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Special Issue Year : 2023

Control theory perspectives on mathematical epidemiology

Abstract

Mathematical epidemiology may benefit from techniques and concepts from Control theory. As a matter of fact, understanding and controlling the spread of an infectious epidemic necessitates modeling of the phenomena underlying the propagation, estimation of the characteristic parameters and of the state of the epidemic, scheduling and scaling of the control measures. These are generic questions, for which tools have been developed in Control, admittedly in quite different applicative contexts. The aim of this session is precisely to explore in more details potential profit, as well as limitations, of this cross-fertilization. Several common features of the problems arising from the application of Control theory to the handling of epidemics are worth mentioning here. First, the transmission of infection is inherently a nonlinear phenomenon. Second, the usual measurements of prevalence leads to a lack of observability and identifiability of the studied state space models at equilibria, a point which complicates the handling of these issues when the state is closed from these singular points (beginning of outbreak or final stabilization). Last, the cost functions of interest are usually non-conventional, typically proportional to the effort made (and not quadratic), and state constraint are not uncommon. All this, plus the important uncertainty present on the models and on the data, makes the corresponding problems rather sensitive. The six contributions that constitute this session offer a partial vision of issues to be adressed. They are more especially related to observability and identifiability (papers 1 and 2), and to optimal control applied to epidemic processes (papers 2 to 6).
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Dates and versions

hal-04064515 , version 1 (11-04-2023)

Identifiers

  • HAL Id : hal-04064515 , version 1

Cite

Pierre-Alexandre Bliman, Alain Rapaport. Control theory perspectives on mathematical epidemiology. 2023, 22nd World Congress of the International Federation of Automatic Control. ⟨hal-04064515⟩
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