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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 evi ...
, 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 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 ...
is the expected number of cases directly generated by one case in a population where all individuals are susceptible 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 stimulat ...
). Some definitions, such as that of the Australian Department of Health, add the absence of "any deliberate intervention in disease transmission". The basic reproduction number is not necessarily the same as the effective reproduction number R (usually written R_t 't'' for time sometimes R_e), which is the number of cases generated in the current state of a population, which does not have to be the uninfected state. R_0 is a dimensionless number (persons infected per person infecting) and not a time rate, which would have units of time−1, or units of time like
doubling time The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things ...
. R_0 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. R_0 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. R_0 does not by itself give an estimate of how fast an infection spreads in the population. The most important uses of R_0 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 R_0 > 1 the infection will be able to start spreading in a population, but not if R_0 < 1. Generally, the larger the value of R_0, 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 1 - 1 / R_0. 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 1 / R_0. 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 1 - 1 / R_0 may underestimate the herd immunity threshold. The basic reproduction number is affected by several factors, including the duration of infectivity 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 old ...
, 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,
Alfred Lotka Alfred James Lotka (March 2, 1880 – December 5, 1949) was a US mathematician, physical chemist, and statistician, famous for his work in population dynamics and energetics. An American biophysicist, Lotka is best known for his proposa ...
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 minister. He was a pioneering figure in the field of modern fantasy literature and the mentor of fellow writer Lewis Carroll ...
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. ...
. In his work he called the quantity basic reproduction rate and denoted it by Z_0. "Rate" in this context means per person, which makes 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.


Definitions in specific cases


Contact rate and infectious period

Suppose that infectious individuals make an average of \beta infection-producing contacts per unit time, with a mean infectious period of \tau. Then the basic reproduction number is:R_0 = \beta\,\tauThis simple formula suggests different ways of reducing R_0 and ultimately infection propagation. It is possible to decrease the number of infection-producing contacts per unit time \beta 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 asJ.H. Jones
Notes on R0
Stanford University (2007).
:R_0 = \overline\, T\, \tau, where \overline is the rate of contact between susceptible and infected individuals and T is the transmissibility, i.e, the probability of infection given a contact. It is also possible to decrease the infectious period \tau 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:R_0 = R_0^ + R_0^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 (the disease develops years after the infection) considered above as SLOW tuberculosis.


Heterogeneous populations

In populations that are not homogeneous, the definition of 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 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 R_0 must account for this difference. An appropriate definition for R_0 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 \beta 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 \dfrac, then the basic reproduction number is just R_0 = \dfrac. 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 of contact between people. Such a network can be represented mathematically with a graph 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 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 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: R_0 = \frac - 1, where is the mean-degree (average degree) of the network and is the second
moment Moment or Moments may refer to: * Present time Music * The Moments, American R&B vocal group Albums * ''Moment'' (Dark Tranquillity album), 2020 * ''Moment'' (Speed album), 1998 * ''Moments'' (Darude album) * ''Moments'' (Christine Guldbrand ...
of the transmission network degree distribution. 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 \beta is the transmission rate per person and the disease has a mean infectious period of \dfrac, then the basic reproduction number is R_0 = \dfrac since -^2 = for a Poisson distribution.


Compartmental models in epidemiology


Next-generation method

One way to calculate R_0 is to average the expected number of new infections over all possible infected types. The next-generation method is a general method of deriving R_0 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 of the next-generation matrix G gives the basic reproduction number, R_0 = \rho(G). 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 f and the expected number of infected gender 2 is m , we can know how many would be infected in the next-generation. Such that the ''next-generation matrix'' G can be written as:G = \begin 0 & f \\ m & 0 \end, where each element g_ is the expected number of secondary infections of gender i caused by a single infected individual of gender j , assuming that the population of gender i is entirely susceptible. Diagonal elements are zero because people of the same gender cannot transmit the disease to each other but, for example, each f can transmit the disease to m , on average. Meaning that each element g_ is a reproduction number, but one where who infects whom is accounted for. If generation a is represented with \phi_a then the next generation \phi_ would be G\phi_a . The spectral radius of the next-generation matrix is the basic reproduction number, R_0 = \rho(G) = \sqrt, that is here, the
geometric mean In mathematics, the geometric mean is a mean or average which indicates a central tendency of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the ...
of the expected number of each gender in the next-generation. Note that multiplication factors f and m 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 m ×f . The average per generation multiplication factor is therefore \sqrt . Note that G 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, 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 n coupled equations of form \dot= = f(C_1, C_2, ..., C_n) which shows how the number of people in compartment C_i changes over time. For example, in a SIR model, C_1 = S, C_2 = I , and C_3 = R . 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, I=0 . In other words, as a rule, there is an infection-free steady state. 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, R_0 is a threshold for stability of a disease-free equilibrium such that: : R_0 \le 1 \Rightarrow \lim_ (C_1(t),C_2(t),\cdots, C_n(t)) = \textrm : R_0 > 1 , I(0)> 0 \Rightarrow \lim_ (C_1(t),C_2(t),\cdots, C_n(t)) = \textrm. : To calculate R_0 , 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 R_0 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 of this operator to unity determines whether the generations of infected people grow or not. R_0 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 quick ...
, 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 \mu and birth rate \lambda where a communicable disease is spreading. As in the previous example, we can use the transition rates between the compartments per capita such that \beta be the infection rate, \gamma be the recovery rate, and \kappa be the rate at which a latent individual becomes infectious. Then, we can define the model dynamics using the following equations: \begin \dot = \lambda - \mu S - \beta SI, \\\\ \dot = \beta SI - (\mu+\kappa)E, \\\\ \dot = \kappa E - (\mu+\gamma)I, \\\\ \dot = \gamma I - \mu R. \end Here we have 4 compartments and we can define vector \mathrm = (S, E, I, R) where \mathrm_i denotes the number or proportion of individuals in the ''i ''-th compartment. Let F_i(\mathrm) be the rate of appearance of new infections in compartment ''i '' 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 V_i^+ is the rate of transfer of individuals into compartment ''i '' by all other means and V_i^- is the rate of transfer of individuals out of the ''i ''-th compartment, then the difference F_i(\mathrm) - V_i(\mathrm) gives the rate of change of such that V_i(\mathrm) = V_i^-(\mathrm) - V_i^+ (\mathrm) . We can now make matrices of partial derivatives of ''F '' and ''V '' such that F_ = and V_ = , where \mathrm^* = (S^*, E^*, I^*, R^*) = (\lambda/\mu, 0, 0, 0) is the disease-free equilibrium. We now can form the next-generation matrix (operator) G = FV^ . Basically, F is a non-negative matrix which represents the infection rates near the equilibrium, and V is an M-matrix for linear transition terms making V^ a matrix which represents the average duration of infectiousness. Therefore, G_ gives the rate at which infected individuals in ''\mathrm_j '' produce new infections in ''\mathrm_i '', times the average length of time an individual spends in a single visit to compartment ''j. '' Finally, for this SEIR process we can have: F = \begin 0 & \beta S^* \\ 0 & 0 \end and V = \begin \mu + \kappa & 0 \\ -\kappa & \gamma + \mu \end and so R_0 = \rho( FV^) = \frac.


Estimation methods

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) over time t is known. In the early stages of an epidemic, growth is exponential, with a logarithmic growth rateK := \frac.For exponential growth, N 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 R_0, assumptions are necessary about the time delay between infection and diagnosis and the time between infection and starting to be infectious. In exponential growth, K is related to the
doubling time The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things ...
T_d asK=\frac.


Simple model

If an individual, after getting infected, infects exactly R_0 new individuals only after exactly a time \tau (the serial interval) has passed, then the number of infectious individuals over time grows asn_E(t) = n_E(0)\, R_0^ = n_E(0)\,e^or\ln(n_E(t)) = \ln(n_E(0))+\ln(R_0)t/\tau.The underlying matching differential equation is\frac =n_E(t)\frac .or\frac =\frac .In this case, R_0 = e^ or K = \frac. For example, with \tau=5~\mathrm and K=0.183~\mathrm^, we would find R_0=2.5. If R_0 is time dependent\ln(n_E(t)) = \ln(n_E(0))+\frac\int\limits_^\ln(R_0(t))dtshowing that it may be important to keep \ln(R_0) 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 \tau_E. # Latent infectious: an individual is infected, has no symptoms, but does infect others. The average duration of the latent infectious state is \tau_I. The individual infects R_0 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 model and R_0 may be written in the following formR_0 = 1 + K(\tau_E+\tau_I) + K^2\tau_E\tau_I.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 quick ...
and SARS. It follows from the differential equation for the number of exposed individuals n_E and the number of latent infectious individuals n_I,\frac \begin n_E \\ n_I \end = \begin -1/\tau_E & R_0/\tau_I \\ 1/\tau_E & -1/\tau_I \end \begin n_E \\ n_I \end.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 denote ...
of the matrix is the logarithmic growth rate K, which can be solved for R_0. In the special case \tau_I = 0, this model results in R_0=1+K\tau_E, which is different from the simple model above (R_0=\exp(K\tau_E)). For example, with the same values \tau=5~\mathrm and K=0.183~\mathrm^, we would find R_0=1.9, rather than the true value of 2.5. 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 \tau_E 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 time ...
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 R_e or R is used. R_t 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 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 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 R_0 in the popular press has led to misunderstandings and distortions of its meaning. R_0 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 physi ...
. Each of these can give a different estimate of 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 with invariant assumptions. R_0 values for past outbreaks might not be valid for current outbreaks of the same disease. Generally speaking, R_0 can be used as a threshold, even if calculated with different methods: if R_0 < 1, the outbreak will die out, and if R_0 > 1, the outbreak will expand. In some cases, for some models, values of R_0 < 1 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. ...
. Therefore, comparisons between values from the "Values of R_0 of well-known infectious diseases" table should be conducted with caution. Although R_0 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 R_0 often depends on the paper, disease, and what if any intervention is being studied. This creates some confusion, because R_0 is not a constant; whereas most mathematical parameters with "nought" subscripts are constants. R depends on many factors, many of which need to be estimated. Each of these factors adds to uncertainty in estimates of R. Many of these factors are not important for informing public policy. Therefore, public policy may be better served by metrics similar to R, but which are more straightforward to estimate, such as
doubling time The doubling time is the time it takes for a population to double in size/value. It is applied to population growth, inflation, resource extraction, consumption of goods, compound interest, the volume of malignant tumours, and many other things ...
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 ...
(t_). Methods used to calculate R_0 include the survival function, 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 denote ...
of the
Jacobian matrix In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. When this matrix is square, that is, when the function takes the same number of variable ...
, 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 In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
. Even fewer actually calculate the average number of secondary infections. Since R_0 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 R_0mentioned in the previous section, estimates have been made for a number of
genera Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial nomenclat ...
, 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 appropriat ...
, strains, or variants. Estimations of R_0 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 Influenza, commonly known as "the flu", is an infectious disease caused by influenza viruses. Symptoms range from mild to severe and often include fever, runny nose, sore throat, muscle pain, headache, coughing, and fatigue. These symptom ...
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 quick ...
).
Estimates for strains of
influenza Influenza, commonly known as "the flu", is an infectious disease caused by influenza viruses. Symptoms range from mild to severe and often include fever, runny nose, sore throat, muscle pain, headache, coughing, and fatigue. These symptom ...
.
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 R_0 are presented to reflect the progression of a fatal viral infection from case studies to a pandemic.


See also

* Compartmental models in epidemiology *
E-epidemiology E-epidemiology (also known as Digital Epidemiology) is the science underlying the acquisition, maintenance and application of epidemiological knowledge and information using digital media such as the internet, mobile phones, digital paper, digita ...
*
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 The science of epidemiology has matured significantly from the times of Hippocrates, Semmelweis and John Snow. The techniques for gathering and analyzing epidemiological data vary depending on the type of disease being monitored but each study wil ...
*
Epidemiological transition In demography and medical geography, epidemiological transition is a theory which "describes changing population patterns in terms of fertility, life expectancy, mortality, and leading causes of death." For example, a phase of development marke ...


Notes

* Compartmental models in epidemiology 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, R(0) and R_0 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 Articles containing video clips Epidemiology Epidemics Pandemics Disease ecology