Related papers: Discrete-time staged progression epidemic models
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…
We propose a dynamical model for describing the spread of epidemics. This model is an extension of the SIQR (susceptible-infected-quarantined-recovered) and SIRP (susceptible-infected-recovered-pathogen) models used earlier to describe…
In this paper, we use a series of small world networks to simulate the epidemic spreading in the real world. To make our model more similar to the real world, we employ a parameter $p_{move}$ to denote its moving probability, which…
A stochastic SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a social network is analysed. The underlying social network is described by an Erd\H{o}s-R\'{e}nyi random graph but, during the course of the epidemic,…
In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for…
Our study is devoted to a four-compartment epidemic model of a constant population of independent random walkers. Each walker is in one of four compartments (S-susceptible, C-infected but not infectious (period of incubation), I-infected…
Strategic test allocation plays a major role in the control of both emerging and existing pandemics (e.g., COVID-19, HIV). Widespread testing supports effective epidemic control by (1) reducing transmission via identifying cases, and (2)…
Infectious diseases outbreaks are often characterized by a spatial component induced by hosts' distribution, mobility, and interactions. Spatial models that incorporate hosts' movements are being used to describe these processes, to…
We extend our BDI (birth-death-immigration) process based stochastic model of an infectious disease to time-nonhomogeneous cases. First, we discuss the deterministic model, and derive the expected value of the infection process. Then as an…
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.…
Infectious diseases are practically represented by models with multiple states and complex transition rules corresponding to, for example, birth, death, infection, recovery, disease progression, and quarantine. In addition, networks…
Testing individuals for pathogens can affect the spread of epidemics. Understanding how individual-level processes of sampling and reporting test results can affect community- or population-level spread is a dynamical modeling question. The…
The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…
We study the early stages of viral infection, and the distribution of times to obtain a persistent infection. The virus population proliferates by entering and reproducing inside a target cell until a sufficient number of new virus…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
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 numerically study the dynamics of the SIR disease model on small-world networks by using a large-deviation approach. This allows us to obtain the probability density function of the total fraction of infected nodes and of the maximum…
Stochastic modeling of disease dynamics has had a long tradition. Among the first epidemic models including a spatial structure in the form of local interactions is the contact process. In this article we investigate two extensions of the…
We consider the spread of infectious disease through contact networks of Configuration Model type. We assume that the disease spreads through contacts and infected individuals recover into an immune state. We discuss a number of existing…
This paper analyses an SIRS-type model for infectious diseases with account for behavioural changes associated with the simultaneous spread of awareness in the population. Two types of awareness are included into the model: private…