Cost-efficiency analysis of voluntary vaccination against n-serovar diseases using antibody-dependent enhancement: A game approach.

Records of epidemics acknowledge immunological multi-serotype illnesses as an important aspect of the occurrence and control of contagious diseases. These patterns occur due to antibody-dependent-enhancement (ADE) among serotype diseases, which leads to infection of secondary infectious classes. One example of this is dengue hemorrhagic fever and dengue shock syndrome, which comprises the following four serotypes: DEN-1, DEN-2, DEN-3, and DEN-4. The evolutionary vaccination game approach is able to shed light on this long-standing issue in a bid to evaluate the success of various control programs. Although immunization is regarded as one of the most accepted approaches for minimizing the risk of infection, cost and efficiency are important factors that must also be considered. To analyze the n-serovar aspect alongside ADE consequence in voluntary vaccination, this study establishes a new mathematical epidemiological model that is dovetailed with evolutionary game theory, an approach through which we explored two vaccine programs: primary and secondary. Our findings illuminate that the 'cost-efficiency' effect for vaccination decision exhibits an impact on controlling n-serovar infectious diseases and should be designed in such a manner as to avoid adverse effects. Furthermore, our numerical result justifies the fact that adopting ADE significantly boosted emerging disease incidence, it also suggest that the joint vaccine policy works even better when the complex cyclical epidemic outbreak takes place among multi serotypes interactions. Research also exposes that the primary vaccine is a better controlling tool than the secondary; however, introducing a highly-efficiency secondary vaccine against secondary infection plays a key role to control the disease prevalence.

Enhancing vaccination strategies for epidemic control through effective lockdown measures.

Evolutionary epidemiology models have substantially impacted the study of various infections and prevention methods in the biology field. These models are called Susceptible, Lockdown, Vaccinated, Infected, and Recovered (SLVIR) epidemic dynamics. We explore how human behavior, particularly in the context of disease transmission, is influenced by two intervention strategies: vaccination and lockdown, both of which are grounded in the principles of evolutionary game theory (EGT). This comprehensive study using evolutionary game theory delves into the dynamics of epidemics, explicitly focusing on the transition rate from susceptibility to immunity and susceptibility to lockdown measures. Our research involves a thorough analysis of the structural aspects of the SLVIR epidemic model, which delineates disease-free equilibria to ensure stability in the system. Our investigation supports the notion that implementing lockdown measures effectively reduces the required level of vaccinations to curtail the prevalence of new infections. Furthermore, it highlights that combining both strategies is particularly potent when an epidemic spreads rapidly. In regions where the disease spreads comparatively more, our research demonstrates that lockdown measures are more effective in reducing the spread of the disease than relying solely on vaccines. Through significant numerical simulations, our research illustrates that integrating lockdown measures and efficient vaccination strategies can indirectly lower the risk of infection within the population, provided they are both dependable and affordable. The outcomes reveal a nuanced and beneficial scenario where we examine the interplay between the evolution of vaccination strategies and lockdown measures, assessing their coexistence through indicators of average social payoff.

Modelling the dynamic vaccination game with evolutionary feedback: exploring pairwise interactions and vaccine strategies.

A novel approach rooted in co-evolutionary game theory has been introduced to investigate how the interaction between human decision-making and the dynamics of the epidemic environment can shape vaccine acceptance during disease outbreaks. This innovative framework combines two key game concepts: the cooperation-defection game and the cost-benefit vaccination game. By doing so, it enables us to delve into the various factors that influence the success of a vaccination campaign amid an outbreak. Within this framework, individuals engage in a thorough evaluation of the risks, benefits and incentives associated with either cooperating by getting vaccinated or defecting by refusing the vaccine. Additionally, it involves a careful analysis of the costs and benefits linked to vaccine acceptance. The outcomes of this study stress the importance of two main factors: the effectiveness of the vaccine and the prevalence of a cooperative culture within society. This insight into the strategic interactions between individuals and their decisions about vaccination holds significant implications for public health policymakers. It equips to boost vaccination coverage and address vaccine hesitancy within society ultimately contributing to better public health outcomes during epidemic outbreaks.

Behavioral game of quarantine during the monkeypox epidemic: Analysis of deterministic and fractional order approach.

This work concerns the epidemiology of infectious diseases like monkeypox (mpox) in humans and animals. Our models examine transmission scenarios, including transmission dynamics between humans, animals, and both. We approach this using evolutionary game theory, specifically the intervention game-theoretical (IGT) framework, to study how human behavior can mitigate disease transmission without perfect vaccines and treatments. To do this, we use non-pharmaceutical intervention, namely the quarantine policy, which demonstrates the delayed effect of the epidemic. Additionally, we contemplate quarantine-based behavioral intervention policies in deterministic and fractional-order models to show behavioral impact in the context of the memory effect. Firstly, we extensively analyzed the model's positivity and boundness of the solution, reproduction number, disease-free and endemic equilibrium, possible stability, existence, concavity, and Ulam-Hyers stability for the fractional order. Subsequently, we proceeded to present a numerical analysis that effectively illustrates the repercussions of varying quarantine-related factors, information probability, and protection probability. We aimed to comprehensively examine the effects of non-pharmaceutical interventions on disease control, which we conveyed through line graphs and 2D heat maps. Our findings underscored the significant influence of strict quarantine measures and the protection of both humans and animals in mitigating disease outbreaks. These measures not only significantly curtailed the spread of the disease but also delayed the occurrence of the epidemic's peak. Conversely, when quarantine maintenance policies were implemented at lower rates and protection levels diminished, we observed contrasting outcomes that exacerbated the situation. Eventually, our analysis revealed the emergence of animal reservoirs in cases involving disease transmission between humans and animals.

Understanding the relationship between stay-at-home measures and vaccine shortages: a conventional, heterogeneous, and fractional dynamic approach.

In light of the global prevalence of a highly contagious respiratory disease, this study presents a novel approach to address the pressing and unanticipated issues by introducing a modified vaccination and lockdown-centered epidemic model. The rapid spread of the disease is attributed to viral transmissibility, the emergence of new strains (variants), lack of immunization, and human unawareness. This study aims to provide policymakers with crucial insights for making informed decisions regarding lockdown strategies, vaccine availability, and other control measures. The research adopts three types of models: deterministic, heterogeneous, and fractional-order dynamics, on both theoretical and numerical approaches. The heterogeneous network considers varying connectivity and interaction patterns among individuals, while the ABC fractional-order derivatives analyze the impact of integer-order control in different semi-groups. An extensive theoretical analysis is conducted to validate the proposed model. A comprehensive numerical investigation encompasses deterministic, stochastic, and ABC fractional-order derivatives, considering the combined effects of an effective vaccination program and non-pharmaceutical interventions, such as lockdowns and shutdowns. The findings of this research are expected to be valuable for policymakers in different countries, helping them implement dynamic strategies to control and eradicate the epidemic effectively.

Analyzing evolutionary game theory in epidemic management: A study on social distancing and mask-wearing strategies.

When combating a respiratory disease outbreak, the effectiveness of protective measures hinges on spontaneous shifts in human behavior driven by risk perception and careful cost-benefit analysis. In this study, a novel concept has been introduced, integrating social distancing and mask-wearing strategies into a unified framework that combines evolutionary game theory with an extended classical epidemic model. To yield deeper insights into human decision-making during COVID-19, we integrate both the prevalent dilemma faced at the epidemic's onset regarding mask-wearing and social distancing practices, along with a comprehensive cost-benefit analysis. We explore the often-overlooked aspect of effective mask adoption among undetected infectious individuals to evaluate the significance of source control. Both undetected and detected infectious individuals can significantly reduce the risk of infection for non-masked individuals by wearing effective facemasks. When the economical burden of mask usage becomes unsustainable in the community, promoting affordable and safe social distancing becomes vital in slowing the epidemic's progress, allowing crucial time for public health preparedness. In contrast, as the indirect expenses associated with safe social distancing escalate, affordable and effective facemask usage could be a feasible option. In our analysis, it was observed that during periods of heightened infection risk, there is a noticeable surge in public interest and dedication to complying with social distancing measures. However, its impact diminishes beyond a certain disease transmission threshold, as this strategy cannot completely eliminate the disease burden in the community. Maximum public compliance with social distancing and mask-wearing strategies can be achieved when they are affordable for the community. While implementing both strategies together could ultimately reduce the epidemic's effective reproduction number ([Formula: see text]) to below one, countries still have the flexibility to prioritize either of them, easing strictness on the other based on their socio-economic conditions.

Impact of human cooperation on vaccination behaviors.

This paper studies a dynamic vaccination game model embedded with vaccine cost-effectiveness and dyadic game during an epidemic, assuming the appearance of cooperation among individuals from an evolutionary perspective. The infection dynamics of the individuals' states follow a modified S/VIS (susceptible/vaccinated-infected-susceptible) dynamics. Initially, we assume that the individuals are unsure about their infection status. Thus, they make decisions regarding their options based on their neighbors' perceptions, the prevalence of the disease, and the characteristics of the available vaccines. We then consider the strategy updating process IBRA (individuals-based risk assessment) concerning an individual's committing vaccination based on a neighbor's decision. In the perspective of social dilemma, it presents the idea of social efficiency deficit to find the gap between social optimum and Nash equilibrium point based on dilemma strength by considering vaccine decision. The cost and cooperative behavior depend on disease severity, neighbor's attitude, and vaccine properties to obtain a reduced-order optimal solution to control infectious diseases. Vaccine factors (efficiency, cost, and benefit) are crucial in changing human vaccine decisions and cooperative behavior. It turns out that, even in the prisoner's dilemma case, where all defection attitude occurs, vaccine uptake (cooperation) increases. Finally, extensive numerical studies were presented that illustrate interesting phenomena and investigate the ultimate extent of the epidemic, vaccination coverage, average social benefits, and the social efficiency deficit concerning optimal strategies and the dynamic vaccine attitudes of individuals. PACS numbers. Theory and modeling; computer simulation, 87.15. Aa; Dynamics of evolution, 87.23. Kg.

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.

Coupled simultaneous analysis of vaccine and self-awareness strategies on evolutionary dilemma aspect with various immunity.

On evolutionary game theory (EGT), two intervention policies: vaccination and self-awareness, are considered to account for how human attitude impacts disease spreading. Although these interventions can impose, their implementation may depend on the various immunity systems such as shield immunity, innate immunity, waning immunity, natural immunity, and artificial immunity. This framework provides an epidemic SEIRVA (susceptible-exposed-infected-removed-vaccinated-aware) model and two EGT dynamics to analyze the interplay between the immunity system and social learning interventions. The prospect of exploring the individual's strategy and social dilemma for removing a disease could assist design an effective vaccine program and self-awareness policy. Also, we evaluated the indicator of social efficiency deficit (SED) for a social dual-dilemma to measure the presence of a dilemma situation. Extensive theoretical analysis displays that stability includes the reproduction number, conditions for positivity and uniqueness, and the strength number analyzed in the equilibria, including fundamental properties validated by numerical simulation of the discretization method that appraises a variety of graphs at adjusting parameters. We present extensive numerical studies investigating the affect of controlling parameters, individual vulnerability, optimal policies, and individual costs. It turns out that, even with the affordable vaccine, individuals may have very different behaviors; self-awareness strategy plays a vital role in controlling diseases.

Understanding the Impact of Vaccination and Self-Defense Measures on Epidemic Dynamics Using an Embedded Optimization and Evolutionary Game Theory Methodology.

Explaining how individual choice and government policy can appear in the same context in real society is one of the most challenging scientific problems. Controlling infectious diseases requires effective prevention and control measures, including vaccination and self-defense measures. In this context, optimal control strategies incorporating vaccination and self-defense measures have been proposed using the framework of evolutionary game theory. This approach accounts for individuals' behavior and interactions in a population. It can provide insights into the effectiveness of different strategies for controlling the spread of infectious diseases. The optimal control strategy involves balancing the costs and benefits of vaccination, considering the dynamic interplay between the infected and susceptible populations. By combining evolutionary game theory with optimal control theory, we can identify the optimal allocation of resources for vaccination and self-defense measures, which can maximize the control of infectious diseases while minimizing costs. The model is utilized to analyze public health policies diseases, such as vaccination and self-defense strategies, to mitigate the spread of infectious in the context of delayed decision-making.

A non-singular fractional-order logistic growth model with multi-scaling effects to analyze and forecast population growth in Bangladesh.

This paper is primarily concerned with data analysis employing the nonlinear least squares curve fitting method and the mathematical prediction of future population growth in Bangladesh. Available actual and adjusted census data (1974-2022) of the Bangladesh population were applied in the well-known autonomous logistic population growth model and found that all data sets of the logistic (exact), Atangana-Baleanu-Caputo (ABC) fractional-order derivative approach, and logistic multi-scaling approximation fit with good agreement. Again, the existence and uniqueness of the solution for fractional-order and Hyers-Ulam stability have been studied. Generally, the growth rate and maximum environmental support of the population of any country slowly fluctuate with time. Including an approximate closed-form solution in this analysis confers several advantages in assessing population models for single species. Prior studies predominantly employed constant growth rates and carrying capacity, neglecting the investigation of fractional-order methods. Thus, the current study fills a crucial gap in the literature by introducing a more formal approach to analyzing population dynamics. Therefore, we bank on the findings of this article to contribute to accurate population forecasting and planning, national development, and national progress.

Social distancing as a public-good dilemma for socio-economic cost: An evolutionary game approach.

Partaking in social distancing can contribute to a public good affected by the perceived risk of infection and socioeconomic cost. Although social distancing can save lives by slowing down the disease transmission before introducing any effective medical intervention, the economic fallout of social distancing can be brutal for the poorest, vulnerable, and marginalized members of society. We combined the epidemiological and evolutionary game theoretical (EGT) framework through the consolidations of the SEIR (Susceptible-Exposed-Infected-Removed) disease model to analyze behavior enticements in a social distancing dilemma situation with the complex behavioral decision-making aspect. Extensive theoretical and numerical analyses reveal that socioeconomic cost and infected individuals' compliance behavior are critical factors in reining disease spread in the community. Lower cost for maintaining relative safety distance encourages maximum avoidance of public interactions by a detected infected individual. The benefitted fraction due to compliance is parted from the naturally immunized population. People get insignificant benefits from social distancing when the disease transmission rate is too low or crosses critical higher values. Average Social Payoff (ASP) analysis suggests the correspondence of significant safety distance with lowest cost setting as the best strategy to derive the maximum goods. But mounting inherent cost converts social distancing obedience to a public good dilemma.

Prosocial behavior of wearing a mask during an epidemic: an evolutionary explanation.

In the midst of the COVID-19 pandemic, with limited or no supplies of vaccines and treatments, people and policymakers seek easy to implement and cost-effective alternatives to combat the spread of infection during the pandemic. The practice of wearing a mask, which requires change in people's usual behavior, may reduce disease transmission by preventing the virus spread from infectious to susceptible individuals. Wearing a mask may result in a public good game structure, where an individual does not want to wear a mask but desires that others wear it. This study develops and analyzes a new intervention game model that combines the mathematical models of epidemiology with evolutionary game theory. This approach quantifies how people use mask-wearing and related protecting behaviors that directly benefit the wearer and bring some advantage to other people during an epidemic. At each time-step, a suspected susceptible individual decides whether to wear a facemask, or not, due to a social learning process that accounts for the risk of infection and mask cost. Numerical results reveal a diverse and rich social dilemma structure that is hidden behind this mask-wearing dilemma. Our results highlight the sociological dimension of mask-wearing policy.

Hypothetical assessment of efficiency, willingness-to-accept and willingness-to-pay for dengue vaccine and treatment: a contingent valuation survey in Bangladesh.

In 2019, Bangladesh has grappled with a record-breaking surge in dengue fever, experiencing the highest number of dengue cases since the year 2000. Together, the intensification of dengue fever combined with a lack of dengue vaccines and appropriate medicines is expected to further the public and government's interests in appropriate and potential dengue vaccines to control the epidemic. We considered people's characteristics, dengue experience, and knowledge to assess their willingness-to-accept (WTA) and willingness-to-pay (WTP) for a hypothetical dengue vaccine and ex-post treatment in Bangladesh (June-July 2019). This study implemented a contingent valuation (CV) method with 3,251 respondents in 10 different locations of Bangladesh. All respondents participated in a hypothetical dengue vaccine scenario consisting of 65% (vaccine A), 80% (vaccine B), and 95% (vaccine C) effectiveness levels with three doses of each vaccine and ex-post dengue treatment. Around 71.2% of respondents were willing to pay for at least one of the hypothetical vaccines: A, B, or C. The average WTPs of the three vaccines amounted to US$ 47.0, US$ 66.0, and US$ 89.0, which were defined as the total cost of the doses necessary to obtain immunity. In Bangladesh, there is a significant demand for low-priced dengue vaccines, which was proven by people's higher acceptance of vaccination practices. Though dengue vaccines are not yet available in Bangladesh, this study provides significant support that both the government and private sectors should work together to develop a reliable and affordable dengue vaccine.

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.

Evolutionary game theory modelling to represent the behavioural dynamics of economic shutdowns and shield immunity in the COVID-19 pandemic.

The unprecedented global spread of COVID-19 has prompted dramatic public-health measures like strict stay-at-home orders and economic shutdowns. Some governments have resisted such measures in the hope that naturally acquired shield immunity could slow the spread of the virus. In the absence of empirical data about the effectiveness of these measures, policymakers must turn to epidemiological modelling to evaluate options for responding to the pandemic. This paper combines compartmental epidemiological models with the concept of behavioural dynamics from evolutionary game theory (EGT). This innovation allows us to model how compliance with an economic lockdown might wane over time, as individuals weigh the risk of infection against the certainty of the economic cost of staying at home. Governments can, however, increase spending on social programmes to mitigate the cost of a shutdown. Numerical analysis of our model suggests that emergency-relief funds spent at the individual level are effective in reducing the duration and overall economic cost of a pandemic. We also find that shield immunity takes hold in a population most easily when a lockdown is enacted with relatively low costs to the individual. Our qualitative analysis of a complex model provides evidence that the effects of shield immunity and economic shutdowns are complementary, such that governments should pursue them in tandem.

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.

Modelling and analysing the coexistence of dual dilemmas in the proactive vaccination game and retroactive treatment game in epidemic viral dynamics.

The dynamics of a spreadable disease are largely governed by four factors: proactive vaccination, retroactive treatment, individual decisions, and the prescribing behaviour of physicians. Under the imposed vaccination policy and antiviral treatment in society, complex factors (costs and expected effects of the vaccines and treatments, and fear of being infected) trigger an emulous situation in which individuals avoid infection by the pre-emptive or ex post provision. Aside from the established voluntary vaccination game, we propose a treatment game model associated with the resistance evolution of antiviral/antibiotic overuse. Moreover, the imperfectness of vaccinations has inevitably led to anti-vaccine behaviour, necessitating a proactive treatment policy. However, under the excessively heavy implementation of treatments such as antiviral medicine, resistant strains emerge. The model explicitly exhibits a dual social dilemma situation, in which the treatment behaviour changes on a local time scale, and the vaccination uptake later evolves on a global time scale. The impact of resistance evolution and the coexistence of dual dilemmas are investigated by the control reproduction number and the social efficiency deficit, respectively. Our investigation might elucidate the substantial impacts of both vaccination and treatment in the framework of epidemic dynamics, and hence suggest the appropriate use of antiviral treatment.

Behavioral incentives in a vaccination-dilemma setting with optional treatment.

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.

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.