The Risk of Contagion Spreading and its Optimal Control in the Economy

Abstract

The global crisis of 2008 provoked a heightened interest among scientists to study the phenomenon, its propagation and negative consequences. The process of modelling the spread of a virus is commonly used in epidemiology. Conceptually, the spread of a disease among a population is similar to the contagion process in economy. This similarity allows considering the contagion in the world financial system using the same mathematical model of infection spread that is often used in epidemiology. Our research focuses on the dynamic behaviour of contagion spreading in the global financial network. The effect of infection by a systemic spread of risks in the network of national banking systems of countries is tested. An optimal control problem is then formulated to simulate a control that may avoid significant financial losses. The results show that the proposed approach describes well the reality of the world economy, and emphasizes the importance of international relations between countries on the financial stability.

Control of COVID-19 dynamics through a fractional-order model

“…Similar functionals (13) to be optimized, e.g. for optimal control problems in the combat of Zika and Ebola, have been previously considered in the literature, see [41,42] and references therein.…”

Control of COVID-19 dynamics through a fractional-order model

“…Optimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system, over a period of time, such that an objective function is minimized or maximized. Along the years, optimal control theory has found applications in several fields, containing process control, aerospace, robotics, economics, bio-engineering, management sciences, finance, and medicine [13][14][15]. In particular, the study of epidemic models is strongly related to the study of control strategies, as screening and educational campaigns [16], vaccination [17], and resource allocation [18].…”

A Geometrical Approach for the Optimal Control of Sequencing Batch Bio-Reactors

“…Classical tools of optimal control theory (PMP, direct methods, shooting methods, ...) allowed also to provide control strategies for SBRs. These tools are also utilized for optimal control in many real chemical, biological and physical processes as in [1] and [6]. In [8], a strategy to determine the switching instants between aerobic and anoxic phases is available.…”