Vaccination behavior by coupling the epidemic spreading with the human decision under the game theory

Wang, Xinyu; Jia, Dawei; Gao, Shupeng; Xia, Chengyi; Li, Xuelong; Wang, Zhen

doi:10.1016/j.amc.2020.125232

Cited by 27 publications

(17 citation statements)

References 36 publications

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“…This was later generalized into the so-called ‘vaccination games’ framework (see [24] for a comprehensive review). Such approach led to many interesting observations and predictions in vaccination protocols [14] , [47] , [48] , [49] , [50] , [51] , [52] , [53] , [54] , [55] , [56] , [57] , [58] , [59] , [60] .…”

Section: Introductionmentioning

confidence: 99%

An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics

Amaral

Oliveira

Javarone

2021

Chaos, Solitons & Fractals

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During pandemic events, strategies such as social distancing can be fundamental to reduce simultaneous infections and mitigate the disease spreading, which is very relevant to the risk of a healthcare system collapse. Although these strategies can be recommended, or even imposed, their actual implementation may depend on the population perception of the risks associated with a potential infection. The current COVID-19 crisis, for instance, is showing that some individuals are much more prone than others to remain isolated. To better understand these dynamics, we propose an epidemiological SIR model that uses evolutionary game theory for combining in a single process social strategies, individual risk perception, and viral spreading. In particular, we consider a disease spreading through a population, whose agents can choose between self-isolation and a lifestyle careless of any epidemic risk. The strategy adoption is individual and depends on the perceived disease risk compared to the quarantine cost. The game payoff governs the strategy adoption, while the epidemic process governs the agent’s health state. At the same time, the infection rate depends on the agent’s strategy while the perceived disease risk depends on the fraction of infected agents. Our results show recurrent infection waves, which are usually seen in previous historic epidemic scenarios with voluntary quarantine. In particular, such waves re-occur as the population reduces disease awareness. Notably, the risk perception is found to be fundamental for controlling the magnitude of the infection peak, while the final infection size is mainly dictated by the infection rates. Low awareness leads to a single and strong infection peak, while a greater disease risk leads to shorter, although more frequent, peaks. The proposed model spontaneously captures relevant aspects of a pandemic event, highlighting the fundamental role of social strategies.

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Section: Introductionmentioning

confidence: 99%

An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics

Amaral

Oliveira

Javarone

2021

Chaos, Solitons & Fractals

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“…There are several variants [2][3][4][5][6][7][8][9][10] of the SIR model, including stochastic variants [11][12][13][14][15][16][17][18][19][20][21][22][23][24] and there is a large amount of related work in the context of the SIR model in the presence of vaccination. Many works deal with vaccination strategies [13,[25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43], transmission among an interconnected group or population [44] and vaccination behavior by coupling the epidemic spreading with human decisions [45], or policies [46,47] using the SIR model with limited resources [48]. One of the classical v...…”

Section: Introductionmentioning

confidence: 99%

Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations

Schlickeiser

Kröger

2021

Physics

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With the vaccination against Covid-19 now available, how vaccination campaigns influence the mathematical modeling of epidemics is quantitatively explored. In this paper, the standard susceptible-infectious-recovered/removed (SIR) epidemic model is extended to a fourth compartment, V, of vaccinated persons. This extension involves the time t-dependent effective vaccination rate, v(t), that regulates the relationship between susceptible and vaccinated persons. The rate v(t) competes with the usual infection, a(t), and recovery, μ(t), rates in determining the time evolution of epidemics. The occurrence of a pandemic outburst with rising rates of new infections requires k+b<1−2η, where k=μ(0)/a(0) and b=v(0)/a(0) denote the initial values for the ratios of the three rates, respectively, and η≪1 is the initial fraction of infected persons. Exact analytical inverse solutions t(Q) for all relevant quantities Q=[S,I,R,V] of the resulting SIRV model in terms of Lambert functions are derived for the semi-time case with time-independent ratios k and b between the recovery and vaccination rates to the infection rate, respectively. These inverse solutions can be approximated with high accuracy, yielding the explicit time-dependences Q(t) by inverting the Lambert functions. The values of the three parameters k, b and η completely determine the reduced time evolution of the SIRV-quantities Q(τ). The influence of vaccinations on the total cumulative number and the maximum rate of new infections in different countries is calculated by comparing with monitored real time Covid-19 data. The reduction in the final cumulative fraction of infected persons and in the maximum daily rate of new infections is quantitatively determined by using the actual pandemic parameters in different countries. Moreover, a new criterion is developed that decides on the occurrence of future Covid-19 waves in these countries. Apart from in Israel, this can happen in all countries considered.

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“…A crucial aspect of controlling epidemic processes is human behavior and the strategic interactions among individuals, which determine their decisions over time in response to their (perceived) payoffs. Game theory provides a natural framework and tools for studying such strategic interactions, and several recent studies adopted an evolutionary or population game framework [18][19][20][21][22][23][24][25][26][27][28][29]. We refer an interested reader to [30] and references therein for a comprehensive survey of earlier studies.…”

Section: Related Literaturementioning

confidence: 99%

Epidemic Population Games With Nonnegligible Disease Death Rate

Certorio¹,

Martins²,

La³

2022

Preprint

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A recent article that combines normalized epidemic compartmental models and population games put forth a system theoretic approach to capture the coupling between a population's strategic behavior and the course of an epidemic. It introduced a payoff mechanism that governs the population's strategic choices via incentives, leading to the lowest endemic proportion of infectious individuals subject to cost constraints. Under the assumption that the disease death rate is approximately zero, it uses a Lyapunov function to prove convergence and formulate a quasi-convex program to compute an upper bound for the peak size of the population's infectious fraction. In this article, we generalize these results to the case in which the disease death rate is nonnegligible. This generalization brings on additional coupling terms in the normalized compartmental model, leading to a more intricate Lyapunov function and payoff mechanism. Moreover, the associated upper bound can no longer be determined exactly, but it can be computed with arbitrary accuracy by solving a set of convex programs.

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Vaccination behavior by coupling the epidemic spreading with the human decision under the game theory

Cited by 27 publications

References 36 publications

An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics

An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics

Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations

Epidemic Population Games With Nonnegligible Disease Death Rate

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