How and to what extent does the anti-social behavior of violating self-quarantine measures increase the spread of disease?

COVID-19 has shown that quarantine (or self-isolation) may be the only available tool against an unknown infectious disease if neither an effective vaccine nor anti-viral medication is available. Motivated by the fact that a considerable number of people were not compliant with the request for self-quarantine made by public authorities, this study used a multi-agent simulation model, whose results were validated by theory work, which highlights how and to what extent such an anti-social behavior hampers the confinement of a disease. Our framework quantifies two important scenarios: in one scenario a certain number of individuals totally ignore quarantine, whereas in the second scenario a larger number of individuals partially ignore the imposed policy. Our results reveal that the latter scenario can be more hazardous even if the total amount of social deficit of activity-measured by the total number of severed links in a physical network-would be same as the former scenario has, of which quantitative extent is dependent on the fraction of asymptomatic infected cases and the level of quarantine intensity the government imposing. Our findings have significance not only to epidemiology but also to research in the broader field of network science. PACS numbers: Theory and modeling; computer simulation, 87.15.Aa; Dynamics of evolution, 87.23.Kg.

Investigating the trade-off between self-quarantine and forced quarantine provisions to control an epidemic: An evolutionary approach.

During a pandemic event like the present COVID-19, self-quarantine, mask-wearing, hygiene maintenance, isolation, forced quarantine, and social distancing are the most effective nonpharmaceutical measures to control the epidemic when the vaccination and proper treatments are absent. In this study, we proposed an epidemiological model based on the SEIR dynamics along with the two interventions defined as self-quarantine and forced quarantine by human behavior dynamics. We consider a disease spreading through a population where some people can choose the self-quarantine option of paying some costs and be safer than the remaining ones. The remaining ones act normally and send to forced quarantine by the government if they get infected and symptomatic. The government pays the forced quarantine costs for individuals, and the government has a budget limit to treat the infected ones. Each intervention derived from the so-called behavior model has a dynamical equation that accounts for a proper balance between the costs for each case, the total budget, and the risk of infection. We show that the infection peak cannot be reduced if the authority does not enforce a proactive (quantified by a higher sensitivity parameter) intervention. While comparing the impact of both self- and forced quarantine provisions, our results demonstrate that the latter is more influential to reduce the disease prevalence and the social efficiency deficit (a gap between social optimum payoff and equilibrium payoff).

Stochasticity of disease spreading derived from the microscopic simulation approach for various physical contact networks.

COVID-19 has emphasized that a precise prediction of a disease spreading is one of the most pressing and crucial issues from a social standpoint. Although an ordinary differential equation (ODE) approach has been well established, stochastic spreading features might be hard to capture accurately. Perhaps, the most important factors adding such stochasticity are the effect of the underlying networks indicating physical contacts among individuals. The multi-agent simulation (MAS) approach works effectively to quantify the stochasticity. We systematically investigate the stochastic features of epidemic spreading on homogeneous and heterogeneous networks. The study quantitatively elucidates that a strong microscopic locality observed in one- and two-dimensional regular graphs, such as ring and lattice, leads to wide stochastic deviations in the final epidemic size (FES). The ensemble average of FES observed in this case shows substantial discrepancies with the results of ODE based mean-field approach. Unlike the regular graphs, results on heterogeneous networks, such as Erdos-Rényi random or scale-free, show less stochastic variations in FES. Also, the ensemble average of FES in heterogeneous networks seems closer to that of the mean-field result. Although the use of spatial structure is common in epidemic modeling, such fundamental results have not been well-recognized in literature. The stochastic outcomes brought by our MAS approach may lead to some implications when the authority designs social provisions to mitigate a pandemic of un-experienced infectious disease like COVID-19.

Free ticket, discount ticket or intermediate of the best of two worlds - Which subsidy policy is socially optimal to suppress the disease spreading?

With the aid of the evolutionary vaccination game on a scale-free network, we design a new subsidy policy, named degree dependent subsidy, where cooperative agents get incentives according to their connectivity or degree. That is, agents, having a greater degree, receive a higher incentive, and vice versa. Here we presume that vaccinators are cooperative agents. The new scheme can be said to an intermediate policy between two previously studies policies, namely free ticket and flat discount policies. The former policy distributes free tickets to cooperative hub agents as a priority, whereas the latter dispenses a fixed discount to every cooperator. We compare the efficiency of each policy in terms of having a less infectious state with a minimum social cost. While investigating the performance of the three policies in terms of average social payoff-which takes into account the cost of vaccination as well as infection-the free ticket scheme is found to be the most appealing policies among the three when the budget for subsidy is quite low. The degree dependent subsidy policy outperforms others for a moderate budget size, while the flat discount policy requires a higher budget to effectively suppress the disease. We further estimate threshold levels of the subsidy budget for each policy beyond which subsidizing results in excessive use of vaccination. As a whole, concerning vaccination coverage and final epidemic size, the degree-dependent subsidy scheme outperforms the flat discount scheme, but is dominated by the free ticket policy.

An agent-based nested model integrating within-host and between-host mechanisms to predict an epidemic.

The COVID-19 pandemic has remarkably heightened concerns regarding the prediction of communicable disease spread. This study introduces an innovative agent-based modeling approach. In this model, the quantification of human-to-human transmission aligns with the dynamic variations in the viral load within an individual, termed "within-host" and adheres to the susceptible-infected-recovered (SIR) process, referred to as "between-host." Variations in the viral load over time affect the infectivity between individual agents. This model diverges from the traditional SIR model, which employs a constant transmission probability, by incorporating a dynamic, time-dependent transmission probability influenced by the viral load in a host agent. The proposed model retains the time-integrated transmission probability characteristic of the conventional SIR model. As observed in this model, the overall epidemic size remains consistent with the predictions of the standard SIR model. Nonetheless, compared to predictions based on the classical SIR process, notable differences existed in the peak number of the infected individuals and the timing of this peak. These nontrivial differences are induced by the direct correlation between the time-evolving transmission probability and the viral load within a host agent. The developed model can inform targeted intervention strategies and public health policies by providing detailed insights into disease spread dynamics, crucial for effectively managing epidemics.

Time delay of the appearance of a new strain can affect vaccination behavior and disease dynamics: An evolutionary explanation.

The emergence of a novel strain during a pandemic, like the current COVID-19, is a major concern to the healthcare system. The most effective strategy to control this type of pandemic is vaccination. Many previous studies suggest that the existing vaccine may not be fully effective against the new strain. Additionally, the new strain's late arrival has a significant impact on the disease dynamics and vaccine coverage. Focusing on these issues, this study presents a two-strain epidemic model in which the new strain appears with a time delay. We considered two vaccination provisions, namely preinfection and postinfection vaccinations, which are governed by human behavioral dynamics. In such a framework, individuals have the option to commit vaccination before being infected with the first strain. Additionally, people who forgo vaccination and become infected with the first train have the chance to be vaccinated (after recovery) in an attempt to avoid infection from the second strain. However, a second strain can infect vaccinated and unvaccinated individuals. People may have additional opportunities to be vaccinated and to protect themselves from the second strain due to the time delay. Considering the cost of the vaccine, the severity of the new strain, and the vaccine's effectiveness, our results indicated that delaying the second strain decreases the peak size of the infected individuals. Finally, by estimating the social efficiency deficit, we discovered that the social dilemma for receiving immunization decreases with the delay in the arrival of the second strain.

Investigating the efficiency of dynamic vaccination by consolidating detecting errors and vaccine efficacy.

Vaccination, if available, is the best preventive measure against infectious diseases. It is, however, needed to prudently design vaccination strategies to successfully mitigate the disease spreading, especially in a time when vaccine scarcity is inevitable. Here we investigate a vaccination strategy on a scale-free network where susceptible individuals, who have social connections with infected people, are being detected and given vaccination before having any physical contact with the infected one. Nevertheless, detecting susceptible (also infected ones) may not be perfect due to the lack of information. Also, vaccines do not confer perfect immunity in reality. We incorporate these pragmatic hindrances in our analysis. We find that if vaccines are highly efficacious, and the detecting error is low, then it is possible to confine the disease spreading-by administering a less amount of vaccination-within a short period. In a situation where tracing susceptible seems difficult, then expanding the range for vaccination targets can be socially advantageous only if vaccines are effective enough. Our analysis further reveals that a more frequent screening for vaccination can reduce the effect of detecting errors. In the end, we present a link percolation-based analytic method to approximate the results of our simulation.

Impact of the baseline payoff on evolutionary outcomes.

Do individuals enjoying a higher baseline payoff behave similarly in competitive scenarios compared to their counterparts? The classical replicator equation does not answer such a question since it is invariant to the background or baseline payoff of individuals. In reality, however, if one's baseline payoff is higher than the possible payoffs of an interaction (or game), the individual may respond generously or indifferently if s(he) is satisfied with the prevailing benchmark payoff. This work intends to explore such a phenomenon within the realm of pairwise interactions-taking the prisoner's dilemma as a metaphor-in well-mixed finite and infinite populations. In this framework, a player uses the payoff (comprising baseline and game payoffs) -expectation difference to estimate a degree of eagerness and, with that degree of eagerness, revises his or her strategy with a certain probability. We adopt two approaches to explore such a context, naming them as the Fermi and imitation processes, in which the former uses a pairwise Femi function and the latter considers the relative fitness to estimate probabilities for strategy revision. In a finite population, we examine the effect of intensities to payoff-expectation and strategic payoff differences (denoted by k_{1} and k_{2}, respectively) as well as the level of contentment (ω) on the fixation probability and fixation time (for a single defector). We observe that the fixation probability surges with the increase of intensity parameters. Nevertheless, the maximum fixation probability may require a substantially larger time to fixate, especially when the expectation is lower than the baseline payoff. This means that cooperators can persist for a longer period of time. A higher expectation or greed, however, considerably reduces the fixation time. Interestingly, our numerical simulation reveals that both approaches are equivalent under weak k_{2}(≪1) in the Fermi process. We further derive mean-field equations for both approaches in the context of an infinite population, where we observe two possible evolutionary consequences: either full-scale defection or the persistence of the initial frequency of cooperators. The latter scenario indicates players' uninterested or neutral behavior in relation to the interaction due to their satisfaction on the baseline payoff.

Evolution of cooperation in social dilemmas under the coexistence of aspiration and imitation mechanisms.

Imitation and aspiration update rules are frequently observed in human and animal populations. While the imitation process entails payoff comparisons with surroundings, the aspiration process refers to self-evaluation. This work explores the evolution of cooperation in dyadic games under the coexistence of these two dynamics in an infinitely large well-mixed population. Two situations have been explored: (i) individuals adopt either an imitation or aspiration update rule with a certain probability, and (ii) the entire population is divided into two groups where one group only uses imitative rules and the other obeys aspiration updating alone. Both premises have been modeled by taking an infinite approximation of the finite population. In particular, the second mixing principle follows an additive property: the outcome of the whole population is the weighted average of outcomes from imitators and aspiration-driven individuals. Our work progressively investigates several variants of aspiration dynamics under strong selection, encompassing symmetric, asymmetric, and adaptive aspirations, which then coalesce with imitative dynamics. We also demonstrate which of the update rules performs better, under different social dilemmas, by allowing the evolution of the preference of update rules besides strategies. Aspiration dynamics always outperform imitation dynamics in the prisoner's dilemma, however, in the chicken and stag-hunt games the predominance of either update rule depends on the level of aspirations as well as on the extent of greed and fear present in the system. Finally, we examine the coevolution of strategies, aspirations, and update rules which leads to a binary state of obeying either imitation or aspiration dynamics. In such a circumstance, when aspiration dynamics prevail over imitation dynamics, cooperators and defectors coexist to an equal extent.

Social efficiency deficit deciphers social dilemmas.

What do corruption, resource overexploitation, climate inaction, vaccine hesitancy, traffic congestion, and even cancer metastasis have in common? All these socioeconomic and sociobiological phenomena are known as social dilemmas because they embody in one form or another a fundamental conflict between immediate self-interest and long-term collective interest. A shortcut to the resolution of social dilemmas has thus far been reserved solely for highly stylised cases reducible to dyadic games (e.g., the Prisoner's Dilemma), whose nature and outcome coalesce in the concept of dilemma strength. We show that a social efficiency deficit, measuring an actor's potential gain in utility or fitness by switching from an evolutionary equilibrium to a social optimum, generalises dilemma strength irrespective of the underlying social dilemma's complexity. We progressively build from the simplicity of dyadic games for which the social efficiency deficit and dilemma strength are mathematical duals, to the complexity of carcinogenesis and a vaccination dilemma for which only the social efficiency deficit is numerically calculable. The results send a clear message to policymakers to enact measures that increase the social efficiency deficit until the strain between what is and what could be incentivises society to switch to a more desirable state.

Interplay between cost and effectiveness in influenza vaccine uptake: a vaccination game approach.

Pre-emptive vaccination is regarded as one of the most protective measures to control influenza outbreak. There are mainly two types of influenza viruses-influenza A and B with several subtypes-that are commonly found to circulate among humans. The traditional trivalent (TIV) flu vaccine targets two strains of influenza A and one strain of influenza B. The quadrivalent (QIV) vaccine targets one extra B virus strain that ensures better protection against influenza; however, the use of QIV vaccine can be costly, hence impose an extra financial burden to society. This scenario might create a dilemma in choosing vaccine types at the individual level. This article endeavours to explain such a dilemma through the framework of a vaccination game, where individuals can opt for one of the three options: choose either of QIV or TIV vaccine or none. Our approach presumes a mean-field framework of a vaccination game in an infinite and well-mixed population, entangling the disease spreading process of influenza with the coevolution of two types of vaccination decision-making processes taking place before an epidemic season. We conduct a series of numerical simulations as an attempt to illustrate different scenarios. The framework has been validated by the so-called multi-agent simulation (MAS) approach.