EIGENVALUES OF THE LESLIE MATRIX AND ITS APPLICATION TO FEMALE POPULATION GROWTH RATE IN BANYUMAS REGENCY

Abstract

The Leslie matrix model is used to estimate the size and growth rate of the female population based on fertility and survival rates in each age group. This study aims to analyze the behavior of the dominant eigenvalues of the Leslie matrix and apply it to estimate the growth rate of the female population in Banyumas Regency. The data used in this study consist of the female population in 2019 and 2024, as well as the number of female births during the period 2019–2024. The research stages include proving that the Leslie matrix has an unique positive eigenvalues and that two consecutive entries in the first row of the Leslie matrix are nonzero. The subsequent stages involve determining age groups, calculating fertility and survival rates, constructing the Leslie matrix and the initial age-distribution vector, and determining the dominant eigenvalues to estimate the growth rate of the female population in Banyumas Regency. The results show that the Leslie matrix has dominant positive eigenvalues. Furthermore, the dominant eigenvalues obtained from the female population growth model in Banyumas Regency is 0.991. It is indicating that the female population growth rate is expected to decline 99,1% in each five-year period. This result suggests a long-term slowdown in the growth of the female population in Banyumas Regency.