Basic reproduction number
From Wikipedia, the free encyclopedia
| Disease | Transmission | R0 |
|---|---|---|
| Measles | Airborne | 12–18 |
| Pertussis | Airborne droplet | 12–17 |
| Diphtheria | Saliva | 6–7 |
| Smallpox | Airborne droplet | 5–7 |
| Polio | Fecal-oral route | 5–7 |
| Rubella | Airborne droplet | 5–7 |
| Mumps | Airborne droplet | 4–7 |
| HIV/AIDS | Sexual contact | 2–5 |
| SARS | Airborne droplet | 2–5[2] |
| Influenza (1918 pandemic strain) |
Airborne droplet | 2–3[3] |
| Ebola | Bodily fluids | 1–4 |
This metric is useful because it helps determine whether or not an infectious disease can spread through a population. The roots of the basic reproduction concept can be traced through the work of Alfred Lotka, Ronald Ross, and others, but its first modern application in epidemiology was by George MacDonald in 1952, who constructed population models of the spread of malaria.
When
- R0 < 1
- R0 > 1
Generally, the larger the value of R0, the harder it is to control the epidemic. For simple models, the proportion of the population that needs to be vaccinated to prevent sustained spread of the infection is given by 1 − 1/R0. The basic reproductive rate is affected by several factors including the duration of infectivity of affected patients, the infectiousness of the organism, and the number of susceptible people in the population that the affected patients are in contact with.
In populations that are not homogeneous, the definition of R0 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 who become infected early in an epidemic may be more (or less) likely to transmit than a randomly chosen individual early in the epidemic, then our computation of R0 must account for this tendency. An appropriate definition for R0 in this case is "the expected number of secondary cases produced by a typical infected individual early in an epidemic".[5]
Contents
Other uses
R0 is also used as a measure of individual reproductive success in population ecology,[6] evolutionary invasion analysis and life history theory. It represents the average number of offspring produced over the lifetime of an individual (under ideal conditions).For simple population models, R0 can be calculated, provided an explicit decay rate (or "death rate") is given. In this case, the reciprocal of the decay rate (usually 1/d) gives the average lifetime of an individual. When multiplied by the average number of offspring per individual per timestep (the "birth rate" b), this gives R0 = b / d. For more complicated models that have variable growth rates (e.g. because of self-limitation or dependence on food densities), the maximum growth rate should be used.
Limitations of R0
When calculated from mathematical models, particularly ordinary differential equations, what is often claimed to be R0 is, in fact, simply a threshold, not the average number of secondary infections. There are many methods used to derive such a threshold from a mathematical model, but few of them always give the true value of R0. This is particularly problematic if there are intermediate vectors between hosts, such as malaria.What these thresholds will do is determine whether a disease will die out (if R0 < 1) or whether it may become epidemic (if R0 > 1), but they generally can not compare different diseases. Therefore, the values from the table above should be used with caution, especially if the values were calculated from mathematical models.
Methods include the survival function, rearranging the largest eigenvalue of the Jacobian matrix, the next-generation method,[7] calculations from the intrinsic growth rate,[8] existence of the endemic equilibrium, the number of susceptibles at the endemic equilibrium, the average age of infection [9] 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 R0 is rarely observed in the field and is usually calculated via a mathematical model, this severely limits its usefulness.[10]
In popular culture
In the 2011 film Contagion, a fictional medical disaster thriller, R0 calculations are presented to reflect the progression of a fatal viral infection from case studies to a pandemic.Further reading
- Jones, James Holland. "Notes on R0". Retrieved 15 September 2014.
See also
- E-epidemiology
- Epi Info software program
- Epidemic model
- Epidemiological methods
- Epidemiological Transition
References
- Unless noted R0 values are from: History and Epidemiology of Global Smallpox Eradication From the training course titled "Smallpox: Disease, Prevention, and Intervention". The CDC and the World Health Organization. Slide 16-17.
- Wallinga J, Teunis P (2004). "Different epidemic curves for severe acute respiratory syndrome reveal similar impacts of control measures". Am. J. Epidemiol. 160 (6): 509–16. doi:10.1093/aje/kwh255. PMID 15353409.
- Mills CE, Robins JM, Lipsitch M (2004). "Transmissibility of 1918 pandemic influenza". Nature 432 (7019): 904–6. doi:10.1038/nature03063. PMID 15602562.
- Christophe Fraser; Christl A. Donnelly, Simon Cauchemez et al. (19 June 2009). "Pandemic Potential of a Strain of Influenza A (H1N1): Early Findings". Science 324 (5934): 1557–1561. doi:10.1126/science.1176062. PMC 3735127. PMID 19433588. Free text
- O Diekmann; J.A.P. Heesterbeek and J.A.J. Metz (1990). "On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations". Journal of Mathematical Biology 28: 356–382. doi:10.1007/BF00178324.
- de Boer, Rob J. Theoretical Biology. Retrieved 2007-11-13.
- Diekmann O and Heesterbeek JAP (2000). Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. New York: Wiley.
- Chowell G, Hengartnerb NW, Castillo-Chaveza C, Fenimorea PW and Hyman JM (2004). "The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda". Journal of Theoretical Biology 229 (1): 119–126. doi:10.1016/j.jtbi.2004.03.006. PMID 15178190.
- Ajelli M, Iannelli M, Manfredi P and Ciofi degli Atti, ML (2008). "Basic mathematical models for the temporal dynamics of HAV in medium-endemicity Italian areas". Vaccine 26 (13): 1697–1707. doi:10.1016/j.vaccine.2007.12.058. PMID 18314231.
- Heffernan JM, Smith RJ, Wahl LM (2005). "Perspectives on the Basic Reproductive Ratio". Journal of the Royal Society Interface 2 (4): 281–93. doi:10.1098/rsif.2005.0042. PMC 1578275. PMID 16849186.
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end quote from:
A virus's basic reproduction number
In August research by WHO (World Health Organization) through the United Nations said that Ebola presently has an RO of 1.4 to 1.7. Since less than 1 means a virus is dying out, 1.4 to 1.7 means that every single case of Ebola has an average of 1.4 to 1.7 new cases from it in August. If you do the math this is why for example if you take the present 5000 approximate cases you would see that if you multiply these cases by 1.4 or 1.7, this is likely how many new cases added on top of the 5000 presently diagnosed ones that there will be. Then you would have to keep multiplying the new group(s) which would be 5000 plus 7000(5000 thousand times 1.4) equals 12,000. by this number until the RO became lower then 1. Once the RO becomes lower than one it means the virus is on the wane.
LIkewise if you multiply 5000 by 1.7 this is:8500. then if you add 5000 to 8500 you get 13,500 cases. Then a useful way to figure out how many might die of this group would be to multiply by .77 since a useful model has shown 77% of those who contract Ebola presently are dying. This is why countries like Liberia are panicking and the infrastructure is collapsing from people just laying down and dying in the streets. Then soldiers or policemen have to guard these bodies from people touching them and becoming infected too. Touching is a big part of friends and relatives in these west African cultures so not touching is extremely difficult for them culturally.
Another problem is touching the dead Ebola infected bodies at funerals which is presently where most new cases are coming from. So, most of these people are not medically educated or disciplined in regard to Western Medicine. This is a big problem for the whole world.
In August research by WHO (World Health Organization) through the United Nations said that Ebola presently has an RO of 1.4 to 1.7. Since less than 1 means a virus is dying out, 1.4 to 1.7 means that every single case of Ebola has an average of 1.4 to 1.7 new cases from it in August. If you do the math this is why for example if you take the present 5000 approximate cases you would see that if you multiply these cases by 1.4 or 1.7, this is likely how many new cases added on top of the 5000 presently diagnosed ones that there will be. Then you would have to keep multiplying the new group(s) which would be 5000 plus 7000(5000 thousand times 1.4) equals 12,000. by this number until the RO became lower then 1. Once the RO becomes lower than one it means the virus is on the wane.
LIkewise if you multiply 5000 by 1.7 this is:8500. then if you add 5000 to 8500 you get 13,500 cases. Then a useful way to figure out how many might die of this group would be to multiply by .77 since a useful model has shown 77% of those who contract Ebola presently are dying. This is why countries like Liberia are panicking and the infrastructure is collapsing from people just laying down and dying in the streets. Then soldiers or policemen have to guard these bodies from people touching them and becoming infected too. Touching is a big part of friends and relatives in these west African cultures so not touching is extremely difficult for them culturally.
Another problem is touching the dead Ebola infected bodies at funerals which is presently where most new cases are coming from. So, most of these people are not medically educated or disciplined in regard to Western Medicine. This is a big problem for the whole world.
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