Model of orangutan population dynamics by considering infanticide and Minimum Viable Population factors.

Orangutans are rare animals whose populations are threatened with extinction. Several factors that influence the extinction of orangutans are influenced by humans, such as deforestation and hunting activities. Herein we will focus on studying the factors of extinction caused without human intervention. These factors include the slow life cycle due to the long interbirth interval of orangutans and the presence of infanticide. To examine the behavior, a model of a three-dimensional non-linear system of differential equations is constructed to modeled orangutan population. The model is constructed based on the age structure due to different levels of productivity. This model also considers the Minimum Viable Population (MVP) and infanticide cases which are represented by the functional response of Holling type II and Allee effect, respectively. In this study, the existence and stability of the equilibrium point are investigated analytically for cases without infanticide. Meanwhile, the general case is analyzed numerically. Numerical simulations are also carried out to examine the existence of the bifurcation and at the same time to confirm the analytical results. From this model, we get three equilibrium points where two interior equilibria and one trivial equilibrium. Our analysis shows that the trivial equilibrium is always unconditionally stable. This means that if the orangutan population is close to extinction, then the orangutan population will be headed for extinction. The boundary of the extinction area is also obtained to maintain the coexistence of the orangutan population by paying attention to the proportion of orangutans that must always be above that boundary. In addition, numerical results confirm that the greater the infanticide factor, the wider the area of population extinction, which has an impact on the smaller proportion of the orangutan population. The results of this study suggest to policy makers to always keep the population proportion above the boundary that we find so that extinction can be avoided. [ABSTRACT FROM AUTHOR]