Related papers: Coupling a branching process to an infinite dimens…
We propose a generative model and an inference scheme for epidemic processes on dynamic, adaptive contact networks. Network evolution is formulated as a link-Markovian process, which is then coupled to an individual-level stochastic SIR…
Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterize…
We consider a threshold epidemic model on a clustered random graph with overlapping communities. In other words, our epidemic model is such that an individual becomes infected as soon as the proportion of her infected neighbors exceeds the…
Let $(Z_n)_{n\geqslant 0}$ be a branching process in a random environment defined by a Markov chain $(X_n)_{n\geqslant 0}$ with values in a finite state space $\mathbb X$ starting at $X_0=i \in\mathbb X$. We extend from the i.i.d.…
Branching processes are widely used to model the viral epidemic evolution. For more adequate investigation of viral epidemic modelling, we suggest to apply branching processes with transport of particles usually called branching random…
This paper presents a novel extension of the edge-based compartmental model for epidemics with arbitrary distributions of transmission and recovery times. Using the message passing approach we also derive a new pairwise-like model for…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
Understanding the timing of the peak of a disease outbreak forms an important part of epidemic forecasting. In many cases, such information is essential for planning increased hospital bed demand and for designing of public health…
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…
Epidemics are inherently stochastic, and stochastic models provide an appropriate way to describe and analyse such phenomena. Given temporal incidence data consisting of, for example, the number of new infections or removals in a given time…
In this paper we introduce a novel method to conduct inference with models defined through a continuous-time Markov process, and we apply these results to a classical stochastic SIR model as a case study. Using the inverse-size expansion of…
We are interested in the invasion phase for stochastic processes with interactions when a single mutant with positive fitness arrives in a resident population at equilibrium. By a now classic approach, the first stage of the invasion is…
A branching process in a Markovian environment consists of an irreducible Markov chain on a set of "environments" together with an offspring distribution for each environment. At each time step the chain transitions to a new random…
Hybrid systems, and Piecewise Deterministic Markov Processes in particular, are widely used to model and numerically study systems exhibiting multiple time scales in biochemical reaction kinetics and related areas. In this paper an almost…
Epidemic models are used to analyze the progression or outcome of an epidemic under different control policies like vaccinations, quarantines, lockdowns, use of face-masks, pharmaceutical interventions, etc. When these models accurately…
Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved.…
We consider a branching random walk in a random space-time environment of disasters where each particle is killed when meeting a disaster. This extends the model of the "random walk in a disastrous random environment" introduced by [15]. We…
Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the…
We present an importance sampling algorithm that can produce realisations of Markovian epidemic models that exactly match observations, taken to be the number of a single event type over a period of time. The importance sampling can be used…
In this paper, a branching process approximation for the spread of a Reed-Frost epidemic on a network with tunable clustering is derived. The approximation gives rise to expressions for the epidemic threshold and the probability of a large…