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Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using…
We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models…
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations…
The susceptible-infected-recovered (SIR) model has been used extensively to model disease spread and other processes. Despite the widespread usage of this ordinary differential equation (ODE) based model which represents the mean-field…
In real social networks, person-to-person interactions are known to be heterogeneous, which can affect the way a disease spreads through a population, reaches a tipping point in the fraction of infected individuals, and becomes an epidemic.…
In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for…
We study the following model of disease spread in a social network. At first, all individuals are either infected or healthy. Next, in discrete rounds, the disease spreads in the network from infected to healthy individuals such that a…
Standard epidemiological models for COVID-19 employ variants of compartment (SIR) models at local scales, implicitly assuming spatially uniform local mixing. Here, we examine the effect of employing more geographically detailed diffusion…
Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the…
We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the $n$-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread…
Interactions in time-varying complex systems are often very heterogeneous at the topological level (who interacts with whom) and at the temporal level (when interactions occur and how often). While it is known that temporal heterogeneities…
Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an…
We consider Susceptible-Infected-Recovered (SIR) models on dense dynamic random graphs, in which the joint dynamics of vertices and edges are co-evolutionary, i.e., they influence each other bidirectionally. In particular, edges appear and…
The study of SIS epidemics on networks has stressed the role of the network topology on the spreading process. However, accurate models of SIS epidemics rely on the complete knowledge of the network topology, which is often not available.…
One approach to understand people's efforts to reduce disease transmission, is to consider the effect of behaviour on case rates. In this paper we present a spatial infection-reducing game model of public behaviour, formally equivalent to a…
Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have…
The rapid worldwide spread of the severe acute respiratory syndrome (SARS) demonstrated the potential threat an infectious disease poses in a closely interconnected and interdependent world. Here we introduce a probabilistic model which…
We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erd\H{o}s-R\'{e}nyi and Barab\'asi-Albert networks. It is known that the contact network influences the spread of an epidemic within a…
Infectious disease modeling is used to forecast epidemics and assess the effectiveness of intervention strategies. Although the core assumption of mass-action models of homogeneously mixed population is often implausible, they are…
Epidemic spreading of infectious diseases is ubiquitous and has often considerable impact on public health and economic wealth. The large variability in spatio-temporal patterns of epidemics prohibits simple interventions and demands for a…