Related papers: Epidemic spread, parameter sensitivity and vaccina…
When an epidemic spreads into a population, it is often unpractical or impossible to have a continuous monitoring of all subjects involved. As an alternative, algorithmic solutions can be used to infer the state of the whole population from…
In this paper, we propose a realistic mathematical model taking into account the mutual interference among the interacting populations. This model attempts to describe the control (vaccination) function as a function of the number of…
Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…
This paper is concerned with the analysis of vaccination strategies in a stochastic SIR (susceptible $\to$ infected $\to$ removed) model for the spread of an epidemic amongst a population of individuals with a random network of social…
Controlling and understanding epidemic outbreaks has recently drawn great interest in a large spectrum of research communities. Vaccination is one of the most well-established and effective strategies in order to contain an epidemic. In the…
This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic model properties (relying on a large community) are presented. The purpose of modelling is illustrated by…
We introduce a new percolation model to describe and analyze the spread of an epidemic on a general directed and locally finite graph. We assign a two-dimensional random weight vector to each vertex of the graph in such a way that the…
When modelling epidemics or spread of information on online social networks, it is crucial to include not just the density of the connections through which infections can be transmitted, but also the variability of susceptibility. Different…
A more connected world has brought major consequences such as facilitate the spread of diseases all over the world to quickly become epidemics, reason why researchers are concentrated in modeling the propagation of epidemics and outbreaks…
Understanding how the network topology affects the spread of an epidemic is a main concern in order to develop efficient immunization strategies. While there is a great deal of work dealing with the macroscopic topological properties of the…
In this paper, we study the spread of a classical SIR process on a two-layer random network, where the first layer represents the households, while the second layer models the contacts outside the households by a random scale-free graph. We…
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…
We study a simple model of epidemics where an infected node transmits the infection to its neighbors independently with probability $p$. This is also known as the independent cascade or Susceptible-Infected-Recovered (SIR) model with fixed…
Many real-world networks display a community structure. We study two random graph models that create a network with similar community structure as a given network. One model preserves the exact community structure of the original network,…
Consider a random graph, having a pre-specified degree distribution F but other than that being uniformly distributed, describing the social structure (friendship) in a large community. Suppose one individual in the community is externally…
Working in the multi-type Galton-Watson branching-process framework we analyse the spread of a pandemic via a general multi-type random contact graph. Our model consists of several communities, and takes, as input, parameters that outline…
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…
The spread of viruses in biological networks, computer networks, and human contact networks can have devastating effects; developing and analyzing mathematical models of these systems can be insightful and lead to societal benefits. Prior…
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…
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…