Related papers: SIR epidemics on evolving graphs
We study SIR type epidemics on graphs in two scenarios: (i) when the initial infections start from a well connected central region, (ii) when initial infections are distributed uniformly. Previously, \'Odor et al. demonstrated on a few…
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…
We consider the Susceptible-Infected-Recovered (SIR) epidemic model on a Euclidean network in one dimension in which nodes at a distance $l$ are connected with probability $P(l) \propto l^{-\delta}$ in addition to nearest neighbors. The…
We study the Susceptible-Infected-Susceptible model of the spread of an endemic infection. We calculate an exact expression for the mean number of transmissions for all values of the population and the infectivity. We derive the large-N…
Starting from a stochastic individual-based description of an SIS epidemic spreading on a random network, we study the dynamics when the size $n$ of the network tends to infinity. We recover in the limit an infinite-dimensional…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set…
In a metapopulation network, infectious diseases spread widely because of the travel of individuals. In the present study, we consider a modified metapopulation Susceptible-Infected-Removed (SIR) model with a latent period, which we call…
We investigate the expected time to extinction in the susceptible-infectious-susceptible (SIS) model of disease spreading. Rather than using stochastic simulations, or asymptotic calculations in network models, we solve the extinction time…
We study the SIR model of epidemics on positively correlated heterogeneous networks with population variability, and explore the dependence of the final outbreak size on the network heterogeneity strength and basic reproduction number $R_0$…
In this work we study a modified Susceptible-Infected-Susceptible (SIS) model in which the infection rate $\lambda$ decays exponentially with the number of reinfections $n$, saturating after $n=l$. We find a critical decaying rate…
A model for epidemics on an adaptive network is considered. Nodes follow an SIRS (susceptible-infective-recovered-susceptible) pattern. Connections are rewired to break links from non-infected nodes to infected nodes and are reformed to…
A network epidemic model is studied. The underlying social network has two different types of group structures, households and workplaces, such that each individual belongs to exactly one household and one workplace. The random network is…
We are interested in a variation of the SIR (Susceptible/Infected/Recovered) dynamics on the complete graph, in which infected individuals may only spread to neighboring susceptible individuals at fixed rate $\lambda>0$ while recovered…
We study an individual-based stochastic SIR epidemic model with infection-age dependent infectivity on a large random graph, capturing individual heterogeneity and non-homogeneous connectivity. Each individual is associated with particular…
Many complex networks exhibit vulnerability to spreading of epidemics, and such vulnerability relates to the viral strain as well as to the network characteristics. For instance, the structure of the network plays an important role in…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite…
The mobility patterns of individuals in China during the early outbreak of the COVID-19 pandemic exhibit reversible changes -- in many regions, the mobility first decreased significantly and later restored. Based on this observation, here…
Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a…
It is the main purpose of this paper to introduce a graph-valued stochastic process in order to model the spread of a communicable infectious disease. The major novelty of the SIR model we promote lies in the fact that the social network on…