Related papers: Dynamics of epidemic spreading on connected graphs
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…
We investigate the SIR epidemic on a dynamic inhomogeneous Erd\H{o}s-R\'enyi random graph, in which vertices are of one of $k$ types and in which edges appear and disappear independently of each other. We establish a functional law of large…
Random networks with specified degree distributions have been proposed as realistic models of population structure, yet the problem of dynamically modeling SIR-type epidemics in random networks remains complex. I resolve this dilemma by…
We consider an SIR-type (Susceptible $\to$ Infected $\to$ Recovered) stochastic epidemic process with multiple modes of transmission on a contact network. The network is given by a random graph following a multilayer configuration model…
In this paper, we study the trajectory of a classic SIR epidemic on a family of dynamic random graphs of fixed size, whose set of edges continuously evolves over time. We set general infection and recovery times, and start the epidemic from…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
We study a system of reaction-diffusion equations posed on a bounded domain composed of subdomains separated by a connected network with a metric graph structure. The reaction-diffusion dynamics with anisotropic diffusion on the graph edges…
Epidemic spreading is well understood when a disease propagates around a contact graph. In a stochastic susceptible-infected-susceptible setting, spectral conditions characterise whether the disease vanishes. However, modelling human…
One of the popular dynamics on complex networks is the epidemic spreading. An epidemic model describes how infections spread throughout a network. Among the compartmental models used to describe epidemics, the…
The spread of an infectious disease depends on intrinsic properties of the disease as well as the connectivity and actions of the population. This study investigates the dynamics of an SIR type model which accounts for human tendency to…
We consider an SIR epidemic model propagating on a configuration model network, where the degree distribution of the vertices is given and where the edges are randomly matched. The evolution of the epidemic is summed up into three…
In the standard SIR model, infected vertices infect their neighbors at rate $\lambda$ independently across each edge. They also recover at rate $\gamma$. In this work we consider the SIR-$\omega$ model where the graph structure itself…
This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of…
Most epidemic models assume equal mixing among members of a population. An alternative approach is to model a population as random network in which individuals may have heterogeneous connectivity. This paper builds on previous research by…
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…
We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…
The interplay between disease spreading and personal risk perception is of key importance for modelling the spread of infectious diseases. We propose a planar system of ordinary differential equations (ODEs) to describe the co-evolution of…
In this paper we study a discrete-time SIS (susceptible-infected-susceptible) model, where the infection and healing parameters and the underlying network may change over time. We provide conditions for the model to be well-defined and…
In this paper we study the susceptible-infectious (SI) epidemiological model using dynamical graphs. Dynamical structures have been recently applied in many areas including complex systems. Dynamical structures include the mutual…
Infectious disease superspreading caused by heterogeneity in contact behavior has been observed to be an important determinant of epidemic dynamics and size in both empirical and theoretical settings. However, it has also been observed that…