ASSESSMENT OF THE ADEQUACY OF THE LOTKA – VOLTERRA MODEL FOR DETERMINING HUMAN ECOLOGICAL WELL-BEING

Abstract

Background. The use of mathematics in the field of environmental safety has long roots. The most famous mathematical model in ecology is the Lotka – Volterra model, which describes the relationship between predator and prey in a natural ecosystem. The authors proposed an improved three-element Lotka – Volterra model that takes into account the interaction of three elements of the territorial technosphere: a person, the environment, and an object of the technosphere. The aim of the study is to test the adequacy of the improved Lotka – Volterra model to the process of interaction of elements in the territorial technosphere. Model adequacy testing is formulated as the task of testing the assumption that the value of the model response differs from the real response of the system by no more than a given value. The object of the study is the improved Lotka – Volterra model, which takes into account the interaction of man, the environment and the object of the technosphere. Materials and methods. The study was carried out using an integrated systematic approach and methods of analysis and synthesis, grouping and generalization. Results. Of all the analyzed criteria for the adequacy of the model, there is Pearson's с2 goodness-of-fit test, Smirnov – Kolmogorov's test, Fisher's (Fischer – Snedekor's) test, Fisher's test is the most preferable, since it is suitable for comparing very small samples, it can be one-sided and two-sided. Conclusions. The improved Lotka – Volterra mathematical model describing the interaction of elements in the territorial technosphere adequately reflects the state of the territorial technosphere in forecasting and in terms of the absolute values of risk factors.

Keywords

• mathematical model
• lotka – volterra equation
• modeling
• forecasting
• adequacy
• fisher f-criterion