the study of graphs as a representation of relations between discrete objects
* Network science, an academic field that studies complex networks
Mathematics
...
of contact between people. Such a network can be represented mathematically with a
graph
Graph may refer to:
Mathematics
*Graph (discrete mathematics), a structure made of vertices and edges
**Graph theory, the study of such graphs and their properties
*Graph (topology), a topological space resembling a graph in the sense of discre ...
and is called the contact network. Every node in a contact network is a representation of an individual and each link (edge) between a pair of nodes represents the contact between them. Links in the contact networks may be used to transmit the disease between the individuals and each disease has its own
dynamics on top of its contact network. For example, individuals in a population can be assigned to
compartments with labels – for example, S, I, or R, (Susceptible, Infectious, or Recovered) and they progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for instance,
SIR
''Sir'' is a formal honorific address in English for men, derived from Sire in the High Middle Ages. Both are derived from the old French "Sieur" (Lord), brought to England by the French-speaking Normans, and which now exist in French only as ...
means each individual is originally susceptible then changes to infectious and finally gets recovered and remained recovered (immune) forever. On the other hand,
public health
Public health is "the science and art of preventing disease, prolonging life and promoting health through the organized efforts and informed choices of society, organizations, public and private, communities and individuals". Analyzing the det ...
may apply some interventions such as vaccination or
contact tracing
In public health, contact tracing is the process of identifying persons who may have been exposed to an infected person ("contacts") and subsequent collection of further data to assess transmission. By tracing the contacts of infected individua ...
to reduce the spread of an
epidemic
An epidemic (from Greek ἐπί ''epi'' "upon or above" and δῆμος ''demos'' "people") is the rapid spread of disease to a large number of patients among a given population within an area in a short period of time.
Epidemics of infectious ...
disease. The combination of disease dynamics under the influence of interventions, if any, on a contact network may be modeled with another network, known as a transmission network. In a transmission network, all the links are responsible for transmitting the disease. If such a network is a locally tree-like network, meaning that any local neighborhood in such a network takes the form of a
tree
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...
, 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
In the study of graphs and networks, the degree of a node in a network is the number of connections it has to other nodes and the degree distribution is the probability distribution of these degrees over the whole network.
Definition
The degre ...
. It is, however, not always straightforward to find the transmission network out of the contact network and the disease dynamics. For example, if a contact network can be approximated with an
Erdős–Rényi graph with a
Poissonian degree distribution,and the disease spreading parameters are as defined in the example above, such that
is the transmission rate per person and the disease has a mean infectious period of
, then the basic reproduction number is
since
for a Poisson distribution.
Compartmental models in epidemiology
Next-generation method
One way to calculate
is to average the expected number of new infections over all possible infected types. The next-generation method is a general method of deriving
when more than one class of infectives is involved. This method, originally introduced by Diekmann ''et al''. (1990), can be used for models with underlying age structure or spatial structure, among other possibilities.
In this picture, the
spectral radius
In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectru ...
of the
next-generation matrix gives the basic reproduction number,
Consider a sexually transmitted disease. In a naive population where almost everyone is susceptible, but the infection seed, if the expected number of gender 1 is
and the expected number of infected gender 2 is
, we can know how many would be infected in the next-generation. Such that the ''next-generation matrix''
can be written as:
where each element
is the expected number of secondary infections of gender
caused by a single infected individual of gender
, assuming that the population of gender
is entirely susceptible. Diagonal elements are zero because people of the same gender cannot transmit the disease to each other but, for example, each
can transmit the disease to
, on average. Meaning that each element
is a reproduction number, but one where who infects whom is accounted for. If generation
is represented with
then the next generation
would be
.
The
spectral radius
In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectru ...
of the next-generation matrix is the basic reproduction number,
, that is here, the
geometric mean of the expected number of each gender in the next-generation. Note that multiplication factors
and
alternate because, the infectious person has to ‘pass through’ a second gender before it can enter a new host of the first gender. In other words, it takes two generations to get back to the same type, and every two generations numbers are multiplied by
×
. The average per generation multiplication factor is therefore
. Note that
is a non-negative matrix so it has single, unique, positive, real eigenvalue which is strictly greater than all the others.
Next-generation matrix for compartmental models
In
mathematical modelling of infectious disease
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including in plants) and help inform public health and plant health interventions. Models use basic assumptions or collected statistics alo ...
, the dynamics of spreading is usually described through a set of non-linear
ordinary differential equation
In mathematics, an ordinary differential equation (ODE) is a differential equation whose unknown(s) consists of one (or more) function(s) of one variable and involves the derivatives of those functions. The term ''ordinary'' is used in contrast ...
s (ODE). So there is always
coupled equations of form
which shows how the number of people in compartment
changes over time. For example, in a SIR model,
,
, and
. Compartmental models have a disease-free equilibrium (DFE) meaning that it is possible to find an equilibrium while setting the number of infected people to zero,
. In other words, as a rule, there is an infection-free
steady state
In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties ''p' ...
. This solution, also usually ensures that the disease-free equilibrium is also an equilibrium of the system. There is another
fixed point known as an Endemic Equilibrium (EE) where the disease is not totally eradicated and remains in the population. Mathematically,
is a threshold for stability of a disease-free equilibrium such that:
:
:
:
To calculate
, the first step is to linearise around the disease-free equilibrium (DFE), but for the infected subsystem of non-linear ODEs which describe the production of new infections and changes in state among infected individuals. Epidemiologically, the linearisation reflects that
characterizes the potential for initial spread of an infectious person in a naive population, assuming the change in the susceptible population is negligible during the initial spread. A linear system of ODEs can always be described by a matrix. So, the next step is to construct a linear positive operator that provides the next generation of infected people when applied to the present generation. Note that this operator (matrix) is responsible for the number of infected people, not all the compartments. Iteration of this operator describes the initial progression of infection within the heterogeneous population. So comparing the
spectral radius
In mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectru ...
of this operator to unity determines whether the generations of infected people grow or not.
can be written as a product of the infection rate near the disease-free equilibrium and average duration of infectiousness. It is used to find the peak and final size of an epidemic.
= The SEIR model with vital dynamics and constant population
=
As described in the example above, so many epidemic processes can be described with a SIR model. However, for many important infections, such as
COVID-19
Coronavirus disease 2019 (COVID-19) is a contagious disease caused by a virus, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The first known case was identified in Wuhan, China, in December 2019. The disease quickly ...
, there is a significant latency period during which individuals have been infected but are not yet infectious themselves. During this period the individual is in compartment ''E'' (for exposed). Here, the formation of the next-generation matrix from the
SEIR model involves determining two compartments, infected and non-infected, since they are the populations that spread the infection. So we only need to model the exposed, ''E'', and infected, ''I'', compartments. Consider a population characterized by a death rate
and birth rate
where a communicable disease is spreading. As in the previous example, we can use the transition rates between the compartments per capita such that
be the infection rate,
be the recovery rate, and
be the rate at which a latent individual becomes infectious. Then, we can define the model dynamics using the following equations:
Here we have 4 compartments and we can define vector
where
denotes the number or proportion of individuals in the ''
''-th compartment. Let
be the rate of appearance of new infections in compartment ''
'' such that it includes only infections that are newly arising, but does not include terms which describe the transfer of infectious individuals from one infected compartment to another. Then if
is the rate of transfer of individuals into compartment ''
'' by all other means and
is the rate of transfer of individuals out of the ''
''-th compartment, then the difference
gives the rate of change of such that
.
We can now make matrices of partial derivatives of ''
'' and ''
'' such that
and
, where
is the disease-free equilibrium.
We now can form the next-generation matrix (operator)
.
Basically,
is a
non-negative matrix which represents the infection rates near the equilibrium, and
is an
M-matrix In mathematics, especially linear algebra, an ''M''-matrix is a ''Z''-matrix with eigenvalues whose real parts are nonnegative. The set of non-singular ''M''-matrices are a subset of the class of ''P''-matrices, and also of the class of inverse-p ...
for linear transition terms making
a matrix which represents the average duration of infectiousness. Therefore,
gives the rate at which infected individuals in ''
'' produce new infections in ''
'', times the average length of time an individual spends in a single visit to compartment ''
''
Finally, for this SEIR process we can have:
and
and so
Estimation methods
The basic reproduction number can be estimated through examining detailed transmission chains or through
genomic sequencing
DNA sequencing is the process of determining the nucleic acid sequence – the order of nucleotides in DNA. It includes any method or technology that is used to determine the order of the four bases: adenine, guanine, cytosine, and thymine. The ...
. However, it is most frequently calculated using epidemiological models. During an epidemic, typically the number of diagnosed infections
over time
is known. In the early stages of an epidemic, growth is exponential, with a logarithmic growth rate
For exponential growth,
can be interpreted as the cumulative number of diagnoses (including individuals who have recovered) or the present number of infection cases; the logarithmic growth rate is the same for either definition. In order to estimate
, assumptions are necessary about the time delay between infection and diagnosis and the time between infection and starting to be infectious.
In exponential growth,
is related to the
doubling time as
Simple model
If an individual, after getting infected, infects exactly
new individuals only after exactly a time
(the serial interval) has passed, then the number of infectious individuals over time grows as
or
The underlying matching differential equation is
or
In this case,
or
.
For example, with
and
, we would find
.
If
is time dependent
showing that it may be important to keep
below 0, time-averaged, to avoid exponential growth.
Latent infectious period, isolation after diagnosis
In this model, an individual infection has the following stages:
# Exposed: an individual is infected, but has no symptoms and does not yet infect others. The average duration of the exposed state is
.
# Latent infectious: an individual is infected, has no symptoms, but does infect others. The average duration of the latent infectious state is
. The individual infects
other individuals during this period.
#
Isolation after diagnosis: measures are taken to prevent further infections, for example by isolating the infected person.
This is a
SEIR
Seir or SEIR may refer to:
*Mount Seir, a mountainous region stretching between the Dead Sea and the Gulf of Aqaba
*Seir the Horite, chief of the Horites, a people mentioned in the Torah
*Sa'ir, also Seir, a Palestinian town in the Hebron Governor ...
model and
may be written in the following form
This estimation method has been applied to
COVID-19
Coronavirus disease 2019 (COVID-19) is a contagious disease caused by a virus, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The first known case was identified in Wuhan, China, in December 2019. The disease quickly ...
and
SARS
Severe acute respiratory syndrome (SARS) is a viral respiratory disease of zoonotic origin caused by the severe acute respiratory syndrome coronavirus (SARS-CoV or SARS-CoV-1), the first identified strain of the SARS coronavirus species, ''seve ...
. It follows from the differential equation for the number of exposed individuals
and the number of latent infectious individuals
,
The largest
eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted ...
of the matrix is the logarithmic growth rate
, which can be solved for
.
In the special case
, this model results in
, which is different from the
simple model above (
). For example, with the same values
and
, we would find
, rather than the true value of
. The difference is due to a subtle difference in the underlying growth model; the matrix equation above assumes that newly infected patients are currently already contributing to infections, while in fact infections only occur due to the number infected at
ago. A more correct treatment would require the use of
delay differential equation
In mathematics, delay differential equations (DDEs) are a type of differential equation in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times.
DDEs are also called tim ...
s.
Effective reproduction number
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
or
is used.
is 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
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
drops below 1 in a basic
SIR simulation, "
herd immunity
Herd immunity (also called herd effect, community immunity, population immunity, or mass immunity) is a form of indirect protection that applies only to contagious diseases. It occurs when a sufficient percentage of a population has become im ...
" has been achieved and the number of cases occurring in the population will gradually decrease to zero.
Limitations of ''R''0
Use of
in the popular press has led to misunderstandings and distortions of its meaning.
can be calculated from many different
mathematical models
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...
. Each of these can give a different estimate of
, which needs to be interpreted in the context of that model. Therefore, the contagiousness of different infectious agents cannot be compared without recalculating
with invariant assumptions.
values for past outbreaks might not be valid for current outbreaks of the same disease. Generally speaking,
can be used as a threshold, even if calculated with different methods: if
, the outbreak will die out, and if
, the outbreak will expand. In some cases, for some models, values of
can still lead to self-perpetuating outbreaks. This is particularly problematic if there are intermediate vectors between hosts, such as
malaria
Malaria is a mosquito-borne infectious disease that affects humans and other animals. Malaria causes symptoms that typically include fever, tiredness, vomiting, and headaches. In severe cases, it can cause jaundice, seizures, coma, or death. S ...
.
Therefore, comparisons between values from the "Values of
of well-known infectious diseases" table should be conducted with caution.
Although
cannot be modified through vaccination or other changes in population susceptibility, it can vary based on a number of biological, sociobehavioral, and environmental factors.
It can also be modified by physical distancing and other public policy or social interventions,
although some historical definitions exclude any deliberate intervention in reducing disease transmission, including nonpharmacological interventions.
And indeed, whether nonpharmacological interventions are included in
often depends on the paper, disease, and what if any intervention is being studied.
This creates some confusion, because
is not a constant; whereas most mathematical parameters with "nought" subscripts are constants.
depends on many factors, many of which need to be estimated. Each of these factors adds to uncertainty in estimates of
. Many of these factors are not important for informing public policy. Therefore, public policy may be better served by metrics similar to
, but which are more straightforward to estimate, such as
doubling time or
half-life
Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable at ...
(
).
Methods used to calculate
include the
survival function
The survival function is a function that gives the probability that a patient, device, or other object of interest will survive past a certain time.
The survival function is also known as the survivor function
or reliability function.
The te ...
, rearranging the largest
eigenvalue
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted ...
of the
Jacobian matrix, the
next-generation method, calculations from the intrinsic growth rate, existence of the endemic equilibrium, the number of susceptibles at the endemic equilibrium, the average age of infection and the final size equation. Few of these methods agree with one another, even when starting with the same system of
differential equations.
Even fewer actually calculate the average number of secondary infections. Since
is rarely observed in the field and is usually calculated via a mathematical model, this severely limits its usefulness.
Sample values for various infectious diseases
Despite the difficulties in estimating
mentioned in the previous section, estimates have been made for a number of
genera, and are shown in this table. Each genus may be composed of many
species
In biology, a species is the basic unit of classification and a taxonomic rank of an organism, as well as a unit of biodiversity. A species is often defined as the largest group of organisms in which any two individuals of the appropriate s ...
,
strains, or
variants
Variant may refer to:
In arts and entertainment
* ''Variant'' (magazine), a former British cultural magazine
* Variant cover, an issue of comic books with varying cover art
* ''Variant'' (novel), a novel by Robison Wells
* "The Variant", 2021 e ...
. Estimations of
for species, strains, and variants are typically less accurate than for genera, and so are provided in separate tables below for diseases of particular interest (
influenza and
COVID-19
Coronavirus disease 2019 (COVID-19) is a contagious disease caused by a virus, the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). The first known case was identified in Wuhan, China, in December 2019. The disease quickly ...
).
Estimates for strains of
influenza.
Estimates for variants of
SARS-CoV-2
Severe acute respiratory syndrome coronavirus 2 (SARS‑CoV‑2) is a strain of coronavirus that causes COVID-19 (coronavirus disease 2019), the respiratory illness responsible for the ongoing COVID-19 pandemic. The virus previously had a ...
.
In popular culture
In the 2011 film ''
Contagion'', a fictional medical disaster thriller, a blogger's calculations for
are presented to reflect the progression of a fatal viral infection from case studies to a pandemic.
See also
*
Compartmental models in epidemiology
Compartmental models are a very general modelling technique. They are often applied to the mathematical modelling of infectious diseases. The population is assigned to compartments with labels – for example, S, I, or R, (Susceptible, Infectious ...
*
E-epidemiology
*
Epi Info
Epi Info is statistical software for epidemiology developed by Centers for Disease Control and Prevention (CDC) in Atlanta, Georgia (US).
Epi Info has been in existence for over 20 years and is currently available for Microsoft Windows, Androi ...
software program
*
Epidemiological method
*
Epidemiological transition
Notes
*
Compartmental models in epidemiology
Compartmental models are a very general modelling technique. They are often applied to the mathematical modelling of infectious diseases. The population is assigned to compartments with labels – for example, S, I, or R, (Susceptible, Infectious ...
describe disease dynamics over time in a population of susceptible (S), infectious (I), and recovered (R) people using the SIR model. Note that in the SIR model,
and
are different quantities – the former describes the number of recovered at ''t'' = 0 whereas the latter describes the ratio between the frequency of contacts to the frequency of recovery.
* According to Guangdong Provincial Center for Disease Control and Prevention, "The effective reproductive number (R or R is more commonly used to describe transmissibility, which is defined as the average number of secondary cases generated by per
'sic''infectious case." For example, by one preliminary estimate during the ongoing pandemic, the effective reproductive number for
SARS-CoV-2
Severe acute respiratory syndrome coronavirus 2 (SARS‑CoV‑2) is a strain of coronavirus that causes COVID-19 (coronavirus disease 2019), the respiratory illness responsible for the ongoing COVID-19 pandemic. The virus previously had a ...
was found to be 2.9, whereas for SARS it was 1.77.
References
Further reading
*
*
*
*
{{DEFAULTSORT:Basic Reproduction Number
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