A proposed stochastic growth model for monitoring the population dynamics in Ghana

Population size modelling offers crucial insights into societal, economic, environmental, and public health dynamics, aiding in informed decision-making and sustainable development efforts. In the absence of suitable population models, complete enumeration (census) would be necessary to track population dynamics. A census may yield erroneous results due to undercounting, even though it is costly, time-consuming, and resource-intensive. A typical human population is susceptible to birth, death, immigration and emigration. Several authors have attempted to model population growth based on these characteristics except that most of them considered some but not all the above characteristics in their models. This study proposed a stochastic growth model to monitor the population dynamics considering; birth, death, immigration and emigration rates. Through the developed model, the expected size of the population and its variability over time was obtained. The study also derived the limiting distribution of the population size and specified its parameters. The long-run probability of zero offspring (probability of ultimate extinction) was also deduced. The results of the study indicates that the long-run probability of zero offspring of the Ghanaian population is approximately 0.21, the net migration and intrinsic growth rates per 1000 Ghanaian population are $-0.544$ and 22.458 with standard errors of 0.206 and 0.530 respectively. This indicates that although the average birth rate is higher than the average death rate in Ghana, the average emigration rate (rate at which individuals travel out of the population either by the land borders, sea or air ports) is relatively higher than the immigration rate (rate at which individuals come into the population either by the land borders, sea or air ports). The estimated population sizes were almost the same across all bootstrap samples. This indicates that the proposed model is stable. The study therefore recommends the use of the proposed stochastic population growth model to monitor any population that is susceptible to birth, death, immigration and emigration.