Optimal control and differential game solutions for social distancing in response to epidemics of infectious diseases on networks

Contagion is an age-old method of signifying infectious diseases like influenza and is a rich metaphor with strong biopolitical connotations for understandings of social distance, that is, the self as distinct from the other in the sense of space and identity. Contagion is therefore an important metaphor for the social distancing approaches recommended by experts during a pandemic, as was the case in 2009. This chapter, therefore, examines how research participants enacted social distancing as a method for reducing risk. It reflects on how these narratives reflected the meanings of contagion linked with distance, in particular, the notion that threat emerges elsewhere and in the figure of the other.

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Evaluating the Effectiveness of COVID-19 Bluetooth-Based Smartphone Contact Tracing Applications

Applied Sciences ◽

10.3390/app10207113 ◽

2020 ◽

Vol 10 (20) ◽

pp. 7113 ◽

Cited By ~ 2

Author(s):

Enrique Hernández-Orallo ◽

Carlos T. Calafate ◽

Juan-Carlos Cano ◽

Pietro Manzoni

Keyword(s):

Infectious Diseases ◽

Epidemic Model ◽

Contact Tracing ◽

Reproductive Number ◽

Smartphone Applications ◽

Social Distancing ◽

Implementation Model ◽

Decentralized Model ◽

Centralized Model

One of the strategies to control the spread of infectious diseases is based on the use of specialized applications for smartphones. These apps offer the possibility, once individuals are detected to be infected, to trace their previous contacts in order to test and detect new possibly-infected individuals. This paper evaluates the effectiveness of recently developed contact tracing smartphone applications for COVID-19 that rely on Bluetooth to detect contacts. We study how these applications work in order to model the main aspects that can affect their performance: precision, utilization, tracing speed and implementation model (centralized vs. decentralized). Then, we propose an epidemic model to evaluate their efficiency in terms of controlling future outbreaks and the effort required (e.g., individuals quarantined). Our results show that smartphone contact tracing can only be effective when combined with other mild measures that can slightly reduce the reproductive number R0 (for example, social distancing). Furthermore, we have found that a centralized model is much more effective, requiring an application utilization percentage of about 50% to control an outbreak. On the contrary, a decentralized model would require a higher utilization to be effective.

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Optimal Control for Stochastic Delay Systems Under Model Uncertainty: A Stochastic Differential Game Approach

Journal of Optimization Theory and Applications ◽

10.1007/s10957-013-0484-4 ◽

2013 ◽

Vol 167 (3) ◽

pp. 998-1031 ◽

Cited By ~ 16

Author(s):

Olivier Menoukeu Pamen

Keyword(s):

Optimal Control ◽

Differential Game ◽

Model Uncertainty ◽

Delay Systems ◽

Stochastic Differential Game ◽

Stochastic Delay

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Solving the Problem of UAV Air Combat Game Based on Differential Variational Inequality and D-Gap Function

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1042.172 ◽

2014 ◽

Vol 1042 ◽

pp. 172-177

Author(s):

Guang Yan Xu ◽

Ping Li ◽

Biao Zhou

Keyword(s):

Optimal Control ◽

Variational Inequality ◽

Optimal Control Problem ◽

Control Problem ◽

Differential Game ◽

Numerical Solutions ◽

Game Problem ◽

Gap Function ◽

Differential Variational Inequality ◽

Air Combat

The strategy of unmanned aerial vehicle air combat can be described as a differential game problem. The analytical solutions for the general differential game problem are usually difficult to obtain. In most cases, we can only get its numerical solutions. In this paper, a Nash differential game problem is converted to the corresponding differential variational inequality problem, and then converted into optimal control problem via D-gap function. The nonlinear continuous optimal control problem is obtained, which is easy to get numerical solutions. Compared with other conversion methods, the specific solving process of this method is more simple, so it has certain validity and feasibility.

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Approach for Optimal Control to Prevent Infectious Diseases from Community

Journal of Advanced Physics ◽

10.1166/jap.2018.1467 ◽

2018 ◽

Vol 7 (4) ◽

pp. 478-486 ◽

Cited By ~ 2

Author(s):

Muhammad Tahir ◽

Syed Inayat Ali Shah ◽

Gul Zaman

Keyword(s):

Optimal Control ◽

Infectious Diseases

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SOCIAL DISTANCING STRATEGIES AGAINST DISEASE SPREADING

Fractals ◽

10.1142/s0218348x13500199 ◽

2013 ◽

Vol 21 (03n04) ◽

pp. 1350019 ◽

Cited By ~ 10

Author(s):

L. D. VALDEZ ◽

C. BUONO ◽

P. A. MACRI ◽

L. A. BRAUNSTEIN

Keyword(s):

Infectious Diseases ◽

Healthy Individual ◽

Percolation Theory ◽

Quenched Disorder ◽

Epidemic Spreading ◽

Heterogeneous Distribution ◽

Percolation Process ◽

Social Distancing ◽

Disease Spreading

The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies against epidemic spreading on complex networks. We give a general outlook of the relation between link percolation and the susceptible-infected-recovered model, and introduce the node void percolation process to describe the dilution of the network composed by healthy individual, i.e., the network that sustain the functionality of a society. Then, we survey two strategies: the quenched disorder strategy where an heterogeneous distribution of contact intensities is induced in society, and the intermittent social distancing strategy where health individuals are persuaded to avoid contact with their neighbors for intermittent periods of time. Using percolation tools, we show that both strategies may halt the epidemic spreading. Finally, we discuss the role of the transmissibility, i.e., the effective probability to transmit a disease, on the performance of the strategies to slow down the epidemic spreading.

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Optimal control of the COVID-19 pandemic with non-pharmaceutical interventions

10.1101/2020.04.22.20076018 ◽

2020 ◽

Cited By ~ 7

Author(s):

Alex Perkins ◽

Guido Espana

Keyword(s):

Optimal Control ◽

Control Analysis ◽

Optimal Controls ◽

Social Distancing ◽

Considerable Uncertainty ◽

Hospital Capacity ◽

The Us ◽

Alternative Approaches ◽

High Level ◽

Reduced Time

The COVID-19 pandemic has forced societies across the world to resort to social distancing to slow the spread of the SARS-CoV-2 virus. Due to the economic impacts of social distancing, there is growing desire to relax these measures. To characterize a range of possible strategies for control and to understand their consequences, we performed an optimal control analysis of a mathematical model of SARS-CoV-2 transmission. Given that the pandemic is already underway and controls have already been initiated, we calibrated our model to data from the US and focused our analysis on optimal controls from May 2020 through December 2021. We found that a major factor that differentiates strategies that prioritize lives saved versus reduced time under control is how quickly control is relaxed once social distancing restrictions expire in May 2020. Strategies that maintain control at a high level until summer 2020 allow for tapering of control thereafter and minimal deaths, whereas strategies that relax control in the short term lead to fewer options for control later and a higher likelihood of exceeding hospital capacity. Our results also highlight that the potential scope for controlling COVID-19 until a vaccine is available depends on epidemiological parameters about which there is still considerable uncertainty, including the basic reproduction number and the effectiveness of social distancing. In light of those uncertainties, our results do not constitute a quantitative forecast and instead provide a qualitative portrayal of possible outcomes from alternative approaches to control.

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