Non-Pharmaceutical Interventions and Vaccination Controls in a Stochastic SIVR Epidemic Model

Mahrouf, Marouane; Lotfi, El Mehdi; Hattaf, Khalid; Yousfi, Noura

doi:10.1007/s12591-020-00538-4

Cited by 8 publications

(6 citation statements)

References 22 publications

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“…Hence, to model using preventive medicines as an intervention, modelers use different ways to describe the cost and inconvenience of using preventive medicines than getting a vaccine. Many researchers have studied the effect of vaccination on the spreading process [2,11,16,49,59,82,86,112,129], which can be modeled in several ways. One way is to reduce the infection rate between an infectious and a vaccinated individual to β vac < β while those who are not vaccinated suffer a higher infection rate β [2,11,16,59,82,112].…”

Section: How Are Interventions Modeled?mentioning

confidence: 99%

“…How small β vac is depends on the efficacy of the vaccine distributed. Another way to create a new compartment called 'Vaccinated' and the rate at which individuals exit this compartment captures the protection duration of the vaccines [1,86]. The use of antidotes and the deployment of mass treatment accelerate the recovery process.…”

Section: How Are Interventions Modeled?mentioning

confidence: 99%

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Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review

Huang

Zhu

2022

Dyn Games Appl

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This review presents and reviews various solved and open problems in developing, analyzing, and mitigating epidemic spreading processes under human decision-making. We provide a review of a range of epidemic models and explain the pros and cons of different epidemic models. We exhibit the art of coupling between epidemic models and decision models in the existing literature. More specifically, we provide answers to fundamental questions in human decision-making amid epidemics, including what interventions to take to combat the disease, who are decision-makers, and when and how to take interventions, and how to make interventions. Among many decision models, game-theoretic models have become increasingly crucial in modeling human responses or behavior amid epidemics in the last decade. In this review, we motivate the game-theoretic approach to human decision-making amid epidemics. This review provides an overview of the existing literature by developing a multi-dimensional taxonomy, which categorizes existing literature based on multiple dimensions, including (1) types of games, such as differential games, stochastic games, evolutionary games, and static games; (2) types of interventions, such as social distancing, vaccination, quarantine, and taking antidotes; (3) the types of decision-makers, such as individuals, adversaries, and central authorities at different hierarchical levels. A fine-grained dynamic game framework is proposed to capture the essence of game-theoretic decision-making amid epidemics. We showcase three representative frameworks with unique ways of integrating game-theoretic decision-making into the epidemic models from a vast body of literature. Each of the three frameworks has their unique way of modeling and analyzing and develops results from different angles. In the end, we identify several main open problems and research gaps left to be addressed and filled. KeywordsDynamic games • Stochastic games • Infectious diseases • Epidemic spreading • Human-in-the-loop systems • COVID-19 This article is part of the topical collection "Modeling and Control of Epidemics" edited by Quanyan Zhu,

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Section: How Are Interventions Modeled?mentioning

confidence: 99%

Section: How Are Interventions Modeled?mentioning

confidence: 99%

Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review

Huang

Zhu

2022

Dyn Games Appl

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show abstract

“…Pharmaceutical interventions can be adopted when vaccines, antidotes, or effective treatment methods are available. Many works have studied the effect of vaccination on the spreading process [2,6,11,40,50,68,71,89,101], which can be modeled in several ways. One way is to reduce the infection rate between an infectious and a vaccinated individual to 𝛽 𝑣 𝑎𝑐 < 𝛽 while those who are not vaccinated suffer a higher infection rate 𝛽 [2,6,11,50,68,89].…”

Section: How Are Interventions Modeled?mentioning

confidence: 99%

“…How small 𝛽 vac is depends on the efficacy of the vaccine distributed. Another way to create a new compartment called 'Vaccinated' and the rate at which individuals exit this compartment captures the protection duration of the vaccines [1,71]. The use of antidotes and the deployment of mass treatment accelerate the recovery process.…”

Section: How Are Interventions Modeled?mentioning

confidence: 99%

Game-Theoretic Frameworks for Epidemic Spreading and Human Decision Making: A Review

Huang¹,

Zhu²

2021

Preprint

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This review presents and reviews various solved and open problems in developing, analyzing, and mitigating epidemic spreading processes under human decision-making. We provide a review of a range of epidemic models and explain the pros and cons of different epidemic models. We exhibit the art of coupling epidemic models and decision models in the existing literature. More specifically, fundamental questions in human decision-making amid epidemics such as what interventions are taken to combat the disease, who are decisionmakers, when interventions are taken, and how interventions are modeled.Among many decision models, game-theoretic models have become increasingly crucial in modeling human responses/behavior amid epidemics in the last decade. In this review, we motivate the game-theoretic approach to human decision-making amid epidemics. This review provides an overview of the existing literature by developing a multi-dimensional taxonomy, which categorizes existing works based on multiple dimensions, including 1) types of games, such as differential games, stochastic games, evolutionary games, and static games; 2) types of interventions, such as social distancing, vaccination, quarantine, taking antidotes, etc.; 3) the types of decision-makers, such as individuals, adversaries, and central authorities at different hierarchical levels. A fine-grained dynamic game framework is proposed to capture the essence of game-theoretic decision-making amid epidemics. From a vast body of works, we showcase three representative works with unique ways of integrating gametheoretic decision-making into the epidemic models. The uniqueness of each of these three works distinguishes from each other regarding their models, analytical approaches, and results. In the end, we identify several main open problems and research gaps left to be addressed and filled.

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“…Accordingly, compartmental epidemiological models with vaccination have been widely investigated by many researchers [22][23][24][25][26]. For this matter, vaccination strategy can be modeled by two main approaches where the vaccinated population can be modeled by incorporating another new compartment [26,28], or it can be included implicity in the other existing compartments by means of new parameter representing the effect of vaccination [22,27].…”

Section: Introductionmentioning

confidence: 99%

Stochastic and deterministic analysis of a COVID-19 pandemic model under vaccination strategy : Real cases application

Ez-zetouni

Khyar

Allali

et al. 2022

Preprint

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In this paper, we present a novel SICVS COVID-19 pandemic model incorporating a vaccination strategy and crowding effect. First, we investigate the steady states and proved the local stability of the corresponding deterministic problem. Then we study the proposed stochastic epidemic model; we have considered a random incidence highlighting all the improbable fluctuations that appear in the infection process. Hence, the COVID 19 transmission parameter in the considered model will be stochastically perturbed by the white noise. We show the disease extinction of the pandemic according to the stochastic noise intensity. It was established, in the stochastic study, the existence of a possible extinction of the pandemic even if the base reproduction number is greater than unity. Furthermore we discuss the persistence in mean of the studied infection in terms of the stochastic model parameters. Our numerical simulations confirm the theoretical findings. The proposed model was validated and supported by a comparison, during the second wave of the pandemic in Morocco, between the trajectories of the clinical data of Covid-19 and those which represent our SICVS model. In addition, the impact of vaccination and social distancing strategies on reducing the infection severity were observed.

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Non-Pharmaceutical Interventions and Vaccination Controls in a Stochastic SIVR Epidemic Model

Cited by 8 publications

References 22 publications

Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review

Game-Theoretic Frameworks for Epidemic Spreading and Human Decision-Making: A Review

Game-Theoretic Frameworks for Epidemic Spreading and Human Decision Making: A Review

Stochastic and deterministic analysis of a COVID-19 pandemic model under vaccination strategy : Real cases application

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