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Mathematical Modelling In Epidemiology
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] |
Mathematical Model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used 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). 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, and to make predictions about behavior. Elements of a mathematical model Mathematical models can take many forms, including dynamical systems, statisti ... [...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] |
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 units ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Endemic (epidemiology)
In epidemiology, an infection is said to be endemic in a specific population or populated place when that infection is constantly maintained at a baseline level without extra infections being brought into the group as a result of travel or similar means. An endemic disease always has a steady, predictable number of people getting sick, but that number can be high (''hyperendemic'') or low (''hypoendemic''), and the disease can be severe or mild. Also, a disease that is usually endemic can become epidemic. For example, chickenpox is endemic (steady state) in the United Kingdom, but malaria is not. Every year, there are a few cases of malaria reported in the UK, but these do not lead to sustained transmission in the population due to the lack of a suitable vector (mosquitoes of the genus ''Anopheles''). Consequently, the number of people infected by malaria is too variable to be called endemic. However, the number of people who get chickenpox in the UK varies little from year ... [...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, 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 safety reasons or because passive immunity renders the vaccine ineffective. Individuals who are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Exponential Growth
Exponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. 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). If the constant of proportionality is negative, then the quantity decreases over time, and is said to be undergoing exponential decay instead. In the case of a discrete domain of definition with equal intervals, it is also called geometric growth or geometric decay since the function values form a geometric progression. The formula for exponential growth of a variable at the growth rate , as time goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is x_t = x_0(1+r)^t where is the value of at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tag (game)
Tag (also called touch and go AG'', tig, it, tiggy, tips, tick, tip) is a playground game involving two or more players chasing other players in an attempt to "tag" and mark them out of play, usually 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, "Tag, you're 'it'!" 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. Basic rules Players (two or more) decide who is going to be "it", often using a counting-out game such as eeny, meeny, miny, moe. The player selected to be "it" then chases the others, attempting to "tag" one of them (by touching them with a hand) as the others try to avoid being tagged. A tag makes the tagged player "it". In some variations, the previous "it" is no longer "it" and the game can continue indefini ... [...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 disti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transmission Risks And Rates
Transmission of an infection requires three conditions: *an infectious individual *a susceptible individual *an effective contact between them An effective contact is defined as any kind of contact between two individuals such that, if one individual is infectious and the other susceptible, then the first individual infects the second. Whether or not a particular kind of contact will be effective depends on the infectious agent and its route of transmission. The effective contact rate (denoted ''β'') in a given population for a given infectious disease is measured in effective contacts per unit time. This may be expressed as the total contact rate (the total number of contacts, effective or not, per unit time, denoted \gamma), multiplied by the risk of infection, given contact between an infectious and a susceptible individual. This risk is called the transmission risk and is denoted ''p''. Thus: : \beta = \gamma \times p \, The total contact rate, \gamma, will generally be g ... [...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 (coronavirus disease 2019), the respiratory illness responsible for the ongoing COVID-19 pandemic. The virus previously had a Novel coronavirus, provisional name, 2019 novel coronavirus (2019-nCoV), and has also been called the human coronavirus 2019 (HCoV-19 or hCoV-19). First identified in the city of Wuhan, Hubei, China, the World Health Organization declared the outbreak a public health emergency of international concern on January 30, 2020, and a pandemic on March 11, 2020. SARS‑CoV‑2 is a positive-sense single-stranded RNA virus that is Contagious disease, contagious in humans. SARS‑CoV‑2 is a virus of the species ''severe acute respiratory syndrome–related coronavirus'' (SARSr-CoV), related to the Severe acute respiratory syndrome coronavirus 1, SARS-CoV-1 virus that caused the 2002–2004 SARS outbreak. Despite its close relation to SARS-CoV-1, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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. Models ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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