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Register a new userBraesss Paradox in Epidemic Game: Better Condition Results in Less Payoff
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Facing the threats of infectious diseases, we take various actions to protect ourselves, but few studies considered an evolving system with competing strategies. In view of that, we propose an evolutionary epidemic model coupled with human behaviors, where individuals have three strategies: vaccination, self-protection and laissez faire, and could adjust their strategies according to their neighbors strategies and payoffs at the beginning of each new season of epidemic spreading. We found a counter-intuitive phenomenon analogous to the well-known emph{Braesss Paradox}, namely a better condition may lead to worse performance. Specifically speaking, increasing the successful rate of self-protection does not necessarily reduce the epidemic size or improve the system payoff. This phenomenon is insensitive to the network topologies, and can be well explained by a mean-field approximation. Our study demonstrates an important fact that a better condition for individuals may yield a worse outcome for the society.
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Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this paper we analyze the combined effect of these two ingredients on epidemic dynamics on networks. We study the susceptible-infected-susceptible (SIS) and the susceptible-infected-removed (SIR) models on the recently introduced activity-driven networks with memory. By means of an activity-based mean-field approach we derive, in the long time limit, analytical predictions for the epidemic threshold as a function of the parameters describing the distribution of activities and the strength of the memory effects. Our results show that memory reduces the threshold, which is the same for SIS and SIR dynamics, therefore favouring epidemic spreading. The theoretical approach perfectly agrees with numerical simulations in the long time asymptotic regime. Strong aging effects are present in the preasymptotic regime and the epidemic threshold is deeply affected by the starting time of the epidemics. We discuss in detail the origin of the model-dependent preasymptotic corrections, whose understanding could potentially allow for epidemic control on correlated temporal networks.
We study a multi-type SIR epidemic process among a heterogeneous population that interacts through a network. When we base social contact on a random graph with given vertex degrees, we give limit theorems on the fraction of infected individuals. For a given social distancing individual strategies, we establish the epidemic reproduction number $R_0$ which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper we study the equilibrium of the social distancing game, in which individuals choose their social distancing level according to an anticipated global infection rate, which then must equal the actual infection rate following their choices. We give conditions for the existence and uniqueness of equilibrium. For the case of random regular graphs, we show that voluntary social distancing will always be socially sub-optimal.
The detection and management of diseases become quite complicated when pathogens contain asymptomatic phenotypes amongst their ranks, as evident during the recent COVID-19 pandemic. Spreading of diseases has been studied extensively under the paradigm of Susceptible - Infected - Recovered - Deceased (SIRD) dynamics. Various game-theoretic approaches have also addressed disease spread, many of which consider S, I, R, and D as strategies rather than as states. Remarkably, most studies from the above approaches do not account for the distinction between the symptomatic or asymptomatic aspect of the disease. It is well-known that precautionary measures like washing hands, wearing masks and social distancing significantly mitigate the spread of many contagious diseases. Herein, we consider the adoption of such precautions as strategies and treat S, I, R, and D as states. We also attempt to capture the differences in epidemic spreading arising from symptomatic and asymptomatic diseases on various network topologies. Through extensive computer simulations, we examine that the cost of maintaining precautionary measures as well as the extent of mass testing in a population affects the final fraction of socially responsible individuals. We observe that the lack of mass testing could potentially lead to a pandemic in case of asymptomatic diseases. Network topology also seems to play an important role. We further observe that the final fraction of proactive individuals depends on the initial fraction of both infected as well as proactive individuals. Additionally, edge density can significantly influence the overall outcome. Our findings are in broad agreement with the lessons learnt from the ongoing COVID-19 pandemic.
The importance of a strict quarantine has been widely debated during the COVID-19 epidemic even from the purely epidemiological point of view. One argument against strict lockdown measures is that once the strict quarantine is lifted, the epidemic comes back, and so the cumulative number of infected individuals during the entire epidemic will stay the same. We consider an SIR model on a network and follow the disease dynamics, modeling the phases of quarantine by changing the node degree distribution. We show that the system reaches different steady states based on the history: the outcome of the epidemic is path-dependent despite the same final node degree distribution. The results indicate that two-phase route to the final node degree distribution (a strict phase followed by a soft phase) are always better than one phase (the same soft one) unless all the individuals have the same number of connections at the end (the same degree); in the latter case, the overall number of infected is indeed history-independent. The modeling also suggests that the optimal procedure of lifting the quarantine consists of releasing nodes in the order of their degree - highest first.
Evolutionary dynamics in finite populations is known to fixate eventually in the absence of mutation. We here show that a similar phenomenon can be found in stochastic game dynamical batch learning, and investigate fixation in learning processes in a simple 2x2 game, for two-player games with cyclic interaction, and in the context of the best-shot network game. The analogues of finite populations in evolution are here finite batches of observations between strategy updates. We study when and how such fixation can occur, and present results on the average time-to-fixation from numerical simulations. Simple cases are also amenable to analytical approaches and we provide estimates of the behaviour of so-called escape times as a function of the batch size. The differences and similarities with escape and fixation in evolutionary dynamics are discussed.
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