stochastic population modeling

Classical iterative integer-mapping models are valid only under the infinite-population assumption and fail to capture critical individual-level stochasticity—such as demographic noise and extinction risk—in finite populations. Existing noise-perturbation approaches model only environmental stochasticity, neglecting intrinsic noise arising from discrete individual dynamics. Method: We propose a binomial-mapping-based stochastic evolutionary framework that explicitly links deterministic maps—including Logistic and Ricker maps—to individual-based stochastic processes. Contribution/Results: This framework rigorously establishes their non-equivalence and identifies sufficient conditions for equivalence. By embedding discrete-individual dynamics within deterministic map structures, it enables exact modeling of demographic noise, quasi-stationary distributions, and extinction pathways. It provides a unified, analytically tractable paradigm for studying noise-induced phase transitions and extinction risk in population dynamics.

This work addresses the efficient computation of expected termination times for Markov double-chains—a class of epidemiological Markov population processes arising from stochastic discretization of classical compartmental models. We first formally define the model and prove its almost-sure termination under acyclic flow conditions. Methodologically, we develop a PSPACE-approximation algorithm and, within the Blum–Shub–Smale (BSS) computational model, provide an exact algorithm for termination time computation. Our approach integrates Markov process analysis, probabilistic model checking, and formal verification techniques to enable automatic translation into mainstream probabilistic model checkers (e.g., PRISM). Empirical evaluation demonstrates substantial improvements in both accuracy and scalability for predicting termination times in realistic epidemiological scenarios. This constitutes the first termination analysis framework for stochastic epidemic models that simultaneously offers rigorous theoretical guarantees and practical applicability.

Traditional tree-based models struggle to capture the non-tree-like co-evolution of closely interacting groups—such as dialects—under sustained contact. This work presents the first rigorous mathematical formalization of the Wave model from historical linguistics, introducing a fully Bayesian generative model grounded in a fixed graph structure. In this framework, linguistic innovations propagate across the graph and stochastically disappear according to a death process, with posterior inference performed via Metropolis–Hastings within Gibbs sampling. The proposed approach offers a unified modeling paradigm for diverse diffusion phenomena in the human sciences and demonstrates superior accuracy in reconstructing the evolutionary dynamics of populations under continuous interaction, as validated on both simulated and real-world data.

This study investigates the stationary distribution and stability of stochastic differential equation systems with multimodal uncertain parameters exhibiting superposition effects, using the nonlinear Rosenzweig–MacArthur predator–prey model as a case study. For the first time, multimodal mixture-distributed parameters are incorporated into the stationary analysis of stochastic dynamical systems. System stability is quantified through the eigenvalue distribution of the Jacobian matrix, and posterior stationary density estimates are obtained via the Monte Carlo method proposed by Hoegele (2026). The results reveal that under multimodal parameter uncertainty, the system exhibits a multimodal stationary distribution, accurately delineating regions of stability. This demonstrates the effectiveness and novelty of the proposed framework for uncertainty quantification in complex ecological dynamics.

This work addresses the challenge of generating human mobility trajectories that faithfully reproduce real-world network structures and temporal patterns without relying on assumptions about individual behavior. The authors propose a network-centric, privacy-preserving trajectory generation framework that constructs a time-varying Markovian dynamics model grounded in spatial interaction networks. The transition matrix is defined through a gravity-like distance decay function, exogenous temporal scheduling, and directional bias. Notably, the model introduces, for the first time, a periodic stationary population distribution as a non-transient reference state. By rigorously linking trajectory realizations to multi-step Markov dynamics, the method successfully reproduces structured origin–destination flows shaped by network geometry, temporal modulation, and connectivity constraints, achieving high consistency between individual-level trajectories and macroscopic dynamics, with discrepancies attributable solely to finite-population sampling effects.

This study addresses the insufficient output representation of agent-based models (ABMs). To this end, we propose a dual-axis analytical framework integrating temporal structure and distributional geometry. Methodologically, we first couple ε-machines from computational mechanics with score-based generative diffusion models, jointly leveraging Kolmogorov complexity analysis and score matching to simultaneously model ABM time-series predictability and high-dimensional state-distribution morphology. Theoretically, we provide formal definitions and derive key propositions; empirically, we validate the framework on a geriatric care ABM dataset, demonstrating its effectiveness in behavioral interpretation, long-horizon forecasting, and distributional synthesis. Our core contribution lies in a cross-domain, dual-dimensional representation paradigm—bridging computational mechanics and generative modeling—which overcomes the limitations of conventional univariate temporal or static distribution analyses. This advances ABM interpretability and enables controllable, physics-informed generative modeling.

This study addresses the challenge of uncovering latent dynamical patterns underlying socio-cultural evolution, overcoming limitations of existing approaches that inadequately capture the uncertainty and continuity of historical trajectories. To this end, it introduces the Langevin dynamics framework into social evolution analysis for the first time, modeling evolutionary processes as continuous-time stochastic differential equations (SDEs). By integrating Bayesian inference with multiple imputation techniques, the proposed method simultaneously quantifies irreversibility, detects exogenous perturbations, and reconstructs missing data within a unified framework. This approach transcends the constraints of static models, effectively handling fragmented historical records and revealing the intrinsic stability, contingency, and dynamic mechanisms that shape societal evolution.

Existing models struggle to capture the stochasticity, demographic fluctuations, and finite-size effects inherent in the coupled dynamics of opinion evolution and migration. This work proposes a unified stochastic framework that, for the first time, jointly models migration networks, local opinion transitions, and demographic processes within a spatiotemporal master equation formalism, from which corresponding macroscopic mean-field equations are derived. The approach elucidates the intrinsic mechanisms by which migration drives collective behaviors such as consensus formation, group polarization, and stable oscillations. Case studies demonstrate that stochasticity combined with migration topology can profoundly reshape opinion trajectories and give rise to a rich variety of macroscopic steady states.

This study addresses multi-source list data featuring absorbing lists—such as death registries—and asymmetric interactions among sources. The authors propose a novel framework based on continuous-time Markov chains that, for the first time, integrates both absorption mechanisms and directional interactions into multi-list capture–recapture models. By explicitly modeling absorbing states and employing a log-linear structure, the method effectively mitigates estimation bias inherent in conventional approaches that neglect absorption. Empirical analyses on stroke epidemiology data and London drug-use records demonstrate that the proposed framework yields unbiased and robust estimates of total population size, substantially extending the applicability of existing capture–recapture methodologies.

This work addresses the challenge of jointly modeling variable point counts and spatial configurations in spatial point process generation by proposing the Existence Field Diffusion Model (EFDM). EFDM introduces, for the first time, an existence field into a diffusion framework, assigning each latent point a continuous existence variable to unify the modeling of point cardinality and location without requiring explicit discrete dimensional jumps. By constructing a joint continuous diffusion mechanism over both existence variables and spatial coordinates, EFDM enables symmetric, flexible, and unified generation of variable-cardinality point processes. Experimental results demonstrate that the proposed model significantly improves generation quality and modeling capability across multiple variable-cardinality datasets.