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Infinite Horizon Optimal Control of a SIR Epidemic Under an ICU Constraint
No full textThe aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem of a SIR epidemic on an infinite horizon. A state constraint related to intensive care units (ICU) capacity is imposed and the objective functional linearly depends on the state and the control. After preliminary asymptotic and viability analyses, a Γ-convergence argument is developed to reduce the problem to a finite horizon allowing to use a state constrained version of Pontryagin’s theorem to characterize the structure of the optimal controls. Illustrating examples and numerical simulations are given according to the available data on Covid-19 epidemic in Italy
Optimality of Vaccination for an SIR Epidemic with an ICU Constraint
Full text linkThis paper studies an optimal control problem for a class of SIR epidemic models, in scenarios in which the infected population is constrained to be lower than a critical threshold imposed by the intensive care unit (ICU) capacity. The vaccination effort possibly imposed by the health-care deciders is classically modeled by a control input affecting the epidemic dynamic. After a preliminary viability analysis, the existence of optimal controls is established, and their structure is characterized by using a state-constrained version of Pontryagin’s theorem. The resulting optimal controls necessarily have a bang-bang regime with at most one switch. More precisely, the optimal strategies impose the maximum-allowed vaccination effort in an initial period of time, which can cease only once the ICU constraint can be satisfied without further vaccination. The switching times are characterized in order to identify conditions under which vaccination should be implemented or halted. The uniqueness of the optimal control is also discussed. Numerical examples illustrate our theoretical results and the corresponding optimal strategies. The analysis is eventually extended to the infinite horizon by Γ-convergence arguments
Optimal control of a SIR epidemic with ICU constraints and target objectives
No full textThe aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem with SIR dynamics main feature of our study is the presence of state constraints (related to intensive care units ICU capacity) and strict target objectives (related to the immunity threshold). The first class of results provides a comprehensive description of different zones of interest using viability tools. The second achievement is a thorough mathematical analysis of Pontryagin extremals for the aforementioned problem allowing to obtain an explicit closed-loop feedback optimal control. All our theoretical results are numerically illustrated for a further understanding of the geometrical features and scenarios
Corrigendum to “Optimal control of a SIR epidemic with ICU constraints and target objectives” (Applied Mathematics and Computation (2022) 418, (S0096300321008997), (10.1016/j.amc.2021.126816))
No full textThe authors regret that in the printed version of the above article, some figures (those corresponding to Scenario 2 in Section 6) are missed. We believe that this mistake occurred during the publication process. The missed pictures are the following. [Formula presented] The correct and final version follows. The authors would like to apologise for any inconvenience caused
Optimality of Vaccination for Prevalence-Constrained SIRS Epidemics
No full textThe aim of the present paper is to investigate the optimal vaccination policies with prevalence restrictions in an SIRS demographic model. We provide a well-posedness result for the system and give a thorough description of safety zones (immunity and feasible) when intensive care units (ICU) restrictions are enforced on the prevalence. Using Pontryagin’s principle for state-constrained dynamics we show that the optimal vaccination policy is of bang–bang type and give further specifics on the precise structure. The paper is intended as a counter-part to Avram et al. (Appl Math Comput 418:126816, 2022) where non-pharmaceutical interventions have been considered
SIR Epidemics with State-Dependent Costs and ICU Constraints: A Hamilton–Jacobi Verification Argument and Dual LP Algorithms
No full textThe aim of this paper is twofold. On one hand, we strive to give a simpler proof of the optimality of greedy controls when the cost of interventions is control-affine and the dynamics follow a state-constrained controlled SIR model. This is achieved using the Hamilton-Jacobi characterization of the value function, via the verification argument and explicit trajectory-based computations. Aside from providing an alternative to the Pontryagin complex arguments in Avram et al. (Appl Math Comput 418:126816, 2022) (see also Avram et al. in Appl Math Comput 423:127012, 2022), this method allows one to consider more general classes of costs; in particular state-dependent ones. On the other hand, the paper is completed by linear programming methods allowing one to deal with possibly discontinuous costs. In particular, we propose a brief exposition of classes of linearized dynamic programming principles based on our previous work and ensuing dual linear programming algorithms. We emphasize the particularities of our state space and possible generations of forward scenarios using the description of reachable sets
Controlled Compartmental Models with Time-Varying Population: Normalization, Viability and Comparison
No full textThis paper focuses on the characterization of viability zones in compartmental models with varying population size, due both to deaths caused by epidemics and to natural demography. This is achieved with the use of viscosity characterizations of viability and extensively illustrated on several models. An example taking into consideration real data is provided. The paper is completed with a viscosity approach to the optimality of minimal ("greedy") non-pharmaceutical interventions
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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