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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] |
Mathematical Modelling Of Infectious Diseases
Mathematical models can project how infectious diseases progress to show the likely outcome of an epidemic (including Plant disease forecasting, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rubella
Rubella, also known as German measles or three-day measles, is an infection caused by the rubella virus. This disease is often mild, with half of people not realizing that they are infected. A rash may start around two weeks after exposure and last for three days. It usually starts on the face and spreads to the rest of the body. The rash is sometimes itchy and is not as bright as that of measles. Lymphadenopathy, Swollen lymph nodes are common and may last a few weeks. A fever, sore throat, and fatigue may also occur. arthritis, Joint pain is common in adults. Complications may include bleeding problems, orchitis, testicular swelling, encephalitis, and neuritis, inflammation of nerves. Infection during early pregnancy may result in a miscarriage or a child born with congenital rubella syndrome (CRS). Symptoms of CRS manifest as problems with the eyes such as cataracts, deafness, as well as affecting the heart and brain. Problems are rare after the 20th week of pregnancy. Rubel ... [...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 one to four (typically two) days after exposure to the virus and last for about two to eight days. Diarrhea and vomiting can occur, particularly in children. Influenza may progress to pneumonia from the virus or a subsequent bacterial infection. Other complications 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: types 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) primarily infect humans, and influenza D virus (IDV) i ... [...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 "" (Lord), brought to England by the French-speaking Normans, and which now exist in French only as part of "", with the equivalent "My Lord" in English. Traditionally, as governed by law and custom, Sir is used for men who are knights and belong to certain orders of chivalry, as well as later applied to baronets and other offices. As the female equivalent for knighthood is damehood, the ''suo jure'' 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. Etym ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logistic Distribution
In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution. Specification Cumulative distribution function The logistic distribution receives its name from its cumulative distribution function, which is an instance of the family of logistic functions. The cumulative distribution function of the logistic distribution is also a scaled version of the Hyperbolic function, hyperbolic tangent. :F(x; \mu, s) = \frac = \frac12 + \frac12 \operatorname \left(\frac\right). In this equation is the mean, and is a scale parameter proportional to the standard deviation. Probability density function The probability density function is the partia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erlang Distribution
The Erlang distribution is a two-parameter family of continuous probability distributions with Support (mathematics), support x \in [0, \infty). The two parameters are: * a positive integer k, the "shape", and * a positive real number \lambda, the "rate". The "scale", \beta, the reciprocal of the rate, is sometimes used instead. The Erlang distribution is the distribution of a sum of k Independence (probability theory), independent exponential distribution, exponential variables with mean 1/\lambda each. Equivalently, it is the distribution of the time until the ''k''th event of a Poisson process with a rate of \lambda. The Erlang and Poisson distributions are complementary, in that while the Poisson distribution counts the events that occur in a fixed amount of time, the Erlang distribution counts the amount of time until the occurrence of a fixed number of events. When k=1, the distribution simplifies to the exponential distribution. The Erlang distribution is a special ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Distribution
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time between production errors, or length along a roll of fabric in the weaving manufacturing process. It is a particular case of the gamma distribution. It is the continuous analogue of the geometric distribution, and it has the key property of being memoryless. In addition to being used for the analysis of Poisson point processes it is found in various other contexts. The exponential distribution is not the same as the class of exponential families of distributions. This is a large class of probability distributions that includes the exponential distribution as one of its members, but also includ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Mass Action
In chemistry, the law of mass action is the proposition that the rate of a chemical reaction is directly proportional to the product of the activities or concentrations of the reactants. It explains and predicts behaviors of solutions in dynamic equilibrium. Specifically, it implies that for a chemical reaction mixture that is in equilibrium, the ratio between the concentration of reactants and products is constant. Two aspects are involved in the initial formulation of the law: 1) the equilibrium aspect, concerning the composition of a reaction mixture at equilibrium and 2) the kinetic aspect concerning the rate equations for elementary reactions. Both aspects stem from the research performed by Cato M. Guldberg and Peter Waage between 1864 and 1879 in which equilibrium constants were derived by using kinetic data and the rate equation which they had proposed. Guldberg and Waage also recognized that chemical equilibrium is a dynamic process in which rates of reaction ... [...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, representatio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph SIR Model Without Vital Dynamics
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 discrete mathematics *Graph of a function * Graph of a relation *Graph paper *Chart, a means of representing data (also called a graph) Computing *Graph (abstract data type), an abstract data type representing relations or connections *graph (Unix), Unix command-line utility *Conceptual graph, a model for knowledge representation and reasoning *Microsoft Graph, a Microsoft API developer platform that connects multiple services and devices Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also * Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") *List of information graphics software *Stati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 hosts in a given population within a short period of time. For example, in meningococcal infections, an attack rate in excess of 15 cases per 100,000 people for two consecutive weeks is considered an epidemic. Epidemics of infectious disease are generally caused by several factors including a change in the ecology of the host population (e.g., increased stress or increase in the density of a vector species), a genetic change in the pathogen reservoir or the introduction of an emerging pathogen to a host population (by movement of pathogen or host). Generally, an epidemic occurs when host immunity to either an established pathogen or newly emerging novel pathogen is suddenly reduced below that found in the endemic equilibrium and the transmission threshold is exceeded. An epidemic may be restricted to one location; however, if it sp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
