# mathematical model

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## math·e·mat·i·cal mod·el

representation of a system, process, or relationship in mathematical form, using equations to simulate the behavior of the system or process under study.

## mathematical model

EpidemiologyA formal framework for conveying ideas about the components of a host-parasite interaction. Construction of an MM requires three major components: a clear understanding of the interaction between the pathogen and the host; information about the mode and rate of transmission between individuals; and host population characteristics, such as demographics and behaviour. MMs can be used to analyse the system’s behaviour under various conditions, and identify the dominant factors generating observed patterns and phenomena. MMs also aid data collection and interpretation and parameter estimation; they provide tools for identifying approaches to control, and for assessing the potential impact of different intervention measures.

Radiation

A collection of mathematical formulas used to characterise a relationship or process, e.g., in environmental dose reconstruction projects to simulate travel of radionuclides released from weapons facilities through the environment and taken up by the body, which can be used to estimate the health risks caused by said exposures.

## model

a simulation, a copy, occurring naturally or manufactured. Models used in statistical and epidemiological studies may be deterministic, stochastic or random.

**model 1**

the fixed version of the linear additive model used in linear regression analysis.

**model 2**

the random version of the linear additive model used in linear regression analysis.

**animal model**

any condition in an animal that has enough similarities to a condition in humans that studies of the animal disease are will assist in understanding the human disorder.

**causal model**

a model used to determine the part played by multiple factors in the cause or causes of disease; a path model in which the variables are arranged temporally.

**descriptive model**

consist largely of diagrams and maps or charts designed to describe a real-world system.

**deterministic model**

see epidemiological model (below).

**epidemiological model**

a mathematical model, which may be a computer simulation model, of a disease for the purpose of studying the behavior of the disease in a variable animal population under variable conditions of climate, density of population, mix of population, and so on. It may be an

*analytical*model, an*economic decision making*model, an*explanatory*model or a*predictive*model. It may also be a*causal*model, which allows the operator to vary the determinants of prevalence and observe the respective outcomes. It may permit only the use of fixed numbers so that it will always return the same answer to the same question, in which case it is a*deterministic*model, or it may introduce the element of chance into the selection of outcomes, in which case it is a*stochastic*model.Specific computer simulation models have been prepared for the study of rinderpest, the costs of mastitis control, the cost-benefits of foot-and-mouth disease control, and the costs of mortality in dairy calves. For example see reed-frost model.

**linear programming model**

a statistical model of a dependent variable, e.g. Y, as a linear combination of other variables, e.g. X. The model is based on a series of linear equations with a linear equation, called the objective function, as the desired end. Such an end could, in the determination of lowest cost rations, be the total cost of each ration.

**mathematical model**

a representation of a system, process or relationship in a mathematical form; see also mathematical modeling.

**physical model**

e.g. a model of a molecule utilizing colored balls connected by rigid wires.

**probabilistic model**

includes basic concepts of probability theory and may be deterministic or stochastic.

**Reed-Frost model**

a deterministic probability model of a theoretical epidemic.

**stochastic model**

see epidemiological model.

**symbolic model**

mathematical symbols used to describe the status of variables at a given time and to define the manner in which they change and interact.

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