The quantity of data and processes used in modeling projects has been dramatically increasing in recent years due to the progress in computation capability and to the popularity of new approaches such as open data. Modelers face an increasing difficulty in analyzing and modeling complex systems that consist of many heterogeneous entities. Adapting existing models is relevant to avoid dealing with the complexity of writing and studying a new model from scratch. ODD (Overview, Design concepts, Details) protocol has emerged as a solution to document Agent-Based Models (ABMs). It appears to be a convenient solution to address significant problems such as comprehension, replication, and dissemination. However, it lacks a standard that formalizes the use of data in empirical models. This paper tackles this issue by proposing a set of rules that outline the use of empirical data inside an ABM. We call this new protocol ODD+ D (ODD+Decision + Data). ODD+ D integrates a mapping diagram called DAMap (Data to Agent Mapping). This mapping model formalizes how data are processed and mapped to agent-based models. In this paper, we focus on the architecture of ODD+ D, and we illustrate it with a residential mobility model in Marrakesh.

We present a mathematical model of a fishery on several sites with a variable price. The model takes into account the evolution during the time of the resource, fishes and boats movements between the different sites, fishing effort and price that varies with respect to supply and demand. We suppose that boats and fishes movements as well as prices variations occur at a fast time scale. We use methods of aggregation of variables in order to reduce the number of variables and we derive a reduced model governing two global variables, respectively the biomass of the resource and the fishing effort of the whole fishery. We look for the existence of equilibria of the aggregated model. We show that the aggregated model can have 1, 2 or 3 non trivial equilibria. We show that a variation of the total number of sites can induce a switch from over-exploitation to sustainable fisheries.

Mathematical models used in ecology often inherit the complexity found in nature and thus are governed by a large number of variables. Aggregation of variables methods is used to make such models mathematically tractable by building an approximate system governing fewer variables. We extend here aggregation methods for linear discrete models with processes occurring at different time scales. In practical cases, some processes that occur at a fast time scale are often only measured at a slow time scale, like mortality. We present a general class of models with two time scales involving such kind of processes. We show how they should be re-scaled in order to be taken into account at the fast time scale in a more realistic approach. The approximate aggregation of these models is undertaken and justified in mathematical terms. We also provide an application to a model of a structured population in a two-patch environment.

We developed a mathematical model to study the effects of non-pharmaceutical interventions (NPIs) on the dynamics of an epidemic. The level of intervention was assessed as a fraction of the population being isolated and depended on the level of incidence of the epidemic in the population. We performed a mathematical analysis of the model and showed that, depending on the choice of the prevalence-dependent isolation function, it is possible to create new endemic equilibria and to change the stability of the disease-free equilibrium for which the epidemic vanishes. The model was then applied to the case of the COVID-19 pandemic. Several NPI management strategies were considered. In the case of an NPI intensity increasing with the level of infection, it is possible to avoid the initial epidemic peak of great amplitude that would have occurred without intervention and to stabilize the epidemic at a chosen and sufficiently low endemic level. In the case of an NPI intensity decreasing with the level of infection, the epidemic can be driven to extinction by generating an “Allee” effect: when the incidence is below a given level, the epidemic goes extinct whereas, above it, the epidemic will still be able take hold at a lower endemic level. Simulations illustrate that appropriate NPIs could make the COVID-19 vanish relatively fast. We show that, in the context of the COVID-19 pandemic, most countries have not chosen to use the most efficient strategies.