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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, or Recovered). People may progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for example SEIS means susceptible, exposed, infectious, then susceptible again. The origin of such models is the early 20th century, with important works being that of Ross in 1916, Ross and Hudson in 1917, Kermack and McKendrick in 1927 and Kendall in 1956. The Reed-Frost model was also a significant and widely-overlooked ancestor of modern epidemiological modelling approaches. The models are most often run with ordinary differential equations (which are deterministic), but can also be used with a stochastic (random) framework, which is more realistic but much more complicated to analyze. Mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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 modeling 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] |
Diagram Of SIR Epidemic Model States And Transition Rates
A diagram is a symbolic representation of information using visualization techniques. Diagrams have been used since prehistoric times on walls of caves, but became more prevalent during the Enlightenment. Sometimes, the technique uses a three-dimensional visualization which is then projected onto a two-dimensional surface. The word ''graph'' is sometimes used as a synonym for diagram. Overview The term "diagram" in its commonly used sense can have a general or specific meaning: * ''visual information device'' : Like the term "illustration", "diagram" is used as a collective term standing for the whole class of technical genres, including graphs, technical drawings and tables. * ''specific kind of visual display'' : This is the genre that shows qualitative data with shapes that are connected by lines, arrows, or other visual links. In science the term is used in both ways. For example, Anderson (1997) stated more generally: "diagrams are pictorial, yet abstract, representat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Separation Of Variables
In mathematics, separation of variables (also known as the Fourier method) is any of several methods for solving ordinary and partial differential equations, in which algebra allows one to rewrite an equation so that each of two variables occurs on a different side of the equation. Ordinary differential equations (ODE) Suppose a differential equation can be written in the form :\frac f(x) = g(x)h(f(x)) which we can write more simply by letting y = f(x): :\frac=g(x)h(y). As long as ''h''(''y'') ≠ 0, we can rearrange terms to obtain: : = g(x) \, dx, so that the two variables ''x'' and ''y'' have been separated. ''dx'' (and ''dy'') can be viewed, at a simple level, as just a convenient notation, which provides a handy mnemonic aid for assisting with manipulations. A formal definition of ''dx'' as a differential (infinitesimal) is somewhat advanced. Alternative notation Those who dislike Leibniz's notation may prefer to write this as :\frac \frac = g(x), but tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Basic 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 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). 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 u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-linear
In mathematics and science, a nonlinear system is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists because most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a linear combination of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Anderson Gray McKendrick
Lt Col 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." Life McKendrick was born at 2 Chester Street 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 his ... [...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] |
SIR Model Cartoon
''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 part of "Monsieur", with the equivalent "My Lord" in English. Traditionally, as governed by law and custom, Sir is used for men titled as knights, often as members of orders of chivalry, as well as later applied to baronets and other offices. As the female equivalent for knighthood is damehood, the female equivalent term is typically Dame. The wife of a knight or baronet tends to be addressed as Lady, although a few exceptions and interchanges of these uses exist. Additionally, since the late modern period, Sir has been used as a respectful way to address a man of superior social status or military rank. Equivalent terms of address for women are Madam (shortened to Ma'am), in addition to social honorifics such as Mrs, Ms or Miss. Etymolo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology. Mainly the study of differential equations consists of the study of their solutions (the set of functions that satisfy each equation), and of the properties of their solutions. Only the simplest differential equations are solvable by explicit formulas; however, many properties of solutions of a given differential equation may be determined without computing them exactly. Often when a closed-form expression for the solutions is not available, solutions may be approximated numerically using computers. The theor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 symptoms begin from one to four days after exposure to the virus (typically two days) and last for about 2–8 days. Diarrhea and vomiting can occur, particularly in children. Influenza may progress to pneumonia, which can be caused by the virus or by a subsequent bacterial infection. Other complications of infection include acute respiratory distress syndrome, meningitis, encephalitis, and worsening of pre-existing health problems such as asthma and cardiovascular disease. There are four types of influenza virus, termed influenza viruses A, B, C, and D. Aquatic birds are the primary source of Influenza A virus (IAV), which is also widespread in various mammals, including humans and pigs. Influenza B virus (IBV) and Influenza C virus (ICV) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIR Trajectory
''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 part of "Monsieur", with the equivalent "My Lord" in English. Traditionally, as governed by law and custom, Sir is used for men titled as knights, often as members of orders of chivalry, as well as later applied to baronets and other offices. As the female equivalent for knighthood is damehood, the female equivalent term is typically Dame. The wife of a knight or baronet tends to be addressed as Lady, although a few exceptions and interchanges of these uses exist. Additionally, since the late modern period, Sir has been used as a respectful way to address a man of superior social status or military rank. Equivalent terms of address for women are Madam (shortened to Ma'am), in addition to social honorifics such as Mrs, Ms or Miss. Etymolo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Distribution
Logistic may refer to: Mathematics * Logistic function, a sigmoid function used in many fields ** Logistic map, a recurrence relation that sometimes exhibits chaos ** Logistic regression, a statistical model using the logistic function ** Logit, the inverse of the logistic function ** Logistic distribution, the derivative of the logistic function, a continuous probability distribution, used in probability theory and statistics * Mathematical logic, subfield of mathematics exploring the applications of formal logic to mathematics Other uses * Logistics, the management of resources and their distributions ** Logistic engineering, the scientific study of logistics ** Military logistics, the study of logistics at the service of military units and operations See also *Logic (other) Logic is the study of the principles and criteria of valid inference and demonstration Logic may also refer to: *Mathematical logic, a branch of mathematics that grew out of symbolic log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
