Human mobility and innovation spreading in ancient times: a stochastic agent-based simulation approach

Abstract

Human mobility always had a great influence on the spreading of cultural, social and technological ideas. Developing realistic models that allow for a better understanding, prediction and control of such coupled processes has gained a lot of attention in recent years. However, the modeling of spreading processes that happened in ancient times faces the additional challenge that available knowledge and data is often limited and sparse. In this paper, we present a new agent-based model for the spreading of innovations in the ancient world that is governed by human movements. Our model considers the diffusion of innovations on a spatial network that is changing in time, as the agents are changing their positions. Additionally, we propose a novel stochastic simulation approach to produce spatio-temporal realizations of the spreading process that are instructive for studying its dynamical properties and exploring how different influences affect its speed and spatial evolution.

Multilevel ensemble Kalman filtering

“…This SDE is the metastable motion of particles between the two wells, cf. [7,40]. Figure 3 shows the dynamics of a particle over N = 20 observation times.…”

“…The proof of the first inequality is analogous to [20,Lemma 3.4], and the latter inequality follows fromv N n ∈ ∩ p≥2 L p (Ω, R d ), uniformly in N ≥ 1, cf. (7). We next bound the difference between Proof.…”

Mathematical modeling of spatio-temporal population dynamics and application to epidemic spreading

“…In the resulting hybrid modeling approach, the interactions within each subpopulation are described by continuous, deterministic dynamics in form of ODEs, while the comparatively rare exchange between the subpopulations are still treated as stochastic, discrete events. These piecewisedeterministic dynamics can be efficiently simulated by a combination of the stochastic simulation algorithm and an ODE solver [23,24], and the effort is independent of the population size.…”

Data-driven model reduction of agent-based systems using the Koopman generator

“…Agent-based models provide an easily explainable and accessible framework for studying the dynamical behavior of interacting agents without requiring an extensive mathematical background. Models range from (highly detailed) microscopic stochastic descriptions following spatial movement and neighbor interactions [ 9 ] and individual-based stochastic descriptions in a network without movement [ 10 ] to Markov chain approaches for collective population dynamics [ 11 ]. Most agent-based models have in common that they are hard to analyze due to their high-dimensionality.…”