Related papers: Exact mean field dynamics for epidemic-like proces…
Recent studies on network geometry, a way of describing network structures as geometrical objects, are revolutionizing our way to understand dynamical processes on networked systems. Here, we cope with the problem of epidemic spreading,…
Modeling spreading processes in complex random networks plays an essential role in understanding and prediction of many real phenomena like epidemics or rumor spreading. The dynamics of such systems may be represented algorithmically by…
We derive analytic expressions for the possibility, probability, and expected size of global spreading events starting from a single infected seed for a broad collection of contagion processes acting on random networks with both directed…
We derive the master equations for the Susceptible-Infected (SI) model on general hypernetworks with~$N$-body interactions. We solve these equations exactly for infinite~$d$-regular hypernetworks, and obtain an explicit solution for the…
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…
Understanding the dynamics of the spread of diseases within populations is critical for effective public health interventions. We extend the classical SIR model by incorporating additional complexities such as the introduction of a cure and…
Pairwise models are used widely to model epidemic spread on networks. These include the modelling of susceptible-infected-removed (SIR) epidemics on regular networks and extensions to SIS dynamics and contact tracing on more exotic networks…
Recent work from public health experts suggests that incorporating human behavior is crucial in faithfully modeling an epidemic. We present a reaction-diffusion partial differential equation SIR-type population model for an epidemic…
It is common to use a compartmental, fluid model described by a system of ordinary differential equations (ODEs) to model disease spread. In addition to their simplicity, these models are also the mean-field approximations of more accurate…
The dramatic outbreak of the coronavirus disease 2019 (COVID-19) pandemics and its ongoing progression boosted the scientific community's interest in epidemic modeling and forecasting. The SIR (Susceptible-Infected-Removed) model is a…
We define and study an open stochastic SIR (Susceptible -- Infected -- Removed) model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same…
To simplify mathematical models of disease spread, we often assume equal contact rates among hosts, but real-world scenarios differ. Network-based frameworks help capture these complexities and structural variations in actual systems. We…
Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a…
It is generally accepted that scale-free networks is prone to epidemic spreading allowing the onset of large epidemics whatever the spreading rate of the infection. In the paper, we show that disease propagation may be suppressed in…
The identification of which nodes are optimal seeds for spreading processes on a network is a non-trivial problem that has attracted much interest recently. While activity has mostly focused on non-recurrent type of dynamics, here we…
We present a modelling framework for the spreading of epidemics on temporal networks from which both the individual-based and pair-based models can be recovered. The proposed temporal pair-based model that is systematically derived from…
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the…
This report is based on the work in (1). We first review definitions and notation developped there and provide derivations for the exact mathematical description of an SIS epidemic on a hypergraph. We then generalise the work in (1) to a…
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…
We numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum…