Related papers: Statistics of infections with diversity in the pat…

The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…

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…

In this paper we first introduce the general stochastic epidemic model for the spread of infectious diseases. Then we give methods for inferring model parameters such as the basic reproduction number $R_0$ and vaccination coverage $v_c$…

We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong disorder, i.e. a wide…

A simple, but ``classical``, stochastic model for epidemic spread in a finite, but large, population is studied. The progress of the epidemic can be divided into three different phases that requires different tools to analyse. Initially the…

Spatial models for spread of an epidemic may be mapped onto bond percolation. We point out that with disorder in the strength of contacts between individuals patchiness in the spread of the epidemic is very likely, and the criterion for…

Viruses constantly undergo mutations with genomic changes. The propagation of variants of viruses is an interesting problem. We perform numerical simulations of the microscopic epidemic model based on network theory for the spread of…

Stochasticity and spatial heterogeneity are of great interest recently in studying the spread of an infectious disease. The presented method solves an inverse problem to discover the effectively decisive topology of a heterogeneous network…

I study the spreading of infectious diseases on heterogeneous populations. I represent the population structure by a contact-graph where vertices represent agents and edges represent disease transmission channels among them. The population…

A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings…

A model for the spread of an infection is analyzed for different population structures. The interactions within the population are described by small world networks, ranging from ordered lattices to random graphs. For the more ordered…

This article examines how diseases on random networks spread in time. The disease is described by a probability distribution function for the number of infected and recovered individuals, and the probability distribution is described by a…

During infectious disease epidemics, pathogen transmission occurs in host populations made up of interacting subpopulations. Using stochastic simulation and analytical approximations, we examine how outbreak sizes in networked populations…

Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious…

A social (sexual) network is modeled by an extension of the configuration model to the situation where edges have weights, e.g. reflecting the number of sex-contacts between the individuals. An epidemic model is defined on the network such…

Epidemic disease spreading is conventionally often modelled and analyzed by means of rate and diffusion equations, following the paradigms of well-controlled chemical reactions and diffusive dynamics in a test tube. Yet, serious worries…

In the first part of this paper, we review old and new results about the influence of host population heterogeneity on (various characteristics of) epidemic outbreaks. In the second part we highlight a modelling issue that so far has…

A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…

The vast majority of models for the spread of communicable diseases are parametric in nature and involve underlying assumptions about how the disease spreads through a population. In this article we consider the use of Bayesian…

This paper investigates the dynamics of infectious diseases with a non-exponentially distributed infectious period. This is achieved by considering a multi-stage infection model on networks. Using pairwise approximation with a standard…