Types Of Mathematical Models

1. Mathematical models are material-mathematical and logical-mathematical.

Material-mathematical models have mathematical description which identical to physical original.

Logical-mathematical models are abstract models which design from signs as logical calculations.

2. Mathematical models are probabilistic and deterministic.

If researcher uses probabilistic approach to the problem’s solution, he considers that appearances are accidental (casual).

Accidental appearance is such, which happens somewhat differently at many times repeats.

If researcher uses deterministic approach to the problem’s solution, he considers that appearances are strictly subdued to certain laws.

3. Structural models of control processes and models based on artificial intellect (expert models).

4. Mathematical models can take many forms, including but not limited to dynamical systems, statistical models, differential equations, or game theoretic models. These and other types of models can overlap, with a given model involving a variety of abstract structures.

2.1. Probabilistic Models

2.1.1. One-measured probabilistic models.

• Parametric one-measured models based on statistically grounded approximation of empiric distribution. Approximation is executed with using of probabilistic laws, more often normal law.

• Non-parametric one-measured models use in cases when law of empiric distribution is unknown.

2.2. Deterministic Models

2.2.1. Deterministic models with uninterrupted space and time (functional dependencies).

• 2.2.2. Deterministic models with discrete space and time (logical models).

• Logical-informational models are basis of many expert systems. They use logical trees, difference methods of coding, hierarchical schemes, identificators and classificators, sorting algorithms and other.

2.3. Structural Models Of Control Processes

There are most part of “bio-cybernetic” models.

Models with unlocked control contours are model without back relations.

Models with locked control contours are basis of cybernetics.

There are models with back relations. That gives for the system possibility to take into account information about declining of system’s state and results of control.

2.4. Models On Basis Of Artificial Intellect (Expert Systems)

There are models having databases and knowledge bases.

In medicine this models are mainly used in diagnostic systems for discrimination of diseases and taking of medical decision.

Stages of mathematical modelling

I stage is creating of mathematical model basis:

• accumulation of experimental data about original object;

• composition of equations described obtained experimental data.

II stage is checking and correction of a model:

• finding of number values of models parameters and indexes;

• solution of equations which are result of the I stage;

• comparison of solution with experimental data, finding of differences and its causes;

• correction of the model.

III stage is investigation of mathematical model and using it in the practice.

Examples of typical biological and medical mathematical models are:

• model of bacterial population grows;

• model of spreading of infection in the limited territory as village, town or city;

• model of blood circulation;

• model of immune system reaction on enemy antigen invasion;

• model of oscillation of animal number in population system “victim–prey”.