Study of Biological Population Stable Development Based on Mathematical Models

In this paper, we take the elephant population from a large National Park in South Africa as a typical example to study how to keep population stable. According to approximate age and gender data of the elephants emigrated from the park in the last two years, we develop mathematical models to analyze the survival rate, the age structure, the number of contraception and relocation of the elephant population, which helps us provide the correspondence strategies to maintain population development. Firstly, we analyze age structure of elephants in nearly two years. We assume emigrated elephants are randomly selected, so the number of elephants relocated can reflect the actual age structure of the current elephant population. Then a stepwise average model is developed to find the survival rate. Besides, using the proportion of different age group, we calculate the current age structure which is shown in the histogram. Furthermore, we construct the Leslie model to study elephant population growth which can be concluded that the elephant population will grow indefinitely (if the environment permits) without contraception injection. In order to maintain population stable, we obtain the annual number of drafted elephant by establishing the equation about survival rate and reproduction rate. Finally, we use computer simulation method to calculate the number of emigrated elephants in different age groups. With the results, we apply the fitting method to find out the function relation between the number of emigrated elephants and drafted elephants so that we are able to present the correspondence strategies to maintain population development.