相关论文: The basic reproduction number, $R_0$, in structure…

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.…

The ability to actually implement epidemic models is a crucial stake for public institutions, as they may be overtaken by the increasing complexity of current models and sometimes tend to revert to less elaborate models such as the SIR. In…

In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…

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,…

We present a compartmental SEIAR model of epidemic spread as a generalization of the SEIR model. We believe that the asymptomatic infectious cohort is an omitted part of the understanding of the epidemic dynamics of disease COVID-19. We…

What role do asymptomatically infected individuals play in the transmission dynamics? There are many diseases, such as norovirus and influenza, where some infected hosts show symptoms of the disease while others are asymptomatically…

In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of…

This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…

Individual contributions to the spread of an epidemic vary widely due to an individual's location in a social network and their intrinsic ability to spread or contract diseases. While the effect of heterogeneous population structure and…

The impact of spatial structure on the spread of an epidemic is an important issue in the propagation of infectious diseases. Recent studies, both deterministic and stochastic, have made it possible to understand the importance of the…

Epidemic modelling on complex networks has been studied intensively all the time. The majority of relative research assumes that the time scale of the underlying network evolution is much larger compared to the propagation dynamics on it,…

Self-adaptive dynamics occurs in many physical systems such as socio-economics, neuroscience, or biophysics. We formalize a self-adaptive modeling approach, where adaptation takes place within a set of strategies based on the history of the…

At the onset of the Covid-19 pandemic, a number of non-pharmaceutical interventions have been implemented in order to reduce transmission, thus leading to multiple phases of transmission. The disease reproduction number $R_t$, a way of…

Stochastic discrete-time SIS and SIR models of endemic diseases are introduced and analyzed. For the deterministic, mean-field model, the basic reproductive number $R_0$ determines their global dynamics. If $R_0\le 1$, then the frequency of…

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…

We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of…

In contrast to the common assumption in epidemic models that the rate of infection between individuals is constant, in reality, an individual's viral load determines their infectiousness. We compare the average and individual reproductive…

Modeling the spread of COVID-19 is crucial for informing public health policy. All models for COVID-19 epidemiology rely on parameters describing the dynamics of the infection process. The meanings of epidemiological parameters like R_0,…

Capturing the structure of a population and characterising contacts within the population are key to reliable projections of infectious disease. Two main elements of population structure -- contact heterogeneity and age -- have been…

The death toll for Covid-19 may be reduced by dividing the population into two classes, the vulnerable and the fit, with different lockdown regimes. Instead of one reproduction number there now are four parameters. These make it possible to…