Armed forces population dynamics: The effect of movement in state border

Abstract

Armed forces is a professional organization formally authorized by a state to use deadly force and weapons to support security and unity inside a state. One of their main tasks is assigned in war either to defend their state independence or just for political reason. Recruitment rate of military member is an important factor to ensure the sustainability of this military system. This study construct mathematical model which represent the dynamics of citizen and armed forces population in a state. The first model is a systems of time-dependent ordinary differential equation. Dynamical analysis such as existence and stability of equilibrium point are obtained. This model has periodic solution in the neighborhood of coexistence equilibrium point. The model was modified into a system of partial differential equation which is time and space-dependent. The spatial on second model is represented by diffusion which describe the dispersal of individuals in a country. Two different boundary conditions are implemented for the army population which is illustrated in numerical simulation. Diffusion term plays an important role in this model, i.e. changing the behavior of solution become asymptotically stable. Different boundary condition shows different result. Dirichlet boundary condition shows better view since it makes the solution asymptotically stability of positive equilibrium point of non-spatial model.