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Graphs are a standard framework for describing dynamical processes shaped by pairwise interactions among agents. But many systems involve interactions in groups of three or more agents. Here, we develop a method of "$\ell$-hyperedge…
The interplay between local and regional processes in the dynamics of ecological communities remains a challenge to model, analyze and predict. This is especially notable in infectious diseases with multiple strains, where several layers of…
Most infectious diseases spread on a dynamic network of human interactions. Recent studies of social dynamics have provided evidence that spreading patterns may depend strongly on detailed micro-dynamics of the social system. We have…
An outstanding problem of interdisciplinary interest is to understand quantitatively the role of social contacts in contagion dynamics. In general, there are two types of contacts: close ones among friends, colleagues and family members,…
The recent COVID-19 pandemic has shown that when the reproduction number is high and there are no proper measurements in place, the number of infected people can increase dramatically in a short time, producing a phenomenon that many…
Especially in lattice structured populations, homogeneous mixing represents an inadequate assumption. Various improvements upon the ordinary pair approximation based on a number of assumptions concerning the higher-order correlations have…
Extending the stochastic mean-field model by including pairing, an approach is proposed for describing evolutions of complex many-body systems in terms of an ensemble of Time-Dependent Hartree-Fock Bogoliubov trajectories which is…
We propose an extension of the classical susceptible infectious recovered (SIR) model that incorporates the effects of spatial propagation of an epidemic through a small number of additional compartments. The model is designed to capture…
Contagion, a concept from epidemiology, has long been used to characterize social influence on people's behavior and affective (emotional) states. While it has revealed many useful insights, it is not clear whether the contagion metaphor is…
We introduce a Bayesian sequential data assimilation method for COVID-19 forecasting. It is assumed that suitable transmission, epidemic and observation models are available and previously validated and the transmission and epidemic models…
Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information spreading. While devising stochastic models of such processes is relatively easy, analyzing them is very…
For algorithms based on interacting particle systems that admit a mean-field description, convergence analysis is often more accessible at the mean-field level. In order to transfer convergence results obtained at the mean-field level to…
A susceptible-infected-susceptible (SIS) model of multiple contagions on multilayer networks is developed to incorporate different spreading channels and disease mutations. The basic reproduction number for this model is estimated…
Complex contagion adoption dynamics are characterised by a node being more likely to adopt after multiple network neighbours have adopted. We show how to construct multi-type branching processes to approximate complex contagion adoption…
Contact tracing, the practice of isolating individuals who have been in contact with infected individuals, is an effective and practical way of containing disease spread. Here, we show that this strategy is particularly effective in the…
An epidemic model where disease transmission can occur either through global contacts or through local, nearest neighbor interactions is considered. The classical SIR--model describing the global interactions is extended by adding…
The epidemic spreading has been widely studied when each node may get infected by an infected neighbor with the same rate. However, the infection rate between a pair of nodes is usually heterogeneous and even correlated with their nodal…
Network-based models of epidemic spread have become increasingly popular in recent decades. Despite a rich foundation of such models, few low-dimensional systems for modeling SIS-type diseases have been proposed that manage to capture the…
Spreading from a seed is studied by Monte Carlo simulation on a square lattice with two types of sites affecting the rates of birth and death. These systems exhibit a critical transition between survival and extinction. For time- dependent…
We consider SIS contagion processes over networks where, a classical assumption is that individuals' decisions to adopt a contagion are based on their immediate neighbors. However, recent literature shows that some attributes are more…