Control theory methods for epidemiological systems

Emerging and re-emerging diseases are a continuous threat to our planet. This menace has grown over the last decades, leading to serious public health issues, significant mortality, and financial expenses, as the COVID-19 pandemic has shown. Various phenomena, such as urbanization and globalization, might explain this escalation. Many mathematical models are already used to describe the transmission of an epidemic. However, the automatic control theory methods still need to be more widespread in epidemiologic studies. The ANR NOCIME project aims to solve novel, broadly defined control theory problems connected to optimal control and the observation/identification of epidemiological dynamics, which demonstrate many challenging features. In particular, fundamental properties of the system, namely identifiability, and observability, are generally required so that parameter estimation and observer design techniques can then be implemented, with a global guarantee of convergence on the domain or guaranteed upper and lower estimates. Many epidemiological models exhibit several equilibria: all disease-free states are equilibrium points when births and deaths are neglected, which is appropriate at the outbreak time scale. These equilibria are often singular points of the identifiability and observability maps: no information on the disease parameters and susceptible proportion can be inferred in the absence of infected individuals. Assuming that observability (or identifiability) conditions and related sets are settled, the design of associated estimators follows. Different types of observers will be developed, such as nonlinear or adaptive observers [1], [2] and interval observers [3], [4]. The postdoctoral job will first study the observability and identifiability of several epidemiological models and develop specific (analytic and numerical) tools adapted for these kinds of nonlinear models. The question of observer synthesis will be addressed in a second step using different techniques. Finally, using observers with the control laws developed in the project will be a matter of investigation. The young researcher will be expected to exchange with the NOCIME project's other partners based in Paris, Metz, and Montpellier.

Last updated: 30 March 2024