Stochastic Agent-based Models Research Articles

Soliton approximation in continuum models of leader-follower behavior.

Complex biological processes involve collective behavior of entities (bacteria, cells, animals) over many length and time scales and can be described by discrete models that track individuals or by continuum models involving densities and fields. We consider hybrid stochastic agent-based models of branching morphogenesis and angiogenesis (new blood vessel creation from preexisting vasculature), which treat cells as individuals that are guided by underlying continuous chemical and/or mechanical fields. In these descriptions, leader (tip) cells emerge from existing branches and follower (stalk) cells build the new sprout in their wake. Vessel branching and fusion (anastomosis) occur as a result of tip and stalk cell dynamics. Coarse graining these hybrid models in appropriate limits produces continuum partial differential equations(PDEs) for endothelial cell densities that are more analytically tractable. While these models differ in nonlinearity, they produce similar equationsat leading order when chemotaxis is dominant. We analyze this leading order system in a simple quasi-one-dimensional geometry and show that the numerical solution of the leading order PDE is well described by a soliton wave that evolves from vessel to source. This wave is an attractor for intermediate times until it arrives at the hypoxic region releasing the growth factor. The mathematical techniques used here thus identify common features of discrete and continuum approaches and provide insight into general biological mechanisms governing their collective dynamics.

From Compositional Petri Net Modeling to Macro and Micro Simulation by Means of Stochastic Simulation and Agent-Based Models

Computational modeling has become a widespread approach for studying real-world phenomena by using different modeling perspectives, in particular, the microscopic point of view concentrates on the behavior of the single components and their interactions from which the global system evolution emerges, while the macroscopic point of view represents the system’s overall behavior abstracting as much as possible from that of the single components. The preferred point of view depends on the effort required to develop the model, on the detail level of the available information about the system to be modeled, and on the type of measures that are of interest to the modeler; each point of view may lead to a different modeling language and simulation paradigm. An approach adequate for the microscopic point of view is Agent-Based Modeling and Simulation, which has gained popularity in the last few decades but lacks a formal definition common to the different tools supporting it. This may lead to modeling mistakes and wrong interpretation of the results, especially when comparing models of the same system developed according to different points of view. The aim of the work described in this paper is to provide a common compositional modeling language from which both a macro and a micro simulation model can be automatically derived: these models are coherent by construction and may be studied through different simulation approaches and tools. A framework is thus proposed in which a model can be composed using a Petri Net formalism and then studied through both an Agent-Based Simulation and a classical Stochastic Simulation Algorithm, depending on the study goal.

Collective behaviors of stochastic agent-based models and applications to finance and optimization

In this paper, we present a survey of recent progress on the emergent behaviors of stochastic particle models which arise from the modeling of collective dynamics. Collective dynamics of interacting autonomous agents is ubiquitous in nature, and it can be understood as a formation of concentration in a state space. The jargons such as aggregation, herding, flocking and synchronization describe such concentration phenomena. Recently it became one of the emerging topics in the applied mathematics community due to possible engineering applications and close relation with nonlocal partial differential equations. When an autonomous agent system interacts with unknown environment as an open system, the effects of hidden and unidentified interactions between the environment and the autonomous system are often realized by stochastic noises in agent dynamics, and the temporal evolution of the autonomous system results in stochastic collective models. From the viewpoint of dynamical systems theory, it is very interesting how collective dynamics emerges from initial state. As concrete examples, we consider four specific stochastic collective models (stochastic Winfree and Kuramoto models for synchronization, the stochastic Cucker–Smale model for flocking, and a first-order stochastic nonlinear consensus model), and we also briefly review the state-of-the-art results for these models on the emergence of collective dynamics and discuss their applications in finance and optimization.

Estimation of a Within-Herd Transmission Rate for African Swine Fever in Vietnam

We describe results from a panel study in which pigs from a 17-sow African swine fever (ASF) positive herd in Thái Bình province, Vietnam, were followed over time to record the date of onset of ASF signs and the date of death from ASF. Our objectives were to (1) fit a susceptible-exposed-infectious-removed disease model to the data with transmission coefficients estimated using approximate Bayesian computation; (2) provide commentary on how a model of this type might be used to provide decision support for disease control authorities. For the outbreak in this herd, the median of the average latent period was 10 days (95% HPD (highest posterior density interval): 2 to 19 days), and the median of the average duration of infectiousness was 3 days (95% HPD: 2 to 4 days). The estimated median for the transmission coefficient was 3.3 (95% HPD: 0.4 to 8.9) infectious contacts per ASF-infectious pig per day. The estimated median for the basic reproductive number, R0, was 10 (95% HPD: 1.1 to 30). Our estimates of the basic reproductive number R0 were greater than estimates of R0 for ASF reported previously. The results presented in this study may be used to estimate the number of pigs expected to be showing clinical signs at a given number of days following an estimated incursion date. This will allow sample size calculations, with or without adjustment to account for less than perfect sensitivity of clinical examination, to be used to determine the appropriate number of pigs to examine to detect at least one with the disease. A second use of the results of this study would be to inform the equation-based within-herd spread components of stochastic agent-based and hybrid simulation models of ASF.

The relationship between compartment models and their stochastic counterparts: A comparative study with examples of the COVID-19 epidemic modeling.

Deterministic compartment models (CMs) and stochastic models, including stochastic CMs and agent-based models, are widely utilized in epidemic modeling. However, the relationship between CMs and their corresponding stochastic models is not well understood. The present study aimed to address this gap by conducting a comparative study using the susceptible, exposed, infectious, and recovered (SEIR) model and its extended CMs from the coronavirus disease 2019 modeling literature. We demonstrated the equivalence of the numerical solution of CMs using the Euler scheme and their stochastic counterparts through theoretical analysis and simulations. Based on this equivalence, we proposed an efficient model calibration method that could replicate the exact solution of CMs in the corresponding stochastic models through parameter adjustment. The advancement in calibration techniques enhanced the accuracy of stochastic modeling in capturing the dynamics of epidemics. However, it should be noted that discrete-time stochastic models cannot perfectly reproduce the exact solution of continuous-time CMs. Additionally, we proposed a new stochastic compartment and agent mixed model as an alternative to agent-based models for large-scale population simulations with a limited number of agents. This model offered a balance between computational efficiency and accuracy. The results of this research contributed to the comparison and unification of deterministic CMs and stochastic models in epidemic modeling. Furthermore, the results had implications for the development of hybrid models that integrated the strengths of both frameworks. Overall, the present study has provided valuable epidemic modeling techniques and their practical applications for understanding and controlling the spread of infectious diseases.

Efficient Bayesian inference for stochastic agent-based models.

The modelling of many real-world problems relies on computationally heavy simulations of randomly interacting individuals or agents. However, the values of the parameters that underlie the interactions between agents are typically poorly known, and hence they need to be inferred from macroscopic observations of the system. Since statistical inference rests on repeated simulations to sample the parameter space, the high computational expense of these simulations can become a stumbling block. In this paper, we compare two ways to mitigate this issue in a Bayesian setting through the use of machine learning methods: One approach is to construct lightweight surrogate models to substitute the simulations used in inference. Alternatively, one might altogether circumvent the need for Bayesian sampling schemes and directly estimate the posterior distribution. We focus on stochastic simulations that track autonomous agents and present two case studies: tumour growths and the spread of infectious diseases. We demonstrate that good accuracy in inference can be achieved with a relatively small number of simulations, making our machine learning approaches orders of magnitude faster than classical simulation-based methods that rely on sampling the parameter space. However, we find that while some methods generally produce more robust results than others, no algorithm offers a one-size-fits-all solution when attempting to infer model parameters from observations. Instead, one must choose the inference technique with the specific real-world application in mind. The stochastic nature of the considered real-world phenomena poses an additional challenge that can become insurmountable for some approaches. Overall, we find machine learning approaches that create direct inference machines to be promising for real-world applications. We present our findings as general guidelines for modelling practitioners.

Revisiting discrepancies between stochastic agent-based and deterministic models

Revisiting discrepancies between stochastic agent-based and deterministic models

Simulated actin reorganization mediated by motor proteins

Cortical actin networks are highly dynamic and play critical roles in shaping the mechanical properties of cells. The actin cytoskeleton undergoes significant reorganization in many different contexts, including during directed cell migration and over the course of the cell cycle, when cortical actin can transition between different configurations such as open patched meshworks, homogeneous distributions, and aligned bundles. Several types of myosin motor proteins, characterized by different kinetic parameters, have been involved in this reorganization of actin filaments. Given the limitations in studying the interactions of actin with myosin in vivo, we propose stochastic agent-based models and develop a set of data analysis measures to assess how myosin motor proteins mediate various actin organizations. In particular, we identify individual motor parameters, such as motor binding rate and step size, that generate actin networks with different levels of contractility and different patterns of myosin motor localization, which have previously been observed experimentally. In simulations where two motor populations with distinct kinetic parameters interact with the same actin network, we find that motors may act in a complementary way, by tuning the actin network organization, or in an antagonistic way, where one motor emerges as dominant. This modeling and data analysis framework also uncovers parameter regimes where spatial segregation between motor populations is achieved. By allowing for changes in kinetic rates during the actin-myosin dynamic simulations, our work suggests that certain actin-myosin organizations may require additional regulation beyond mediation by motor proteins in order to reconfigure the cytoskeleton network on experimentally-observed timescales.

On the Inadequacy of Economics for Understanding Housing Markets – A Pragmatic Response

ABSTRACT The focus article of this issue of the journal argues for the need to use tools and concepts from many disciplines of social science when analysing real-world housing market. Lux and Sunega argue that analyses relying only on the toolbox of mainstream economics fail to capture important aspects of the working of the markets, we agree. However, part of the critique of mainstream economics is based on a caricature of economics. In order to arrive at a new pragmatic socio-economics of housing markets, we see it as crucial to arrive at explicit, concise and shared interpretations of core concepts, e.g. the concept of norms is often used differently in different disciplines. Two of the lines of future housing market research proposed by Lux and Sunega that we regard as particular promising is design of surveys capturing variation in expectations, preferences and risk attitudes and use of (stochastic) agent-based models.

A martingale formulation for stochastic compartmental susceptible-infected-recovered (SIR) models to analyze finite size effects in COVID-19 case studies

<p style='text-indent:20px;'>Deterministic compartmental models for infectious diseases give the mean behaviour of stochastic agent-based models. These models work well for counterfactual studies in which a fully mixed large-scale population is relevant. However, with finite size populations, chance variations may lead to significant departures from the mean. In real-life applications, <i>finite size effects</i> arise from the variance of individual realizations of an epidemic course about its fluid limit. In this article, we consider the classical stochastic Susceptible-Infected-Recovered (SIR) model, and derive a martingale formulation consisting of a deterministic and a stochastic component. The deterministic part coincides with the classical deterministic SIR model and we provide an upper bound for the stochastic part. Through analysis of the stochastic component depending on varying population size, we provide a theoretical explanation of <i>finite size effects</i>. Our theory is supported by quantitative and direct numerical simulations of theoretical infinitesimal variance. Case studies of coronavirus disease 2019 (COVID-19) transmission in smaller populations illustrate that the theory provides an envelope of possible outcomes that includes the field data.</p>

Frequency-Dependent Competition Between Strains Imparts Persistence to Perturbations in a Model of Plasmodium falciparum Malaria Transmission.

In high-transmission endemic regions, local populations of Plasmodium falciparum exhibit vast diversity of the var genes encoding its major surface antigen, with each parasite comprising multiple copies from this diverse gene pool. This strategy to evade the immune system through large combinatorial antigenic diversity is common to other hyperdiverse pathogens. It underlies a series of fundamental epidemiological characteristics, including large reservoirs of transmission from high prevalence of asymptomatics and long-lasting infections. Previous theory has shown that negative frequency-dependent selection (NFDS) mediated by the acquisition of specific immunity by hosts structures the diversity of var gene repertoires, or strains, in a pattern of limiting similarity that is both non-random and non-neutral. A combination of stochastic agent-based models and network analyses has enabled the development and testing of theory in these complex adaptive systems, where assembly of local parasite diversity occurs under frequency-dependent selection and large pools of variation. We show here the application of these approaches to theory comparing the response of the malaria transmission system to intervention when strain diversity is assembled under (competition-based) selection vs. a form of neutrality, where immunity depends only on the number but not the genetic identity of previous infections. The transmission system is considerably more persistent under NFDS, exhibiting a lower extinction probability despite comparable prevalence during intervention. We explain this pattern on the basis of the structure of strain diversity, in particular the more pronounced fraction of highly dissimilar parasites. For simulations that survive intervention, prevalence under specific immunity is lower than under neutrality, because the recovery of diversity is considerably slower than that of prevalence and decreased var gene diversity reduces parasite transmission. A Principal Component Analysis of network features describing parasite similarity reveals that despite lower overall diversity, NFDS is quickly restored after intervention constraining strain structure and maintaining patterns of limiting similarity important to parasite persistence. Given the described enhanced persistence under perturbation, intervention efforts will likely require longer times than the usual practice to eliminate P. falciparum populations. We discuss implications of our findings and potential analogies for ecological communities with non-neutral assembly processes involving frequency-dependence.

Computational framework to capture the spatiotemporal density of cells with a cumulative environmental coupling

Stochastic agent-based models can account for millions of cells with spatiotemporal movement that can be a function of different factors. However, these simulations can be computationally expensive. In this work, we develop a novel computational framework to describe and simulate stochastic cellular processes that are coupled to the environment. Specifically, through upscaling, we derive a continuum governing equation that considers the cell density as a function of time, space, and a cumulative variable that is coupled to the environmental conditions. For this new governing equation, we consider the stability through an energy analysis, as well as proving uniqueness and well-posedness. To solve the governing equations in free-space, we propose a numerical method using fundamental solutions. As an application, we study a cell moving in an infinite domain that contains a toxic chemical, where a cumulative exposure above a critical value results in cell death. We illustrate the validity of this new modeling framework and associated numerical methods by comparing the density of live cells to results from the corresponding agent-based model.

Interpreting stochastic agent-based models of cell death

Linking individual cell behavior to changes on the cell population and ultimately tissue scale is a key step towards connecting in vitro laboratory experiments to clinically relevant organ-scale behavior. For example, understanding how an individual tumor cell’s response to drug treatments propagates to the macroscale could help guide clinical decision making when tumors are located in high stakes regions. Based on how dying cells interact, macroscale tumor response can be dominated by tumor shrinkage, tumor damage, change in tumor porosity, or some combination of these phenomena. Here we focus on methods of modeling collective cell behavior with the overall goal of understanding how stochastic cell behavior will ultimately manifest on the cell population scale. To do this, we define and implement an agent-based model problem, introduce novel methods for interpreting simulation results, implement a recently developed technique for conducting a variance-based sensitivity analysis, and investigate key model parameters. Operating within an in silico framework allows us to compare our proposed methods with and without reproducible stochastic variations. This is critical because methods that will be functional for interpreting experimental data must also be able to function when aspects of stochastic variation are not reproducible. To demonstrate the utility of our proposed methods, we identify important simulation parameters for our agent-based model, show that two-dimensional and three-dimensional results are not directly equivalent, and highlight the macroscale implications of cell shrinkage. Looking forward, we anticipate that the methods and results presented here will contribute to significant future research in modeling stochastic cell behavior in the multiscale setting.

Development of an agent-based speculation game for higher reproducibility of financial stylized facts

Simultaneous reproduction of all financial stylized facts is so difficult that most existing stochastic process-based and agent-based models are unable to achieve the goal. In this study, by extending the decision-making structure of Minority Game, we propose a novel agent-based model called “Speculation Game,” for better reproducibility of the stylized facts. The new model has three distinct characteristics comparing with preceding agent-based adaptive models for the financial market: the enabling of nonuniform holding and idling periods, the inclusion of magnitude information of price change in history, and the implementation of a cognitive world for the evaluation of investment strategies with capital gains and losses. With these features, Speculation Game succeeds in reproducing 10 out of the currently well studied 11 stylized facts under a single parameter setting.

Dimensionality of Motion and Binding Valency Govern Receptor-Ligand Kinetics As Revealed by Agent-Based Modeling.

Mathematical modeling and computer simulations have become an integral part of modern biological research. The strength of theoretical approaches is in the simplification of complex biological systems. We here consider the general problem of receptor–ligand binding in the context of antibody–antigen binding. On the one hand, we establish a quantitative mapping between macroscopic binding rates of a deterministic differential equation model and their microscopic equivalents as obtained from simulating the spatiotemporal binding kinetics by stochastic agent-based models. On the other hand, we investigate the impact of various properties of B cell-derived receptors—such as their dimensionality of motion, morphology, and binding valency—on the receptor–ligand binding kinetics. To this end, we implemented an algorithm that simulates antigen binding by B cell-derived receptors with a Y-shaped morphology that can move in different dimensionalities, i.e., either as membrane-anchored receptors or as soluble receptors. The mapping of the macroscopic and microscopic binding rates allowed us to quantitatively compare different agent-based model variants for the different types of B cell-derived receptors. Our results indicate that the dimensionality of motion governs the binding kinetics and that this predominant impact is quantitatively compensated by the bivalency of these receptors.

Epidemiological modeling of Trypanosoma cruzi: Low stercorarian transmission and failure of host adaptive immunity explain the frequency of mixed infections in humans.

People living in areas with active vector-borne transmission of Chagas disease have multiple contacts with its causative agent, Trypanosoma cruzi. Reinfections by T. cruzi are possible at least in animal models leading to lower or even hardly detectable parasitaemia. In humans, although reinfections are thought to have major public health implications by increasing the risk of chronic manifestations of the disease, there is little quantitative knowledge about their frequency and the timing of parasite re-inoculation in the course of the disease. Here, we implemented stochastic agent-based models i) to estimate the rate of re-inoculation in humans and ii) to assess how frequent are reinfections during the acute and chronic stages of the disease according to alternative hypotheses on the adaptive immune response following a primary infection. By using a hybrid genetic algorithm, the models were fitted to epidemiological data of Argentinean rural villages where mixed infections by different genotypes of T. cruzi reach 56% in humans. To explain this percentage, the best model predicted 0.032 (0.008–0.042) annual reinfections per individual with 98.4% of them occurring in the chronic phase. In addition, the parasite escapes to the adaptive immune response mounted after the primary infection in at least 20% of the events of re-inoculation. With these low annual rates, the risks of reinfection during the typically long chronic stage of the disease stand around 14% (4%-18%) and 60% (21%-70%) after 5 and 30 years, with most individuals being re-infected 1–3 times overall. These low rates are better explained by the weak efficiency of the stercorarian mode of transmission than a highly efficient adaptive immune response. Those estimates are of particular interest for vaccine development and for our understanding of the higher risk of chronic disease manifestations suffered by infected people living in endemic areas.

A Third Wave in the Economics of Climate Change

Modelling the economics of climate change is daunting. Many existing methodologies from social and physical sciences need to be deployed, and new modelling techniques and ideas still need to be developed. Existing bread-and-butter micro- and macroeconomic tools, such as the expected utility framework, market equilibrium concepts and representative agent assumptions, are far from adequate. Four key issues—along with several others—remain inadequately addressed by economic models of climate change, namely: (1) uncertainty, (2) aggregation, heterogeneity and distributional implications (3) technological change, and most of all, (4) realistic damage functions for the economic impact of the physical consequences of climate change. This paper assesses the main shortcomings of two generations of climate-energy-economic models and proposes that a new wave of models need to be developed to tackle these four challenges. This paper then examines two potential candidate approaches—dynamic stochastic general equilibrium (DSGE) models and agent-based models (ABM). The successful use of agent-based models in other areas, such as in modelling the financial system, housing markets and technological progress suggests its potential applicability to better modelling the economics of climate change.

When push comes to shove: Exclusion processes with nonlocal consequences

Stochastic agent-based models are useful for modelling collective movement of biological cells. Lattice-based random walk models of interacting agents where each site can be occupied by at most one agent are called simple exclusion processes. An alternative motility mechanism to simple exclusion is formulated, in which agents are granted more freedom to move under the compromise that interactions are no longer necessarily local. This mechanism is termed shoving. A nonlinear diffusion equation is derived for a single population of shoving agents using mean-field continuum approximations. A continuum model is also derived for a multispecies problem with interacting subpopulations, which either obey the shoving rules or the simple exclusion rules. Numerical solutions of the derived partial differential equations compare well with averaged simulation results for both the single species and multispecies processes in two dimensions, while some issues arise in one dimension for the multispecies case.

Topological effects of network structure on long-term social network dynamics in a wild mammal.

Social structure influences ecological processes such as dispersal and invasion, and affects survival and reproductive success. Recent studies have used static snapshots of social networks, thus neglecting their temporal dynamics, and focused primarily on a limited number of variables that might be affecting social structure. Here, instead we modelled effects of multiple predictors of social network dynamics in the spotted hyena, using observational data collected during 20 years of continuous field research in Kenya. We tested the hypothesis that the current state of the social network affects its long-term dynamics. We employed stochastic agent-based models that allowed us to estimate the contribution of multiple factors to network changes. After controlling for environmental and individual effects, we found that network density and individual centrality affected network dynamics, but that social bond transitivity consistently had the strongest effects. Our results emphasise the significance of structural properties of networks in shaping social dynamics.

Biased random walks, partial differential equations and update schemes

There is much interest within the mathematical biology and statistical physics community in converting stochastic agent-based models for random walkers into a partial differential equation description for the average agent density. Here a Fokker-Planck equation is used to describe the evolution of a collection of noninteracting asymmetric random walkers. The resulting continuum description is highly dependent on the simulation update schemes. The theoretical results are confirmed with examples. These findings provide insight into the importance of updating schemes to the macroscopic description of stochastic local movement rules in agent-based models. doi:10.1017/S1446181113000369