相关论文: Coupling a branching process to an infinite dimens…

We develop a theory of first passage processes in stochastic non-equilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in…

Stochastic epidemic models provide an interpretable probabilistic description of the spread of a disease through a population. Yet, fitting these models to partially observed data is a notoriously difficult task due to intractability of the…

Given a discrete spatial structure $X$, we define continuous-time branching processes that model a population breeding and dying on $X$. These processes are usually called branching random walks. They are characterized by breeding rates…

Networks have become an important tool for infectious disease epidemiology. Most previous theoretical studies of transmission network models have either considered simple Markovian dynamics at the individual level, or have focused on the…

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…

To deal with very large datasets a mini-batch version of the Monte Carlo Markov Chain Stochastic Approximation Expectation-Maximization algorithm for general latent variable models is proposed. For exponential models the algorithm is shown…

We study the spreading of cooperative infections in an empirical temporal network of contacts between people, including health care workers and patients, in a hospital. The system exhibits a phase transition leading to one or several…

We consider a subcritical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We consider the event $% \mathcal{A}_{i}(n)$ that all individuals alive at time $n$ are offspring of the…

Branching processes are classical growth models in cell kinetics. In their construction, it is usually assumed that cell lifetimes are independent random variables, which has been proved false in experiments. Models of dependent lifetimes…

This paper is concerned with stochastic SIR and SEIR epidemic models on random networks in which individuals may rewire away from infected neighbors at some rate $\omega$ (and reconnect to non-infectious individuals with probability…

Time-limited states characterise many dynamical processes on networks: disease infected individuals recover after some time, people forget news spreading on social networks, or passengers may not wait forever for a connection. These…

We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…

It is well-known that 0 is the absorbing state for a branching system. Each particle in the system lives a random long time and gives a random number of new particles at its death time. It stops when the system has no particle. This paper…

Multistate dynamical processes on networks, where nodes can occupy one of a multitude of discrete states, are gaining widespread use because of their ability to recreate realistic, complex behaviour that cannot be adequately captured by…

A statistical model assuming a preferential attachment network, which is generated by adding nodes sequentially according to a few simple rules, usually describes real-life networks better than a model assuming, for example, a Bernoulli…

A general framework for obtaining exact transition rate matrices for stochastic systems on networks is presented and applied to many well-known compartmental models of epidemiology. The state of the population is described as a vector in…

Stochastic processes can model many emerging phenomena on networks, like the spread of computer viruses, rumors, or infectious diseases. Understanding the dynamics of such stochastic spreading processes is therefore of fundamental interest.…

Compartmental epidemic models have been widely used for predicting the course of epidemics, from estimating the basic reproduction number to guiding intervention policies. Studies commonly acknowledge these models' assumptions but less…

This paper presents a new view of household epidemic models, where the interaction between the households is of mean field type. We thus obtain in the limit of infinitely many households a nonlinear Markov process solution of a McKean -…

We consider the problem of computing first-passage time distributions for reaction processes modelled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem…