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# Typical SIR model solution showing progression of population disease states for susceptible, infected, and recovered compartments. In this example, the entire population becomes infected and even- tually recovers.

Source publication

Agent-based simulation (ABS) is a recent modeling technique that is being widely used in modeling complex social systems. Forrester's System Dynamics (SD) is another longstanding technique for modeling social systems. Several classical models of systems, such as the Kermack-McKendrick model of epidemiology, the Lotka-Volterra equations for modeling...

## Context in source publication

**Context 1**

... is related to the number of contacts an individual has with other individuals and the likelihood that an infected individuals transmits the infection to a susceptible individual upon contact, γ is the rate at which infected individuals recover from an infection, which is taken as 1/(mean duration of illness), and N is the population size, assumed to be constant in this basic representation. In the standard SIR model, the initial conditions for the population consist of one infected individual and no recovereds. The SIR model is also referred to as the homogeneous mixing model because of three implicit assumptions in the formulation: 1) the population is fully mixed, meaning that individuals with whom a susceptible individual has contacts are chosen at random from the whole population, 2) all individuals have approximately the same number of contacts in the same period of time, and 3) all contacts transmit the disease with the same probability. All infected individuals are assumed to transmit the disease to the same number of people, and the all susceptible people have the same chance of becoming infected. A number called the basic reproduction number R0, which is the initial value of dI/dt, is often used to indi- cate the initial severity of an epidemic. Equation system (1) represents the number of susceptibles that become infected in the time interval ∆ t. Let ∆ S be the number of susceptibles becoming infected in ∆ t. Then, ∆ S = (number of susceptibles, S) × Pr[Susceptible becomes infected in ∆ t], where Pr[Susceptible becomes infected] = Pr[Susceptible contacts an infected] × Pr[infection is transmitted from an Infected to a Susceptible upon contact], where Pr[Susceptible contacts an infected] = (Number of contacts per individual) × Pr[A contacted individual is infected], where Pr[A contacted individual is infected] = I / (Number of individuals in the population, N). Therefore, ∆ S = (Number of susceptibles, S) × (Number of contacts per individual) × I / (Number of individuals in population, N) × Pr[infection is transmitted from an infected individual to a susceptible individual upon contact] ∆ S = S × (number of contacts per individual) × I / N × Pr[infection is transmitted from an infected individual to a susceptible individual upon contact] ∆ S = (Number of contacts per indi- vidual) Pr[infection is transmitted from an infected individual to a susceptible individual upon contact] × S I / N. Hence, as noted by Sterman (2000), β in (1) is a composite of two factors, the number of contacts per individual, β c , and the probability that the infection is transmitted from an infected individual to a susceptible individual upon contact, β I , as in: β = β β (2) Whereas, in (2) the composite of c and i appears in the standard SIR model (1), c and i are treated separately in the agent-based SIR model, Model 2, as described below. Note, in this derivation the number of contacts per individual is assumed to be a constant for all disease states. That is, an infected individual has as many contacts with others as does a susceptible individual. For a constant population size, N = S + I + R. The output of a typical solution of the SIR model in (1) is shown in Figure 1. The three population states (numbers of susceptible, infected, and recovered individuals) are shown as they vary over time. The output shows an epidemic, as the entire population of agents becomes infected and the number of susceptible individuals declines to zero over the course of the simulation. Note, the smooth nature of the curves due to the deterministic nature of the model and the mean- field characterizations of agent interactions. Key statistics that one might be interested in from such a simulation are the peak number of infected individuals and the time at which the peak occurs. For this simulation run with a population size of 1000, the peak number of infected individuals is 593 occurs at time ...

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## Citations

... In contrast to other methods like system dynamics, which employ a top-down approach (Ding et al., 2018;Macal, 2010), agent-based modelling addresses the issue of optimisation differently. While a global optimum may yield the highest overall objective function value, it may not necessarily be the best choice for individuals such as small-scale farmers. ...

The bioeconomy, a multidisciplinary approach that utilizes biological resources and processes to produce food, energy, and materials, is crucial for achieving sustainable economic development. As we transition to new value chains and technologies, it is essential to investigate bioeconomic solutions to substitute fossil-based production. Advanced modelling techniques are necessary to address the inherent complexity of bioeconomic systems. This study explores the intersection of simulation modelling and the bioeconomy, highlighting the increasing interest in these methodologies. We identified key trends and research gaps within this domain by conducting a systematic literature review and bibliometric analysis. Our refined search strategy yielded 12 publications focusing on agent-based modelling (ABM) applications in the bioeconomy, providing insights into micro-level and macro-level analyses. The findings reveal ABM's potential to simulate complex interactions within bioeconomic systems, emphasizing its ability to integrate social, economic, and environmental dimensions. The study uncovers gaps in holistically modelling innovative biorefinery technologies. These insights can help guide future research efforts by showing the need for adaptive and interdisciplinary approaches to enhance knowledge about bioeconomic value networks and to derive measures and strategies for their long-term establishment.

... A powerful approach to implement this multi-component model into one framework is the agent-based simulation (Chumachenko et al. 2018;Priest et al. 2021;Carley et al. 2006;Tesfatsion et al. 2002;Alexi et al. 2024). Inspired by previous works (Connell et al. 2009;Lazebnik and Alexi 2022;Macal 2010;Alexi et al. 2023), we formally define the model as a whole, denoted by M , as follows. Let M be a tuple (P, G) where P is a population of agents and G is the interaction graph between them. ...

Sexually transmitted diseases (STDs) are a group of pathogens infecting new hosts through sexual interactions. Due to its social and economic burden, multiple models have been proposed to study the spreading of pathogens. In parallel, in the ever-evolving landscape of digital social interactions, the pervasive utilization of dating apps has become a prominent facet of modern society. Despite the surge in popularity and the profound impact on relationship formation, a crucial gap in the literature persists regarding the potential ramifications of dating apps usage on the dynamics of STDs. In this paper, we address this gap by presenting a novel mathematical framework - an extended Susceptible-Infected-Susceptible (SIS) epidemiological model to elucidate the intricate interplay between dating apps engagement and the propagation of STDs. Namely, as dating apps are designed to make users revisit them and have mainly casual sexual interactions with other users, they increase the number of causal partners, which increases the overall spread of STDS. Using extensive simulation, based on real-world data, explore the effect of dating apps adoption and control on the STD spread. We show that an increased adoption of dating apps can result in an STD outbreak if not handled appropriately.

... Another difference between these two methods is that in ABM, the approach is known as the bottom-up type, because it is done by analyzing the behavior of individual units and how these behaviors change due to interactions, which, then, makes it possible to obtain the behavior of the entire system (BUSCH et al., 2017). Meanwhile, SD is known as the top-down, that is, the system is modeled by dividing it by its main elements and modeling the interactions of the components (MACAL, 2010). ...

O gerenciamento integrado de resíduos sólidos urbanos (GIRSU) é considerado uma tarefa desafiadora devido às múltiplas dimensões que compõem o sistema, às suas mudanças ao longo do tempo e à fragilidade da sustentabilidade financeira no setor. Conhecer as ferramentas que possibilitam a análise desse complexo sistema é importante para auxiliar os tomadores de decisão no gerenciamento dos resíduos. Desta forma, este artigo tem como objetivo apresentar as ferramentas, e indicar a mais adequada, que podem ser utilizadas para análise do comportamento e inter-relação dos elementos que afetam a sustentabilidade financeira dos municípios no GIRSU, ao longo do tempo. Como resultado, a Dinâmica de Sistemas (DS) apresentou vantagens sobre as outras ferramentas e métodos estáticos de pesquisa operacional, quando se considera os sistemas de GIRSU, por sua natureza complexa, mutável e reconhecível dos elementos do mundo real. Esse estudo fornece importantes contribuições para pesquisas futuras e para o planejamento do GIRSU, pois traz informações sobre as ferramentas mais relevantes e atuais para o desenvolvimento de estudos voltados para o gerenciamento de resíduos e a sustentabilidade financeira do sistema.

... Euler's equation has applications in areas such as cell growth, fluid dynamics, quantum, optics, mechanics, and electrical engineering. There are several numerical techniques in existing literature for solving ODEs with initial value problems using Euler's method, for instance, numerical analysis of the linearly implicit Euler method with truncated Wiener process for the stochastic SIR model (Yang et al. 2023b), nonlinear infection-age SIR models (Yang et al. 2023a), deep Euler method to solve ordinary differential equations (Shen et al. 2020), a performant and feature-full agent-based modeling software of minimal code complexity (Datseris et al. 2022), Agent-based simulation from system dynamics model using the forward Euler method (Macal 2010), Extension of a Mathematical model using agent-based simulation to Zombie attack (da Costa Junior et al. 2018). ...

A mob is an event that is organized via social media, email, SMS, or other forms of digital communication technologies in which a group of people (who might have an agenda) get together online or offline to collectively conduct an act and then disperse (quickly or over a long period). In recent years, these events are increasingly happening worldwide due to the anonymity of the internet, affordability of social media, boredom, etc. Studying such a phenomenon is difficult due to a lack of data, theoretical underpinning, and resources. In this research, we use the Agent-Based Modeling (ABM) technique to model the mobbers and the Monte Carlo method to assign random values to the factors extracted from the theory of Collective Action and conduct many simulations. We also leverage our previous research on Deviant Cyber Flash Mobs to implement various scenarios the mobber could face when they decide to act in a mob or not. This resulted in a model that can simulate mobs, estimate the mob success rate, and the needed powerful actors (e.g., mob organizers) for a mob to succeed. We finally evaluate our model using real-world mob data collected from the Meetup social media platform. This research is one step toward fully understanding mob formation and the motivations of its participants and organizers.

... La MBA, además de contar con las ventajas generales de la simulación, también puede ofrecer información adicional de un sistema que otros métodos de simulación no ofrecen, como el de dinámica de sistemas, debido a que es capaz de capturar explícitamente la estocasticidad inherente del sistema (Macal, 2010), permitiendo la autonomía, razonamiento, comunicación y coordinación de los agentes (Dongsheng y Yongan, 2008), y de esta interacción en el micronivel puede emerger el macronivel o agregado (Garcia y Jager, 2011). También permite representar la emergencia y dinámica del sistema, los bucles de realimentación, el carácter heterogéneo de los actores, su evolución y su adaptación (García-Vázquez y Sancho Caparrini, 2016). ...

... Figure 11. Example of an SIR model solution [24] 4. RESULTS Table 3. CSV confirmed cases dataset on GitHub [25] Province ...

... For instance, System Dynamics is a suitable approach because it enables the modeling of imperfections and allows the dynamic influencing of individuals' decision-making (Teufel et al., 2013). From a technological bottom-up perspective, agentbased models (ABMs) are similar (Macal, 2010). Accordingly, they are useful when considering the bounded rationality of actors and understanding the impact of self-organized actions on the overall energy system (Deissenroth et al., 2017). ...

Energy system models are widely used to inform the political decisions required to successfully mitigate climate change in the energy sector. The energy system optimization models (ESOMs) used to identify cost-minimal transformation pathways assume the perfect behavior of market participants from a central planner’s perspective. Neglecting the decision-making under uncertainties or biased perceptions and attitudes leads to inaccurate assumptions regarding the requirements of a successful energy transition. In particular, ESOMs underestimate the required capacities for power generation, storage, and transmission compared with real-world energy systems, a phenomenon known as the “economic granularity gap”. Agent-based models (ABMs) are helpful tools for capturing the behavior of market actors. Hence, attempts have been made to identify and alleviate this phenomenon through the coupling of ESOMs and ABMs. In this paper, we propose an automated workflow for such model coupling and quantify the economic granularity gap for the case of photovoltaic-prosumer self-consumption. Our results show that the current business models and regulatory frameworks affecting prosumer self-consumption patterns require the adaptation of cost-minimal energy system designs. However, if correctly implemented, instruments such as dynamic tariffs could narrow the economic granularity gap, shifting real-world energy systems closer to their ideal counterparts.

... Thus, it can be viewed as a network queue within the relative space dimension and can be used to model different modes of transportation, e.g., privately operated vehicles (POVs) on the road, shared mobility systems, pedestrians, and other active modes. According to Macal (2010) "every wellformulated system dynamics model has an equivalent formulation as [... a] time-stepped agentbased simulation model [...]". Further, he shows how some ABM are equivalent to the system dynamics model without providing additional information or advantages, and other formulations may provide more information than a continuum system dynamics model. ...

Agent-based models have been extensively used to simulate the behavior of travelers in transportation systems because they allow for realistic and versatile modeling of interactions. However, traditional agent-based models suffer from high computational costs and rely on tracking physical locations, raising privacy concerns. This paper proposes an efficient formulation for the agent-based bathtub model (AB2M) in the relative space, where each agent's trajectory is represented by a time series of the remaining distance to its destination. The AB2M can be understood as a microscopic model that tracks individual trips' initiation, progression, and completion and is an exact numerical solution of the bathtub model for generic (time-dependent) trip distance distributions. The model can be solved for a deterministic set of trips with a given demand pattern (defined by the start time of each trip and its distance), or it can be used to run Monte Carlo simulations to capture the average behavior and variation stochastic demand patterns, described by probabilistic distributions of trip distances and departure times. To enhance the computational efficiency, we introduce a priority queue formulation, eliminating the need to update trip positions at each time step and allowing us to run large-scale scenarios with millions of individual trips in seconds. We systematically explore the scaling properties and discuss the introduction of biases and numerical errors. The systematic exploration of scaling properties of the modeling of individual agents in the relative space with the AB2M further enhances its applicability to large-scale transportation systems and opens up opportunities for studying travel time reliability, scheduling, and mode choices.

... SD modeling and ABM are the most prominent approaches in modeling nonlinear systems (Macal, 2010). Light-sights systems that produce similar results on SD modeling and ABM (Macal, 2010). ...

... SD modeling and ABM are the most prominent approaches in modeling nonlinear systems (Macal, 2010). Light-sights systems that produce similar results on SD modeling and ABM (Macal, 2010). This research study adapts SD modeling because of its emphasis on the importance of feedback effects on net stock levels as determinants of system behavior (Macal, 2010;Sterman, 2002). ...

... Light-sights systems that produce similar results on SD modeling and ABM (Macal, 2010). This research study adapts SD modeling because of its emphasis on the importance of feedback effects on net stock levels as determinants of system behavior (Macal, 2010;Sterman, 2002). ...

Purpose
The purpose of this paper is to propose a system dynamic simulated process model for maintenance work management incorporating the Fourth Industrial Revolution (4IR) technologies.
Design/methodology/approach
The extant literature in physical assets maintenance depicts that poor maintenance management is predominantly because of a lack of a clearly defined maintenance work management process model, resulting in poor management of maintenance work. This paper solves this complex phenomenon using a combination of conceptual process modeling and system dynamics simulation incorporating 4IR technologies. A process for maintenance work management and its control actions on scheduled maintenance tasks versus unscheduled maintenance tasks is modeled, replicating real-world scenarios with a digital lens (4IR technologies) for predictive maintenance strategy.
Findings
A process for maintenance work management is thus modeled and simulated as a dynamic system. Post-model validation, this study reveals that the real-world maintenance work management process can be replicated using system dynamics modeling. The impact analysis of 4IR technologies on maintenance work management systems reveals that the implementation of 4IR technologies intensifies asset performance with an overall gain of 27.46%, yielding the best maintenance index. This study further reveals that the benefits of 4IR technologies positively impact equipment defect predictability before failure, thereby yielding a predictive maintenance strategy.
Research limitations/implications
The study focused on maintenance work management system without the consideration of other subsystems such as cost of maintenance, production dynamics, and supply chain management.
Practical implications
The maintenance real-world quantitative data is retrieved from two maintenance departments from company A, for a period of 24 months, representing years 2017 and 2018. The maintenance quantitative data retrieved represent six various types of equipment used at underground Mines. The maintenance management qualitative data (Organizational documents) in maintenance management are retrieved from company A and company B. Company A is a global mining industry, and company B is a global manufacturing industry. The reliability of the data used in the model validation have practical implications on how maintenance work management system behaves with the benefit of 4IR technologies' implementation.
Social implications
This research study yields an overall benefit in asset management, thereby intensifying asset performance. The expected learnings are intended to benefit future research in the physical asset management field of study and most important to the industry practitioners in physical asset management.
Originality/value
This paper provides for a model in which maintenance work and its dynamics is systematically managed. Uncontrollable corrective maintenance work increases the complexity of the overall maintenance work management. The use of a system dynamic model and simulation incorporating 4IR technologies adds value on the maintenance work management effectiveness.

... But sometimes researchers notice that one approach leads to consistently higher or lower output values than another, a phenomenon which is not expected and which could be described as a bias introduced by the modeling process. Simple models for population growth and disease transmission, the logistic and SIR models, exhibit this behavior, as seen in several studies [1][2][3][4]. ...

... For five types of networks tested, the agent based simulation exhibits on average a lower and later peak of infection than the corresponding deterministic ODE model [2]. A comparison for the susceptible/infectious/recovered (SIR) model done by Macal exhibits a similar phenomenon, with the infectious compartment in the deterministic model peaking higher and earlier than the comparable agent based simulation [3]. These observations are consistent with Corollary 3. The author attributes the difference to the ability of the agent based model to capture the stochasticity in the system, but does not comment on why that would produce an average that is lower than the deterministic model. ...

... As in Petroni et al, larger variation leads to a greater difference between the solution and the average of solutions, as seen in Figure 1b,c [1]. As with the SIR and SEIR examples, the average of solutions for S is higher than the solution, while for I it is lower [2,3]. These observations lead to two lines of questioning. ...

Modelers have choices in how they approach a problem, with different approaches potentially leading to different outcomes. Sometimes one approach gives a consistently lower (or higher) result than another. The theorem and corollaries in this study show that if the logistic equation or, equivalently, the SI model, are perturbed at time zero by a range of values with mean zero, the resulting trajectories must average to a value below (for logistic and I) or above (for S) the solution with average initial condition. The proof of the theorem shows that this phenomenon is the result of algebraic properties of the nonlinear quadratic term, although we note it can be extended to a larger class of systems. More importantly it shows that the only necessary criterion is that the perturbations average to zero. The source of them and the properties of their distribution does not matter to the result of the theorem but does affect the magnitude of the proven difference.