Optimal Control of Multi-strain Epidemic Processes in Complex Networks

Gubar, Elena; Zhu, Quanyan; Taynitskiy, Vladislav

doi:10.1007/978-3-319-67540-4_10

Cited by 11 publications

(8 citation statements)

References 16 publications

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“…Since x ≥ 0 and 1 T xd = m d , equality holds in (15). Thus, we conclude that for i ∈ I d such that xd i > 0, i ∈ arg max i∈I d F d i (x).…”

Section: Equilibrium Analysismentioning

confidence: 77%

“…This model has been used to model spreading over networks for a diverse range of applications. For example, in [15], the authors have investigated multi-strain epidemic dynamics over complex networks to study the control policies when a single pathogen creates many strains of infections of different features. Another recent endeavor is [7], where the authors have focused on the optimal quarantining policies when multiple diseases coexist and have observed a switching phenomenon between equilibria.…”

Section: Related Workmentioning

confidence: 99%

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Herd Behaviors in Epidemics: A Dynamics-Coupled Evolutionary Games Approach

Liu¹,

Zhao²,

Zhu³

2021

Preprint

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The recent COVID-19 pandemic has led to an increasing interest in the modeling and analysis of infectious diseases. The pandemic has made a significant impact on the way we behave and interact in our daily life. The past year has witnessed a strong interplay between human behaviors and epidemic spreading. In this paper, we propose an evolutionary game-theoretic framework to study the coupled evolutions of herd behaviors and epidemics. Our framework extends the classical degree-based mean-field epidemic model over complex networks by coupling it with the evolutionary game dynamics. The statistically equivalent individuals in a population choose their social activity intensities based on the fitness or the payoffs that depend on the state of the epidemics. Meanwhile, the spreading of the infectious disease over the complex network is reciprocally influenced by the players' social activities. We analyze the coupled dynamics by studying the stationary properties of the epidemic for a given herd behavior and the structural properties of the game for a given epidemic process. The decisions of the herd turn out to be strategic substitutes. We formulate an equivalent finite-player game and an equivalent network to represent the interactions among the finite populations. We develop structurepreserving approximation techniques to study time-dependent properties of the joint evolution of the behavioral and epidemic dynamics. The resemblance between the simulated coupled dynamics and the real COVID-19 statistics in the numerical experiments indicates the predictive power of our framework.

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“…Since x ≥ 0 and 1 T xd = m d , equality holds in (15). Thus, we conclude that for i ∈ I d such that xd i > 0, i ∈ arg max i∈I d F d i (x).…”

Section: Equilibrium Analysismentioning

confidence: 77%

Section: Related Workmentioning

confidence: 99%

Herd Behaviors in Epidemics: A Dynamics-Coupled Evolutionary Games Approach

Liu¹,

Zhao²,

Zhu³

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Whereas models considering multiple viral strains are rare, one can still find in the literature optimal control approaches based on classical epidemiological models for two viral strains (Bentaleb et al, 2020;Gubar et al, 2017). These are general epidemiological models, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, the discrete network-based model of Gubar et al (2017) relies on individual control measures to be applied separately to each of the two strains.…”

Section: Introductionmentioning

confidence: 99%

Modelling and Optimal Control of Multi Strain Epidemics, with Application to COVID-19

Arruda,

Pastore,

Dias

et al. 2021

Preprint

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This work introduces a novel epidemiological model that simultaneously considers multiple viral strains, reinfections due to waning immunity response over time and an optimal control formulation. This enables us to derive optimal mitigation strategies over a prescribed time horizon under a more realistic framework that does not imply perennial immunity and a single strain, although these can also be derived as particular cases of our formulation. The model also allows estimation of the number of infections over time in the absence of mitigation strategies under any number of viral strains. We validate our approach in the light of the COVID-19 epidemic and present a number of experiments to shed light on the overall behaviour under one or

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“…Using a basic SEI model with saturated incidence rate, Baba et al [14] studied the effect of optimal controller and awareness on the dynamic of Tuberculosis. In these works and in many others (see [15][16][17][18][19][20] and the references therein) the authors have solved the formulated control problems using classical results of control theory, in particular the famous Pontryagin's minimum principle [21].…”

Section: Introduction and Problem Statementmentioning

confidence: 99%

A novel control set-valued approach with application to epidemic models

Boujallal

Elhia

Balatif

2020

J. Appl. Math. Comput.

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This work is considered in the framework of studies dedicated to the control problems, especially in epidemiology where the scientist are concerned to develop effective control strategies to minimize the number of infected individuals. In this paper, we set this problem as an asymptotic target control problem under mixed state-control constraints, for a general class of ordinary differential equations that model the temporal evolution of disease spread. The set of initial data, from which the number of infected people decrease to zero, is generated by a new type of Lyapunov functions defined in the sense of viability theory. The associated controls are provided via selections of adequately designed feedback map. The existence of such selections is improved by using Micheal selection theorem. Finally, an application to the SIRS epidemic model, with numerical simulations, is given to show the efficiency of our approach. To the best of our knowledge, our work is the first one that used a set-valued approach based on the viability theory to deal with an epidemic control problem.

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Optimal Control of Multi-strain Epidemic Processes in Complex Networks

Cited by 11 publications

References 16 publications

Herd Behaviors in Epidemics: A Dynamics-Coupled Evolutionary Games Approach

Herd Behaviors in Epidemics: A Dynamics-Coupled Evolutionary Games Approach

Modelling and Optimal Control of Multi Strain Epidemics, with Application to COVID-19

A novel control set-valued approach with application to epidemic models

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