Related papers: Towards Uncertainty Quantification and Inference i…
Obtaining accurate forecasts for the evolution of epidemic outbreaks from deterministic compartmental models represents a major theoretical challenge. Recently, it has been shown that these models typically exhibit trajectories' degeneracy,…
A stochastic epidemic model accounting for the effect of contact-tracing on the spread of an infectious disease is studied. Precisely, individuals identified as infected may contribute to detecting other infectious individuals by providing…
We develop a new methodology for the efficient computation of epidemic final size distributions for a broad class of Markovian models. We exploit a particular representation of the stochastic epidemic process to derive a method which is…
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.…
Multi-state models are frequently applied for representing processes evolving through a discrete set of state. Important classes of multi-state models arise when transitions between states may depend on the time since entry into the current…
In this paper we introduce a statistical inference framework for estimating the contagion source from a partially observed contagion spreading process on an arbitrary network structure. The framework is based on a maximum likelihood…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
We adapt the article of Forien, Pang, Pardoux and Zotsa: Arxiv preprint Arxiv2210.04667(2022), on epidemic models with varying infectivity and waning immunity, to incorporate the memory of the last infection. To this end, we introduce a…
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…
This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set…
Accurate and reliable forecasting of epidemic incidences is critical for public health preparedness, yet it remains a challenging task due to complex nonlinear temporal dependencies and heterogeneous spatial interactions. Often, point…
This paper proposes a data-driven approximate Bayesian computation framework for parameter estimation and uncertainty quantification of epidemic models, which incorporates two novelties: (i) the identification of the initial conditions by…
Motivation: We consider continuous-time Markov chains that describe the stochastic evolution of a dynamical system by a transition-rate matrix $Q$ which depends on a parameter $\theta$. Computing the probability distribution over states at…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
A standard model for epidemics is the SIR model on a graph. We introduce a simple algorithm that uses the early infection times from a sample path of the SIR model to estimate the parameters this model, and we provide a performance…
A stochastic epidemic model is defined in which each individual belongs to a household, a secondary grouping (typically school or workplace) and also the community as a whole. Moreover, infectious contacts take place in these three settings…
We consider an individual-based SIR stochastic epidemic model in continuous space. The evolution of the epidemic involves the rates of infection and cure of individuals. We assume that individuals move randomly on the two-dimensional torus…
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…
We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we…
In this paper we consider a stochastic SEIQR (susceptible-exposed-infected-quarantined-recovered) epidemic model with a generalized incidence function. Using the Lyapunov method, we establish the existence and uniqueness of a global…