Related papers: Exact epidemic models from a tensor product formul…
In this work we study a model of tax evasion. We considered a fixed population divided in three compartments, namely honest tax payers, tax evaders and a third class between the mentioned two, which we call \textit{susceptibles} to become…
Incorporating dynamic contact networks and delayed awareness into a contagion model with memory, we study the spreading patterns of infectious diseases in connected populations. It is found that the spread of an infectious disease is not…
The problem of targeted network immunization can be defined as the one of finding a subset of nodes in a network to immunize or vaccinate in order to minimize a tradeoff between the cost of vaccination and the final (stationary) expected…
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission…
We study a coupled epidemic-mobility model in which, at each time, individuals move in a network of spatially-distributed regions (sub-populations) according to a Continuous Time Markov Chain (CTMC) and subsequently interact with the local…
Age-dependent dynamics is an important characteristic of many infectious diseases. Age-group epidemic models describe the infection dynamics in different age-groups by allowing to set distinct parameter values for each. However, such models…
We study algorithms to analyze a particular class of Markov population processes that is often used in epidemiology. More specifically, Markov binomial chains are the model that arises from stochastic time-discretizations of classical…
Assessing the practical identifiability of epidemic models is essential for determining whether parameters can be meaningfully estimated from observed data. Monte Carlo (MC) methods provide an accessible and intuitive framework; however,…
We develop a general modelling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-specific traits. We start by formulating an individual-based…
Epidemics in large complete networks is well established. In contrast, we consider epidemics in non-complete networks. We establish the fluid limit macroscopic dynamics of a multi-virus spread over a multipartite network as the number of…
We study the problem of containing epidemic spreading processes in temporal networks. We specifically focus on the problem of finding a resource allocation to suppress epidemic infection, provided that an empirical time-series data of…
We couple a multi-type stochastic epidemic process with a directed random graph, where edges have random lengths. This random graph representation is used to characterise the fractions of individuals infected by the different types of…
In this paper we develop a statistical estimation technique to recover the transition kernel $P$ of a Markov chain $X=(X_m)_{m \in \mathbb N}$ in presence of censored data. We consider the situation where only a sub-sequence of $X$ is…
The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…
To forecast the time dynamics of an epidemic, we propose a discrete stochastic model that unifies and generalizes previous approaches to the subject. Viewing a given population of individuals or groups of individuals with given health state…
Modeling joint probability distributions over sequences has been studied from many perspectives. The physics community developed matrix product states, a tensor-train decomposition for probabilistic modeling, motivated by the need to…
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 derive the master equations for the Susceptible-Infected (SI) model on general hypernetworks with~$N$-body interactions. We solve these equations exactly for infinite~$d$-regular hypernetworks, and obtain an explicit solution for the…
The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case…
Inspired from modern out-of-equilibrium statistical physics models, a matrix product based framework permits the formal definition of random vectors (and random time series) whose desired joint distributions are a priori prescribed. Its key…