Influence of waning immunity on vaccination decision-making: A multi-strain epidemic model with an evolutionary approach analyzing cost and efficacy.

In this research, we introduce a comprehensive epidemiological model that accounts for multiple strains of an infectious disease and two distinct vaccination options. Vaccination stands out as the most effective means to prevent and manage infectious diseases. However, when there are various vaccines available, each with its costs and effectiveness, the decision-making process for individuals becomes paramount. Furthermore, the factor of waning immunity following vaccination also plays a significant role in influencing these choices. To understand how individuals make decisions in the context of multiple strains and waning immunity, we employ a behavioral model, allowing an epidemiological model to be coupled with the dynamics of a decision-making process. Individuals base their choice of vaccination on factors such as the total number of infected individuals and the cost-effectiveness of the vaccine. Our findings indicate that as waning immunity increases, people tend to prioritize vaccines with higher costs and greater efficacy. Moreover, when more contagious strains are present, the equilibrium in vaccine adoption is reached more rapidly. Finally, we delve into the social dilemma inherent in our model by quantifying the social efficiency deficit (SED) under various parameter combinations.

Prosocial punishment bots breed social punishment in human players.

Prosocial punishment, an important factor to stabilize cooperation in social dilemma games, often faces challenges like second-order free-riders-who cooperate but avoid punishing to save costs-and antisocial punishers, who defect and retaliate against cooperators. Addressing these challenges, our study introduces prosocial punishment bots that consistently cooperate and punish free-riders. Our findings reveal that these bots significantly promote the emergence of prosocial punishment among normal players due to their 'sticky effect'-an unwavering commitment to cooperation and punishment that magnetically attracts their opponents to emulate this strategy. Additionally, we observe that the prevalence of prosocial punishment is greatly enhanced when normal players exhibit a tendency to follow a 'copying the majority' strategy, or when bots are strategically placed in high-degree nodes within scale-free networks. Conversely, bots designed for defection or antisocial punishment diminish overall cooperation levels. This stark contrast underscores the critical role of strategic bot design in enhancing cooperative behaviours in human/AI interactions. Our findings open new avenues in evolutionary game theory, demonstrating the potential of human-machine collaboration in solving the conundrum of punishment.

A mixed-flow model for heterogeneous vehicles enforcing a movement control protocol utilizing a vehicular size-based equilibrium speed function.

This work addressed the effect of heterogeneous vehicle sizes on traffic flow fields by introducing a movement control protocol. Considering a continuum traffic model, a new equilibrium velocity function that is dependent on traffic density was introduced to account for the effect of vehicle size. The established model showed a quantitative comparison between the Optimal Velocity and Full Velocity Difference models. A neutral stability test was carried out to evaluate the model's capability of neutralizing flow fields. The density wave behavior near a critical point was portrayed by deducing the Korteweg-de Vries-Burgers equation through a nonlinear analysis. A series of numerical simulations, the outcomes of which agreed well with the analytical results, was performed to observe the overall flow field scenario.

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.

Analyzing the Costs and Benefits of Utilizing a Mixed-Strategy Approach in Infectious Disease Control under a Voluntary Vaccination Policy.

Infectious diseases pose significant public health risks, necessitating effective control strategies. One such strategy is implementing a voluntary vaccination policy, which grants individuals the autonomy to make their own decisions regarding vaccination. However, exploring different approaches to optimize disease control outcomes is imperative, and involves assessing their associated costs and benefits. This study analyzes the advantages and disadvantages of employing a mixed-strategy approach under a voluntary vaccination policy in infectious disease control. We examine the potential benefits of such an approach by utilizing a vaccination game model that incorporates cost and benefit factors, where lower costs and higher benefits lead to reduced infection rates. Here, we introduce a mixed-strategy framework that combines individual-based risk assessment (IB-RA) and society-based risk assessment (SB-RA) strategies. A novel dynamical equation is proposed that captures the decision-making process of individuals as they choose their strategy based on personal or communal considerations. In addition, we explore the implications of the mixed-strategy approach within the context of social dilemmas. We examine deviations from expected behavior and the concept of social efficiency deficit (SED) by allowing for the evolution of vaccine strategy preferences alongside risk perception. By comprehensively evaluating the financial implications and societal advantages associated with the mixed-strategy approach, decision-makers can allocate resources and implement measures to combat infectious diseases within the framework of a voluntary vaccination policy.

Small bots, big impact: solving the conundrum of cooperation in optional Prisoner's Dilemma game through simple strategies.

Cooperation plays a crucial role in both nature and human society, and the conundrum of cooperation attracts the attention from interdisciplinary research. In this study, we investigated the evolution of cooperation in optional Prisoner's Dilemma games by introducing simple bots. We focused on one-shot and anonymous games, where the bots could be programmed to always cooperate, always defect, never participate or choose each action with equal probability. Our results show that cooperative bots facilitate the emergence of cooperation among ordinary players in both well-mixed populations and a regular lattice under weak imitation scenarios. Introducing loner bots has no impact on the emergence of cooperation in well-mixed populations, but it facilitates the dominance of cooperation in regular lattices under strong imitation scenarios. However, too many loner bots on a regular lattice inhibit the spread of cooperation and can eventually result in a breakdown of cooperation. Our findings emphasize the significance of bot design in promoting cooperation and offer useful insights for encouraging cooperation in real-world scenarios.

Impact of simplicial complexes on epidemic spreading in partially mapping activity-driven multiplex networks.

Over the past decade, the coupled spread of information and epidemic on multiplex networks has become an active and interesting topic. Recently, it has been shown that stationary and pairwise interactions have limitations in describing inter-individual interactions , and thus, the introduction of higher-order representation is significant. To this end, we present a new two-layer activity-driven network epidemic model, which considers the partial mapping relationship among nodes across two layers and simultaneously introduces simplicial complexes into one layer, to investigate the effect of 2-simplex and inter-layer mapping rate on epidemic transmission. In this model, the top network, called the virtual information layer, characterizes information dissemination in online social networks, where information can be diffused through simplicial complexes and/or pairwise interactions. The bottom network, named as the physical contact layer, denotes the spread of infectious diseases in real-world social networks. It is noteworthy that the correspondence among nodes between two networks is not one-to-one but partial mapping. Then, a theoretical analysis using the microscopic Markov chain (MMC) method is performed to obtain the outbreak threshold of epidemics, and extensive Monte Carlo (MC) simulations are also carried out to validate the theoretical predictions. It is obviously shown that MMC method can be used to estimate the epidemic threshold; meanwhile, the inclusion of simplicial complexes in the virtual layer or introductory partial mapping relationship between layers can inhibit the spread of epidemics. Current results are conducive to understanding the coupling behaviors between epidemics and disease-related information.

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.

An improved microscopic traffic model for heterogeneous vehicles using the vehicle's mass effect.

This study aims to develop a traffic model for heterogeneous vehicle movement, which introduces the vehicle's heterogeneity by considering the internal mass effect. We explore the behavioral characteristics of the flow field generated by the proposed model and provide a comparative analysis of the conventional model. A linear stability condition is deduced to showcase the model's capacity to neutralize flow. Nonlinear analysis is employed to derive the modified Korteweg-de Vries (mKdV) equation and its corresponding analytical solution, enabling the observation of traffic flow behavior in proximity to the neutral stability condition. A numerical simulation is then conducted, considering cyclic boundary conditions. The results indicate that the mass effect tends to absorb traffic jams provided no time delay is imposed.

Coupled spreading between information and epidemics on multiplex networks with simplicial complexes.

The way of information diffusion among individuals can be quite complicated, and it is not only limited to one type of communication, but also impacted by multiple channels. Meanwhile, it is easier for an agent to accept an idea once the proportion of their friends who take it goes beyond a specific threshold. Furthermore, in social networks, some higher-order structures, such as simplicial complexes and hypergraph, can describe more abundant and realistic phenomena. Therefore, based on the classical multiplex network model coupling the infectious disease with its relevant information, we propose a novel epidemic model, in which the lower layer represents the physical contact network depicting the epidemic dissemination, while the upper layer stands for the online social network picturing the diffusion of information. In particular, the upper layer is generated by random simplicial complexes, among which the herd-like threshold model is adopted to characterize the information diffusion, and the unaware-aware-unaware model is also considered simultaneously. Using the microscopic Markov chain approach, we analyze the epidemic threshold of the proposed epidemic model and further check the results with numerous Monte Carlo simulations. It is discovered that the threshold model based on the random simplicial complexes network may still cause abrupt transitions on the epidemic threshold. It is also found that simplicial complexes may greatly influence the epidemic size at a steady state.

Social dilemma in the excess use of antimicrobials incurring antimicrobial resistance.

The emergence of antimicrobial resistance (AMR) caused by the excess use of antimicrobials has come to be recognized as a global threat to public health. There is a 'tragedy of the commons' type social dilemma behind this excess use of antimicrobials, which should be recognized by all stakeholders. To address this global threat, we thus surveyed eight countries/areas to determine whether people recognize this dilemma and showed that although more than half of the population pays little, if any, attention to it, almost 20% recognize this social dilemma, and 15-30% of those have a positive attitude toward solving that dilemma. We suspect that increasing individual awareness of this social dilemma contributes to decreasing the frequency of AMR emergencies.

A dynamical traffic flow model for a cognitive drivers' sensitivity in Lagrangian scope.

A new microscopic traffic flow model is established based on heterogeneous driver's sensitivity; in this new model, the driver's sensitivity is defined as being dependent on the headway distances to the preceding vehicle, similar to Bando's optimal velocity function. We introduce the formulation of this cognitive driver's sensitivity utilizing a modified form of Bando's optimal velocity function. A simple methodology, which is used for improving Bando's optimal velocity function, has been implemented for developing the cognitive driver's sensitivity function, which establishes a correlation between the flow field's density and human drivers' responses. The model is highly advanced for introducing a human-driven traffic flow field considering the driver's mental behavioral activity. Using the linear stability condition, we elucidate a neutral stability condition. A series of numerical simulations indicates how the present model describes dynamics that differ from the conventional model, which assumes a constant driver's sensitivity.

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.

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 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.

A study on prosocial behavior of wearing a mask and self-quarantining to prevent the spread of diseases underpinned by evolutionary game theory.

In the wake of COVID-19, mask-wearing practice and self-quarantine is thought to be the most effective means of controlling disease spread. The current study develops an epidemiological model based on the SEIR process that takes into account dynamic human behavior toward those two preventive measures. In terms of quantifying the effect of wearing a mask, our model distinguishes itself by accounting for the effect of self-protection as well as the effect of reducing a potential risk to other individuals in different formulations. Each of the two measures derived from the so-called behavior model has a dynamical equation that takes into account the delicate balance between the cost of wearing a mask/self-quarantine and the risk of infection. The dynamical system as a whole contains a social dilemma structure because of whether to commit to preventing measures or seek the possibility of infection-free without paying anything. The numerical result was delivered along the social efficiency deficit, quantifying the extent to which Nash equilibrium has been improved to a social optimal state. PACS numbers Theory and modeling; computer simulation, 87.15.Aa; Dynamics of evolution, 87.23.Kg.

Effects of void nodes on epidemic spreads in networks.

We present the pair approximation models for susceptible-infected-recovered (SIR) epidemic dynamics in a sparse network based on a regular network. Two processes are considered, namely, a Markovian process with a constant recovery rate and a non-Markovian process with a fixed recovery time. We derive the implicit analytical expression for the final epidemic size and explicitly show the epidemic threshold in both Markovian and non-Markovian processes. As the connection rate decreases from the original network connection, the epidemic threshold in which epidemic phase transits from disease-free to endemic increases, and the final epidemic size decreases. Additionally, for comparison with sparse and heterogeneous networks, the pair approximation models were applied to a heterogeneous network with a degree distribution. The obtained phase diagram reveals that, upon increasing the degree of the original random regular networks and decreasing the effective connections by introducing void nodes accordingly, the final epidemic size of the sparse network is close to that of the random network with average degree of 4. Thus, introducing the void nodes in the network leads to more heterogeneous network and reduces the final epidemic size.

Study on Spirulina platensis growth employing non-linear analysis of biomass kinetic models.

Spirulina platensis has been considered a promising source of food supplement to combat malnutrition worldwide. Numerous investigations have stated its immune activity, ability to absorb CO2 during the growth period, and antioxidant potential. Well-known theoretical biomass kinetic model sheds are capable of qualitative analysis of the fast microalgae growth. In this regard, we considered eight popular biomass models: Monod, Haldane, Andrews & Noack, Teissier, Hinshelwood, Yano & Koga, Webb and, Aiba model comprising analytical investigation within the numerical simulation. Besides, in this study, we establish a new mathematical biomass growth model by merging the well-known Hinshelwood and Yano & Koga models. We explored the most suitable Spirulina growth model to minimize the overstated and understated growth trends in the assorted eight biomass kinetic models. Our findings show microalgae biomass growth and substrate diminishes along with time, and these results were compared with available experimental data. Results present a high value of R2(0.9862), a low value of RSS (0.0813), AIC (-9.7277), and BIC (-8.2148) implied significantly fitted with the investigated data for the growth of Spirulina platensis compared with popular eight studied models.

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.