arXiv subjects

Bram A. Siebert

Publications and source records attributed to Bram A. Siebert.

4 recordsLinked to original sources

arXiv2022

Nonlinear random walks optimize the trade-off between cost and prevention in epidemics lockdown measures : the ESIR model

Contagious diseases can spread quickly in human populations, either through airborne transmission or if some other spreading vectors are abundantly accessible. They can be particularly devastating if the impact on individuals' health has severe consequences on the number of hospitalizations or even deaths. Common countermeasures to contain the epidemic spread include introducing restrictions on human interactions or their mobility in general which are often associated with an economic and social cost. In this paper, we present a targeted model of optimal social distancing on metapopulation networks, named ESIR model, which can effectively reduce the disease spreading and at the same time minimize the impact on human mobility and related costs. The proposed model is grounded in a nonlinear random walk process that considers the finite carrying capacity of the network's metanodes, the physical patches where individuals interact within mobility networks. This later constrain is modeled as a slack compartment E for the classic SIR model and quantifies the density of vacant spaces to accommodate the diffusing individuals. Formulating the problem as a multi-objective optimization problem shows that when the walkers avoid crowded nodes, the system can rapidly approach Pareto optimality, thus reducing the spreading considerably while minimzing the impact on human mobility as also validated in empirical transport networks. These results envisage ad hoc mobility protocols that can potentially enhance policy making for pandemic control.

physics.soc-ph↗

arXiv2021

Exact solutions and bounds for network SIR and SEIR models using a rooted-tree approximation

In this paper, we develop a node-based approximate model for Markovian contagion dynamics on networks. We prove that our approximate model is exact for SIR (susceptible-infectious-recovered) and SEIR (susceptible-exposed-infectious-recovered) dynamics on tree graphs with a single source of infection and that the model otherwise gives upper bounds on the probabilities of each node being susceptible. Our analysis of SEIR contagion dynamics is generalised to SEIR models with arbitrarily many distinct classes of exposed state. In the case of trees with a single source of infection, our approach yields a system of partially-decoupled linear differential equations that exactly describes the evolution of node-state probabilities. We use this to state explicit closed-form solutions for SIR dynamics on a chain.

math.DS↗

arXiv2021

Symmetry-breaking mechanism for the formation of cluster chimera patterns

The emergence of order in collective dynamics is a fascinating phenomenon that characterizes many natural systems consisting of coupled entities. Synchronization is such an example where individuals, usually represented by either linear or nonlinear oscillators, can spontaneously act coherently with each other when the interactions' configuration fulfills certain conditions. However, synchronization is not always perfect, and the coexistence of coherent and incoherent oscillators, broadly known in the literature as chimera states, is also possible. Although several attempts have been made to explain how chimera states are created, their emergence, stability, and robustness remain a long-debated question. We propose an approach that aims to establish a robust mechanism through which chimeras originate. We first introduce a stability-breaking method where clusters of synchronized oscillators can emerge. Similarly, one or more clusters of oscillators may remain incoherent within yielding a particular class of patterns that we here name cluster chimera states.

nlin.AO↗

arXiv2020

The role of modularity in self-organisation dynamics in biological networks

Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting structure between different neurons, proteins or species influences the functioning of their respective systems. It is well-established that many biological networks are constructed in a highly hierarchical way with two main properties: short average paths that join two apparently distant nodes (neuronal, species, or protein patches) and a high proportion of nodes in modular aggregations. Although several hypotheses have been proposed so far, still little is known about the relation of the modules with the dynamical activity in such biological systems. Here we show that network modularity is a key ingredient for the formation of self-organising patterns of functional activity, independently of the topological peculiarities of the structure of the modules. In particular, we propose a self-organising mechanism which explains the formation of macroscopic spatial patterns, which are homogeneous within modules. This may explain how spontaneous order in biological networks follows their modular structural organisation. We test our results on real-world networks to confirm the important role of modularity in creating macro-scale patterns.

nlin.PS↗