Nonlinear Models of Economic Dynamics as a Tool for Public Health Research

In the process of modeling the impact of digital economy transformation on public healthcare, it is reasonable to use systems of nonlinear differential equations due to the possibility of taking into account nonlinear effects and feedbacks. The article theoretically substantiates the necessity and feasibility of their use, explains in detail choice of the modified Lotka-Volterra model as a theoretical basis, and conducts numerical integration of modified models. The modified Lotka-Volterra model proposed in the article is used taking into account possible scenarios: with and without internal competition in public healthcare and economy digitalization; as well as focusing on internal competition in public healthcare. Numerical integration of the system of nonlinear differential equations describing interdependencies between public healthcare and economy digitalization, performed via the Python programming language, allowed to obtain a phase portrait of the Lotka-Volterra model. The latter demonstrated presence of closed trajectories, which is a characteristic feature of cyclic dynamics, and existence of stable oscillatory modes. The latter confirmed nonlinear nature of relationships between the studied variables. Dynamics analysis of the Lotka-Volterra model, adapted to the context of public healthcare and digitalization, showed that introduction of digital technologies affects public healthcare with a certain time delay, which should be taken into account when developing public health policies. The article builds a 3D phase portrait of a system of nonlinear differential equations explaining interdependencies between public healthcare and economy digitalization. Such analysis reflects that the trajectory in phase space forms closed cycles, indicating presence of stable oscillatory modes. Modified Lotka-Volterra models are proposed that take into account internal competition in public healthcare, internal competition in public healthcare and in economy digitalization. The results of numerical modeling demonstrate that digitalization contributes to sustainability of public healthcare. At the same time, intensive development of digital technologies can lead to nonlinear effects and oscillatory processes in the system.