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This document is the Part IV of the book 'Stochastic Epidemic Models with Inference' edited by Tom Britton and Etienne Pardoux. It is written by Catherine Lar\'edo, with the contribution of Viet Chi Tran for the Chapter 4. Epidemic data…
Models with intractable normalizing functions arise frequently in statistics. Common examples of such models include exponential random graph models for social networks and Markov point processes for ecology and disease modeling. Inference…
Whole genome sequencing of pathogens from multiple hosts in an epidemic offers the potential to investigate who infected whom with unparalleled resolution, potentially yielding important insights into disease dynamics and the impact of…
Mathematical models of infectious disease transmission typically neglect within-host dynamics. Yet within-host dynamics - including pathogen replication, host immune responses, and interactions with microbiota - are crucial not only for…
We analyze four models of epidemic spreading using a stochastic approach in which the primary stochastic variables are the numbers of individuals in each class. The stochastic approach is described by a master equation and the transition…
Many epidemic models are naturally defined as individual-based models: where we track the state of each individual within a susceptible population. Inference for individual-based models is challenging due to the high-dimensional state-space…
Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach…
Social networks are an important infrastructure for information, viruses and innovations propagation. Since users behavior has influenced by other users activity, some groups of people would be made regard to similarity of users interests.…
We study a simple model of epidemics where an infected node transmits the infection to its neighbors independently with probability $p$. This is also known as the independent cascade or Susceptible-Infected-Recovered (SIR) model with fixed…
The duration, type and structure of connections between individuals in real-world populations play a crucial role in how diseases invade and spread. Here, we incorporate the aforementioned heterogeneities into a model by considering a…
We study a multilayer SIR model with two levels of mixing, namely a global level which is uniformly mixing, and a local level with two layers distinguishing household and workplace contacts, respectively. We establish the large population…
The time varying effective reproduction number is an important parameter for communication and policy decisions during an epidemic. In this paper, we present new statistical methods for estimating the reproduction number based on the…
Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…
Consider a Markovian SIR epidemic model in a homogeneous community. To this model we add a rate at which individuals are tested, and once an infectious individual tests positive it is isolated and each of their contacts are traced and…
By generating the specifics of a network structure only when needed (on-the-fly), we derive a simple stochastic process that exactly models the time evolution of susceptible-infectious dynamics on finite-size networks. The small number of…
It is the main purpose of this paper to introduce a graph-valued stochastic process in order to model the spread of a communicable infectious disease. The major novelty of the SIR model we promote lies in the fact that the social network on…
We study several bayesian inference problems for irreversible stochastic epidemic models on networks from a statistical physics viewpoint. We derive equations which allow to accurately compute the posterior distribution of the time…
Bayesian nonparametric inferential procedures based on Markov chain Monte Carlo marginal methods typically yield point estimates in the form of posterior expectations. Though very useful and easy to implement in a variety of statistical…
We introduce a new method for inference in stochastic epidemic models which uses recursive multinomial approximations to integrate over unobserved variables and thus circumvent likelihood intractability. The method is applicable to a class…
We consider a stochastic epidemic model with sideward contact tracing. We assume that infection is driven by interactions within mixing events (gatherings of two or more individuals). Once an infective is diagnosed, each individual who was…