Optimal Control of a Vaccinating Game toward Increasing Overall Coverage (original) (raw)
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Chaos, Solitons & Fractals, 2019
Pre-emptive vaccination policy used in controlling the rapid spreading of infectious diseases is considered as one of the most challenging issues imposed to mankind, causing enormous death tolls over the years. This paper dedicatedly studies the dilemma effect coming from the failure of getting perfect immunity to those individuals who committed vaccination earlier. Therefore, we propose a new theoretical model that slows down the infection spreading and also facilitates quicker recovery time than what the previous model does even if a vaccinator fails to obtain perfect immunity. We name this effect as the "positive secondary effect" of vaccination as it gives a second chance to the vaccinators which in return subdues the rapid spreading that helps in producing better social average payoff as well as keeping the final epidemic size smaller. Moreover, to address the positive secondary effect more precisely, we introduce two different parameters; namely, relaxation parameter (η) and foster parameter (δ) in two different directions to quantify the individual effects resulting from each of the parameter space as well as their superposition effect. An in-depth discussion focuses on the influential role played by our proposed model via discounting and faster recovery effects while a second chance is given to the vaccinators. In addition, we also examine the situation when discounting effect brought by η outperforms very much than its faster recovery controlled by δ as well as the superposition effects. Unlike all previous studies dealing with vaccination game, we pay much attention to investigating the secondary effect of imperfect vaccination policy. Our proposed theoretical scheme completely reproduces the decision-making process of choosing an imperfect provision based on evolutionary game theory entailed with the widely used SIR (Susceptible-Infected-Recovered) epidemic model. Without considering any spatial structure and perfect vaccination policy, our model presumes the population being infinite and well-mixed to represent the infection spreading dynamics mathematically. This study is conducted throughout using the so-called theoretical approach. Besides that, three different updating rules based on evolutionary game theory have also been considered to investigate all possible situations. Later on, we draw 2D full phase diagrams showing the final epidemic size, vaccination coverage, and average social payoff quantitatively. Finally, our theoretical result is compared with the counterpart result obtained from the multi-agent simulation (MAS) approach and a good agreement is found, hence the appropriateness of the proposed model is fully justified.
Adoption costs of new vaccines - A Stackelberg dynamic game with risk-perception transition states
Infectious Disease Modelling, 2018
Vaccination has become an integral part of public health, since an increase in overall vaccination in a given population contributes to a decline in infectious diseases and mortality. Vaccination also contributes to a lower rate of infection even for nonvaccinators due to herd immunity ((Brisson and Edmunds, 2002)). In this work we model human decision-making (with respect to a vaccination program in a single-payer health care provider country) using a leader-follower game framework. We then extend our model to a discrete dynamic game, where time passing is modelled by risk perception changes among population groups considering whether or not to vaccinate. The risk perception changes are encapsulated by probability transition matrices. We assume that the singlepayer provider has a given fixed budget which would not be sufficient to cover 100% of a new vaccine for the entire population. To increase the potential coverage, we propose the introduction of a partial vaccine adoption policy, whereby an individual would pay a portion of the vaccine price and the single payer would support the rest for the entire population. We show how this policy, together with changes in risk perceptions regarding vaccination, impact the strategic decisions of individuals in each group, the policy cost under budgetary constraints and, ultimately, how it impacts the overall uptake of the vaccine in the entire population.
Behavioral incentives in a vaccination-dilemma setting with optional treatment
Physical Review E
Social dilemmas are situations wherein individuals choose between selfish interest and common good. One example of this is the vaccination dilemma, in which an individual who vaccinates at a cost protects not only himself but also others by helping maintain a common good called herd immunity. There is, however, a strong incentive to forgo vaccination, thus avoiding the associated cost, all the while enjoying the protection of herd immunity. To analyze behavioral incentives in a vaccination-dilemma setting in which an optional treatment is available to infected individuals, we combined epidemiological and game-theoretic methodologies by coupling a disease-spreading model with treatment and an evolutionary decision-making model. Extensive numerical simulations show that vaccine characteristics are more important in controlling the treatment adoption than the cost of treatment itself. The main effect of the latter is that expensive treatment incentivizes vaccination, which somewhat surprisingly comes at a little cost to society. More surprising is that the margin for a true synergy between vaccine and treatment in reducing the final epidemic size is very small. We furthermore find that society-centered decision making helps protect herd immunity relative to individual-centered decision making, but the latter may be better in establishing a novel vaccine. These results point to useful policy recommendations as well as to intriguing future research directions.
Applied Mathematics and Computation, 2019
We build a new analytic scheme that competently reproduces the decision-making process of choosing an imperfect provision based on the evolutionary game theory dovetailed with the SIR model for epidemic spreading dynamics. Aside from considering the two extreme options whether or not taking vaccination, we consider an 'intermediate defense measure' (IDM) that emulates hand-washing, masking, gargling, and taking energy drinks, defined as the third strategy while taking vaccination as well as IDM at the same time as the fourth strategy. In the present study, each of the proposed three imperfect provisions is able to oppress infectious diseases like Flu, Influenza, Ebola, and SARS during an epidemic season with certain extent. Considering an infinite and well-mixed population, a new analytic framework is built to take care of those three cases instead of perfect vaccination. Unlike MAS (multi-agent simulation) approach we conduct our study throughout using the socalled theoretical approach. Besides that, three different strategy updating rules based on evolutionary game theory have also been considered in our proposed model. We successfully obtain phase diagrams showing the final epidemic size, social average payoff and the respective fractions of the different strategy holders using various values of effectiveness and efficiency coefficients. Finally, a comprehensive discussion is made with comparison among the two-, three-and four-strategy models to get a holistic idea justifying how imperfect provisions work during an epidemic spreading.
Medical Decision Making
Background Infectious diseases such as COVID-19 and HIV/AIDS are behaviorally challenging for persons, vaccine and drug companies, and donors. Methods In 3 linked games in which a disease may or may not be contracted, [Formula: see text] persons choose risky or safe behavior (game 1). Two vaccine companies (game 2) and 2 drug companies (game 3) choose whether to develop vaccines and drugs. Each person chooses whether to buy 1 vaccine (if no disease contraction) or 1 drug (if disease contraction). A donor subsidizes vaccine and drug developments and purchases. Nature probabilistically chooses disease contraction, recovery versus death with and without each drug, and whether vaccines and drugs are developed successfully. COVID-19 data are used for parameter estimation. Results Each person chooses risky behavior if its utility outweighs safe behavior, accounting for nature’s probability of disease contraction which depends on how many are vaccinated. Each person buys a vaccine or drug ...
Modeling Behavioral Response to Vaccination Using Public Goods Game
IEEE Transactions on Computational Social Systems, 2019
Epidemics of infectious disease can be traced back to the early days of mankind. Only in the last two centuries vaccination has become a viable strategy to prevent such epidemics. In addition to the clinical efficacy of this strategy, the behavior and public attitudes affect the success of vaccines. This paper describes modeling the efficacy of vaccination considering the cost and benefit of vaccination to individual players. The model is based on the public goods game and is presented as a spatial game on a lattice. Using this model, individuals can contribute to the public health by paying the cost of vaccination or choose to be protected by the public who is vaccinated rather than pay the cost and share the risk of vaccination. Thus, in this model individuals can choose to stay susceptible, can become infected, or choose to vaccinate once in each episode. This paper presents the behavioral changes of the population and the cost to the society as a function of the cost of vaccines, cost of being infected, and the "fear factor" created by the public media.
“Wait and see” vaccinating behaviour during a pandemic: A game theoretic analysis
Vaccine, 2011
During the 2009 H1N1 pandemic, many individuals did not seek vaccination immediately but rather decided to "wait and see" until further information was available on vaccination costs. This behaviour implies two sources of strategic interaction: as more individuals become vaccinated, both the perceived vaccination cost and the probability that susceptible individuals become infected decline. Here we analyze the outcome of these two strategic interactions by combining game theory with a disease transmission model during an outbreak of a novel influenza strain. The model exhibits a "wait and see" Nash equilibrium strategy, with vaccine delayers relying on herd immunity and vaccine safety information generated by early vaccinators. This strategic behaviour causes the timing of the epidemic peak to be strongly conserved across a broad range of plausible transmission rates, in contrast to models without such adaptive behaviour. The model exhibits not only feedback mechanisms but also a feed-forward mechanism: a high initial perceived vaccination cost perpetuates high perceived vaccine costs (and lower vaccine coverage) throughout the remainder of the outbreak. This suggests that any effect of risk communication at the start of a pandemic outbreak will be amplified compared to the same amount of risk communication effort distributed throughout the outbreak.
COVID-19 vaccine incentive scheduling using an optimally controlled reinforcement learning model
2022
We model Covid-19 vaccine uptake as a reinforcement learning dynamic between two populations: the vaccine adopters, and the vaccine hesitant. Using data available from the Center for Disease Control (CDC), we calculate a payoff matrix governing the dynamic interaction between these two groups and show they are playing a Hawk-Dove evolutionary game with an internal evolutionarily stable Nash equilibrium (the asymptotic percentage of vaccinated in the population). We then ask whether vaccine adoption can be improved by implementing dynamic incentive schedules that reward/punish the vaccine hesitant, and if so, what schedules are optimal and how effective are they likely to be? When is the optimal time to start an incentive program, and how large should the incentives be? By using a tailored replicator dynamic reinforcement learning model together with optimal control theory, we show that well designed and timed incentive programs can improve vaccine uptake by shifting the Nash equilib...
Disease Control through Voluntary Vaccination Decisions Based on the Smoothed Best Response
Computational and Mathematical Methods in Medicine, 2014
We investigate game-theory based decisions on vaccination uptake and its effects on the spread of an epidemic with nonlinear incidence rate. It is assumed that each individual's decision approximates his/her best response (called smoothed best response) in that this person chooses to take the vaccine based on its cost-benefit analysis. The basic reproduction number of the resultant epidemic model is calculated and used to characterize the existence and stability of the disease-free and endemic equilibria of the model. The effects on the spread and control of the epidemic are revealed in terms of the sensitivity of the response to changes in costs and benefits, in the "cost" of the vaccination, and in the proportion of susceptible individuals who are faced with the decision of whether or not to be vaccinated per unit time. The effects of the best response decision rule are also analyzed and compared to those of the smoothed best response. Our study shows that, when there is a perceived cost to take the vaccine, the smoothed best response is more effective in controlling the epidemic. However, when this cost is 0, the best response is the more efficient control.