| Abstract [eng] |
This study reviews few mathematical models of population dynamics for human population modelling. The main purpose of this work is to make a prediction about size and structure of Lithuanian population over 35 years, using age and stage structured population dynamic models, namely deterministic and stochastic-matrix population structured by age and gender. The use of logistic model to study human population was received in 1920 by Pearl and Read. Developing theory that does account for differences among individuals (by age, gender, size etc.) within the same population on the basis of structured population models that do account for population structure, was firstly introduced by H. Leslie (1945), latter upgraded by L. P. Lefkovitch (1965), however it is still very much the cutting edge of contemporary of ecological research. Since 1990 Republic of Lithuania regain its independence suddenly changed economical, political and cultural paradigm, had a huge impact for the population and its demographical tendencies, due to dramatically decreased birth rate and increased mortality (demographic Russian cross) and also huge emigration. Nowadays because of worldwide financial turmoil Lithuania again suffers from increasing emigration and decreasing growth rates, so it is very important to model and predict what lies ahead for Lithuanian population dynamics. Also because of aging population tendencies it’s useful to know not only about the size, but also about the structure of future population of Lithuania. In the first part of this work there is an overview of the basics of population modelling, discussing key issues and factors affecting the greatest impact on the population dynamics. In the theory section there is review of two main approaches to population modelling: stochastic and deterministic. Concentrating mostly on analysing two age structured models. We present few ways, and algorithms for solving formulated models, most thoroughly looking into methods to solve linear systems of differential equations. At the end of this paper you will find Lithuanian population size forecast for the near future, which looks much more pessimistic than those made by Lithuanian government or European commission, forecast of the structure of the population suggest further population ageing. |
