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.

Agent based models (ABMs) are a useful tool for modeling spatio-temporal population dynamics, where many details can be included in the model description. Their computational cost though is very high and for stochastic ABMs a lot of individual simulations are required to sample quantities of interest. Especially, large numbers of agents render the sampling infeasible. Model reduction to a metapopulation model leads to a significant gain in computational efficiency, while preserving important dynamical properties. Based on a precise mathematical description of spatio-temporal ABMs, we present two different metapopulation approaches (stochastic and piecewise deterministic) and discuss the approximation steps between the different models within this framework. Especially, we show how the stochastic metapopulation model results from a Galerkin projection of the underlying ABM onto a finite-dimensional ansatz space. Finally, we utilize our modeling framework to provide a conceptual model for the spreading of COVID-19 that can be scaled to real-world scenarios.

Scholars frequently cite fuel scarcity after deforestation as a reason for the abandonment of most of the Roman iron smelting sites on Elba Island (Tuscan Archipelago, Italy) in the 1st century bce. Whereas the archaeological record clearly indicates the decrease in smelting activities, evidence confirming the ‘deforestation narrative’ is ambiguous. Therefore, we employed a stochastic, spatio-temporal model of the wood required and consumed for iron smelting on Elba Island in order to assess the availability of fuelwood on the island. We used Monte Carlo simulations to cope with the limited knowledge available on the past conditions on Elba Island and the related uncertainties in the input parameters. The model includes both, wood required for the furnaces and to supply the workforce employed in smelting. Although subject to high uncertainties, the outcomes of our model clearly indicate that it is unlikely that all woodlands on the island were cleared in the 1st century bce. A lack of fuel seems only likely if a relatively ineffective production process is assumed. Therefore, we propose taking a closer look at other reasons for the abandonment of smelting sites, e.g. the occupation of new Roman provinces with important iron ore deposits; or a resource-saving strategy in Italia. Additionally, we propose to read the development of the ‘deforestation narrative’ originating from the 18th/19th century in its historical context.