Related papers: On a stochastic model of epidemic spread with an a…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
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.…
Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical…
We present an analysis of six deterministic models for epidemic spreading. The evolution of the number of individuals of each class is given by ordinary differential equations of the first order in time, which are set up by using the laws…
The aim of the paper is to describe two models of Covid-19 infection dynamics. For this purpose a special class of branching processes with two types of individuals is considered. These models are intended to use only the observed daily…
The interplay of biological, social, structural and random factors makes disease forecasting extraordinarily complex. The course of an epidemic exhibits average growth dynamics determined by features of the pathogen and the population, yet…
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…
We study contact epidemic models for the spread of infective diseases in finite populations. The size dependence enters in the infection rate. The dynamics of such models is then analyzed within the deterministic approximation, as well as…
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…
Consider a uniformly mixing population which grows as a super-critical linear birth and death process. At some time an infectious disease (of SIR or SEIR type) is introduced by one individual being infected from outside. It is shown that…
These notes describe stochastic epidemics in a homogenous community. Our main concern is stochastic compartmental models (i.e. models where each individual belongs to a compartment, which stands for its status regarding the epidemic under…
Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that…
We study a stochastic epidemic model consisting of elements (organisms in a community or cells in tissue) with fixed positions, in which damage or disease is transmitted by diffusing agents ("signals") emitted by infected individuals. The…
We introduce and study a model stemming from game theory for the spread of an epidemic throughout a given population. Each agent is allowed to choose an action whose value dictates to what extent they limit their social interactions, if at…
We couple a multi-type stochastic epidemic process with a directed random graph, where edges have random lengths. This random graph representation is used to characterise the fractions of individuals infected by the different types of…
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…
We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…