相关论文: Critical Behaviour of the Partner Model
The effective reproduction number is an important descriptor of an infectious disease epidemic. In small populations, ideally we would estimate the effective reproduction number using a Markov Jump Process (MJP) model of the spread of…
One clear aspect of behaviour in the COVID-19 pandemic has been people's focus on, and response to, reported or observed infection numbers in their community. We describe a simple model of infectious disease spread in a pandemic situation…
The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case…
We study a multitype SIR epidemic model where individuals are categorized into different types, and where infection spread is characterized by a next-generation matrix $M=\{m_{ij}\}$ with community fractions $\{\pi_j\}$ for the different…
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 $v_c$…
In this work, we revisit the basic reproduction rate $\mathcal{R}_{0}$ definition for analysis of epidemic-non-epidemic phases describing the dynamics of the discrete stochastic version of the epidemic $SIR$ model based on the Master…
The dynamics of epidemic spreading is often reduced to the single control parameter $R_0$, whose value, above or below unity, determines the state of the contagion. If, however, the pathogen evolves as it spreads, $R_0$ may change over…
A basic reproduction number, $R_0$, is a concept encountered frequently in the study of ecological and epidemiological models. It is routinely used to determine the stability of an extinction or a disease-free fixed point or steady state.…
We present a stochastic epidemic model to study the effect of various preventive measures, such as uniform reduction of contacts and transmission, vaccination, isolation, screening and contact tracing, on a disease outbreak in a…
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.…
To investigate the combined effects of drug resistance, seasonality and vector-bias, we formulate a periodic two-strain reaction-diffusion model. It is a competitive system for resistant and sensitive strains, but the single-strain…
The effect of diffusion rates on the basic reproduction number of a general compartmental reaction-diffusion epidemic model in a heterogeneous environment is considered. It is shown when the diffusion rates tend to zero, the limit of the…
Consider a birth and death chain to model the number of types of a given virus. Each type gives birth to a new type at rate $\lambda$ and dies at rate 1. Each type is also assigned a fitness. When a death occurs either the least fit type…
The duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markovian, containing classic Kermack-McKendrick, pairwise,…
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…
In the system we study, 1's and 0's represent occupied and vacant sites in the contact process with births at rate $\lambda$ and deaths at rate 1. $-1$'s are sterile individuals that do not reproduce but appear spontaneously on vacant sites…
Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\sigma}$. We study the dynamical behavior of the…
Recent evidences show that individuals who recovered from COVID-19 can be reinfected. However, this phenomenon has rarely been studied using mathematical models. In this paper, we propose a SEIRE epidemic model to describe the spread of the…
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…
We introduce the effect of site contamination in a model for spatial epidemic spread and show that the presence of site contamination may have a strict effect on the model in the sense that it can make an otherwise subcritical process…