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Infectious Disease Modelling
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] |
Mathematical Model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right. The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reed–Frost Model
The Reed–Frost model is a mathematical model of epidemics put forth in the 1920s by Lowell Reed and Wade Hampton Frost, of Johns Hopkins University. While originally presented in a talk by Frost in 1928 and used in courses at Hopkins for two decades, the mathematical formulation was not published until the 1950s, when it was also made into a TV episode.Reed, Lowell (1951) ''Epidemic Theory: What Is It?'' (Television programYoutube retrieved 21 March 2021. Johns Hopkins Science Review, Baltimore, MD History During the 1920s, mathematician Lowell Reed and physician Wade Hampton Frost developed a binomial chain model for disease propagation, used in their biostatistics and epidemiology classes at Johns Hopkins University. Despite not having published their results, several other academics have done them in their studies. It was not until 1950 that mathematical formulation was published and turned into a television program entitled ''Epidemic theory: What is it?''. In the progra ... [...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 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] |
Graph Theory
In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph theory), vertices'' (also called ''nodes'' or ''points'') which are connected by ''Glossary of graph theory terms#edge, edges'' (also called ''arcs'', ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a Set (mathematics), set of vertices (also called nodes or points); * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 immune to an infection, whether through previous infections or vaccination, that the communicable pathogen cannot maintain itself in the population, its low incidence thereby reducing the likelihood of infection for individuals who lack immunity. Once the herd immunity has been reached, disease gradually disappears from a population and may result in eradication or permanent reduction of infections to zero if achieved worldwide. Herd immunity created via vaccination has contributed to the reduction of many diseases. Effects Protection of those without immunity Some individuals either cannot develop immunity after vaccination or for medical reasons cannot be vaccinated. Newborn infants are too young to receive many vaccines, either for sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth occurs when a quantity grows as an exponential function of time. The quantity grows at a rate directly proportional to its present size. For example, when it is 3 times as big as it is now, it will be growing 3 times as fast as it is now. In more technical language, its instantaneous rate of change (that is, the derivative) of a quantity with respect to an independent variable is proportional to the quantity itself. Often the independent variable is time. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth). Exponential growth is the inverse of logarithmic growth. Not all cases of growth at an always increasing rate are instances of exponential growth. For example the function f(x) = x^3 grows at an ever increasing rate, but is much slower than growing exponentially. For example, w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tag (game)
Tag (also called chase, tig, it, tiggy, tips, tick, on-on and tip) is a playground game involving one or more players chasing other players in an attempt to "tag" and mark them out of play, typically by touching with a hand. There are many variations; most forms have no teams, scores, or equipment. Usually when a person is tagged, the tagger says, "It!", "Tag, you're 'It'!" or "Tag". The last one tagged during tag is "It" for the next round. The game is known by other names in various parts of the world, including "running and catching" in India and "catch and cook" in the Middle East. Origin of name The game has many different names in different parts of the UK: 'tig' in Yorkshire, Scotland, and in the North West of England; and 'it' in the South of England. In the United States the game is usually called 'tag', and in Australia it is sometimes called 'tips'. In 2018, the internet meme "How old were you when you found out ____" began circulating, which stated that the orig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Social Structure
In the social sciences, social structure is the aggregate of patterned social arrangements in society that are both emergent from and determinant of the actions of individuals. Likewise, society is believed to be grouped into structurally related groups or sets of roles, with different functions, meanings, or purposes. Examples of social structure include family, religion, law, economy, and class. It contrasts with " social system", which refers to the parent structure in which these various structures are embedded. Thus, social structures significantly influence larger systems, such as economic systems, legal systems, political systems, cultural systems, etc. Social structure can also be said to be the framework upon which a society is established. It determines the norms and patterns of relations between the various institutions of the society. Since the 1920s, the term has been in general use in social science, especially as a variable whose sub-components needed to be d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Population Pyramid
A population pyramid (age structure diagram) or "age-sex pyramid" is a graphical illustration of the distribution of a population (typically that of a country or region of the world) by age groups and sex; it typically takes the shape of a pyramid when the population is growing. Males are usually shown on the left and females on the right, and they may be measured in absolute numbers or as a percentage of the total population. The pyramid can be used to visualize the age of a particular population. It is also used in ecology to determine the overall age distribution of a population; an indication of the reproductive capabilities and likelihood of the continuation of a species. Number of people per unit area of land is called population density. Structure A population pyramid often contains continuous stacked-histogram bars, making it a horizontal bar diagram. The population size is shown on the x-axis (horizontal) while the age-groups are represented on the y-axis (vertical). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Severe Acute Respiratory Syndrome Coronavirus 2
Severe acute respiratory syndrome coronavirus 2 (SARS‑CoV‑2) is a strain of coronavirus that causes COVID-19, the respiratory illness responsible for the COVID-19 pandemic. The virus previously had the Novel coronavirus, provisional name 2019 novel coronavirus (2019-nCoV), and has also been called human coronavirus 2019 (HCoV-19 or hCoV-19). First identified in the city of Wuhan, Hubei, China, the World Health Organization designated the outbreak a public health emergency of international concern from January 30, 2020, to May 5, 2023. SARS‑CoV‑2 is a positive-sense single-stranded RNA virus that is Contagious disease, contagious in humans. SARS‑CoV‑2 is a strain of the species ''Betacoronavirus pandemicum'' (SARSr-CoV), as is SARS-CoV-1, the virus that caused the 2002–2004 SARS outbreak. There are animal-borne coronavirus strains more closely related to SARS-CoV-2, the most closely known relative being the BANAL-52 bat coronavirus. SARS-CoV-2 is of Zoonosis, z ... [...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] |
