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Kermack–McKendrick Theory
Kermack–McKendrick theory is a hypothesis that predicts the number and distribution of cases of an immunizing infectious disease over time as it is transmitted through a population based on characteristics of infectivity and recovery, under a strong-mixing assumption. Building on the research of Ronald Ross and Hilda Hudson, A. G. McKendrick and W. O. Kermack published their theory in a set of three articles from 1927, 1932, and 1933. Kermack–McKendrick theory is one of the sources of the SIR model and other related compartmental models. This theory was the first to explicitly account for the dependence of infection characteristics and transmissibility on the age of infection. Because of their seminal importance to the field of theoretical epidemiology, these articles were republished in the '' Bulletin of Mathematical Biology'' in 1991. Epidemic model (1927) In its initial form, Kermack–McKendrick theory is a partial differential-equation model that structures the i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypothesis
A hypothesis (: hypotheses) is a proposed explanation for a phenomenon. A scientific hypothesis must be based on observations and make a testable and reproducible prediction about reality, in a process beginning with an educated guess or thought. If a hypothesis is repeatedly independently demonstrated by experiment to be true, it becomes a scientific theory. In colloquial usage, the words "hypothesis" and "theory" are often used interchangeably, but this is incorrect in the context of science. A working hypothesis is a provisionally-accepted hypothesis used for the purpose of pursuing further progress in research. Working hypotheses are frequently discarded, and often proposed with knowledge (and warning) that they are incomplete and thus false, with the intent of moving research in at least somewhat the right direction, especially when scientists are stuck on an issue and brainstorming ideas. A different meaning of the term ''hypothesis'' is used in formal l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 first born outside Europe. His History of malaria, discovery of the malarial parasite in the digestion, gastrointestinal tract of a mosquito in 1897 proved that malaria was transmitted by mosquitoes, and laid the foundation for the method of vector control, combating the disease. Ross was a polymath, writing a number of poems, publishing several novels, and composing songs. He was also an amateur artist and mathematician. He worked in the Indian Medical Service for 25 years. It was during his service that he made the groundbreaking medical discovery. After resigning from his service in India, he joined the faculty of Liverpool School of Tropical Medicine, and continued as Professor and Chairman of Tropical Medicine of the institute for 10 y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilda Phoebe Hudson
Hilda Phoebe Hudson (11 June 1881 Cambridge – 26 November 1965 London) was an English mathematician who worked on algebraic geometry, in particular on Cremona transformations. Hudson was interested in the link between mathematics and her religious beliefs. Life and work In 1900 Hudson gained a scholarship and entered Newnham College at the University of Cambridge, graduating in 1903, coming 7th equal among the First Class students. After a year of further study at the University of Berlin, she returned to Newnham in 1905, first as lecturer in mathematics and later as Associate Research Fellow. Trinity College Dublin awarded her an ad eundam MA, and later a DSc, in 1906 and 1913, respectively. She was an Invited Speaker of the International Congress of Mathematicians (ICM) in 1912 at Cambridge UK. Although Laura Pisati had been invited to the 1908 ICM, she died just before the start of the conference, so Hudson became the first female invited speaker at an ICM. She spent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anderson Gray McKendrick
Anderson Gray McKendrick DSc FRSE (8 September 1876 – 30 May 1943) was a Scottish military physician and epidemiologist who pioneered the use of mathematical methods in epidemiology. Irwin (see below) commented on the quality of his work, "Although an amateur, he was a brilliant mathematician, with a far greater insight than many professionals." Biography McKendrick was born at on 8 September 1876, in Edinburgh, the fifth and last child of John Gray McKendrick FRS, a distinguished physiologist, and his wife, Mary Souttar. His older brother was John Souttar McKendrick FRSE (1874–1946). He was educated at Kelvinside Academy then trained as a doctor at the University of Glasgow qualifying MB ChB in 1900. He then was commissioned in the British Army and joined the Indian Medical Service. At the rank of Lt Colonel he led an expedition into Somaliland in 1903/4 as part of what was then known as the Dervish Wars. He later worked with Ronald Ross and eventually would continue ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Ogilvy Kermack
William Ogilvy Kermack FRS FRSE FRIC (26 April 1898 – 20 July 1970) was a Scottish biochemist. He made mathematical studies of epidemic spread and established links between environmental factors and specified diseases. He is noteworthy for being blind for the majority of his academic career. Together with Anderson Gray McKendrick he created the Kermack-McKendrick theory of infectious diseases. Early life and education He was born on 26 April 1898 at 36 South Street in Kirriemuir, the son of William Kermack, a postman, and his wife, Helen Eassie Ogilvy. His mother was placed in an asylum soon after his birth and died when he was six and he was raised by his father's sister Margaret Osler Kermack, wife of David Marnie, a blacksmith. He was raised with their four children - his cousins. William was educated at Webster's Seminary in Kirriemuir under headmaster Thomas Pullar. He won a bursary and began studying Mathematics and Natural Philosophy at the University of Aberdeen in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epidemic Model
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 along with mathematics to find parameters for various infectious diseases and use those parameters to calculate the effects of different interventions, like mass vaccination programs. The modelling can help decide which intervention(s) to avoid and which to trial, or can predict future growth patterns, etc. History The modelling of infectious diseases is a tool that has been used to study the mechanisms by which diseases spread, to predict the future course of an outbreak and to evaluate strategies to control an epidemic. The first scientist who systematically tried to quantify causes of death was John Graunt in his book ''Natural and Political Observations made upon the Bills of Mortality'', in 1662. The bills he studied were listings of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bulletin Of Mathematical Biology
The Society for Mathematical Biology (SMB) is an international association co-founded in 1972 in the United States by George Karreman, Herbert Daniel Landahl and (initially chaired) by Anthony Bartholomay for the furtherance of joint scientific activities between Mathematics and Biology research communities. The society publishes the ''Bulletin of Mathematical Biology'', as well as the quarterly SMB newsletter.http://www.smb.org/publications/index.shtml SMB Publications History The Society for Mathematical Biology emerged and grew from the earlier school of mathematical biology, mathematical biophysics, initiated and supported by the Founder of Mathematical biology, Mathematical Biology, Nicolas Rashevsky. Thus, the roots of SMB go back to the publication in 1939 of the first international journal of mathematical biology, previously entitled "The Bulletin of Mathematical Biophysics"—which was founded by Nicolas Rashevsky, and which is currently published by SMB under the name of "' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dirac Delta-function
In mathematical analysis, the Dirac delta function (or distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. Thus it can be represented heuristically as \delta (x) = \begin 0, & x \neq 0 \\ , & x = 0 \end such that \int_^ \delta(x) dx=1. Since there is no function having this property, modelling the delta "function" rigorously involves the use of limits or, as is common in mathematics, measure theory and the theory of distributions. The delta function was introduced by physicist Paul Dirac, and has since been applied routinely in physics and engineering to model point masses and instantaneous impulses. It is called the delta function because it is a continuous analogue of the Kronecker delta function, which is usually defined on a discrete domain and takes values 0 and 1. The mathematical rigor of the delta function was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compartmental Models In Epidemiology
Compartmental models are a mathematical framework used to simulate how populations move between different states or "compartments." While widely applied in various fields, they have become particularly fundamental to the mathematical modelling of infectious diseases. In these models, the population is divided into compartments labeled with shorthand notation – most commonly S, I, and R, representing Susceptible, Infectious, and Recovered individuals. The sequence of letters typically indicates the flow patterns between compartments; for example, an SEIS model represents progression from susceptible to exposed to infectious and then back to susceptible again. These models originated in the early 20th century through pioneering epidemiological work by several mathematicians. Key developments include Hamer's work in 1906, Ronald Ross, Ross's contributions in 1916, collaborative work by Ross and Hilda Phoebe Hudson, Hudson in 1917, the seminal Kermack–McKendrick theory, Kermack and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integro-differential Equation
In mathematics, an integro-differential equation is an equation that involves both integrals and derivatives of a function (mathematics), function. General first order linear equations The general first-order, linear (only with respect to the term involving derivative) integro-differential equation is of the form : \fracu(x) + \int_^x f(t,u(t))\,dt = g(x,u(x)), \qquad u(x_0) = u_0, \qquad x_0 \ge 0. As is typical with differential equations, obtaining a closed-form solution can often be difficult. In the relatively few cases where a solution can be found, it is often by some kind of integral transform, where the problem is first transformed into an algebraic setting. In such situations, the solution of the problem may be derived by applying the inverse transform to the solution of this algebraic equation. Example Consider the following second-order problem, : u'(x) + 2u(x) + 5\int_^u(t)\,dt = \theta(x) \qquad \text \qquad u(0)=0, where : \theta(x) = \left\{ \begin{ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Epidemiology
Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and Risk factor (epidemiology), determinants of health and disease conditions in a defined population, and application of this knowledge to prevent diseases. It is a cornerstone of public health, and shapes policy decisions and evidence-based practice by identifying Risk factor (epidemiology), risk factors for disease and targets for preventive healthcare. Epidemiologists help with study design, collection, and statistical analysis of data, amend interpretation and dissemination of results (including peer review and occasional systematic review). Epidemiology has helped develop methodology used in clinical research, public health studies, and, to a lesser extent, basic research in the biological sciences. Major areas of epidemiological study include disease causation, transmission (medicine), transmission, outbreak investigation, disease surveillance, environmental epidemiology, forensic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
