Related papers: Exact epidemic models from a tensor product formul…
Epidemic models are useful tools in the fight against infectious diseases, as they allow policy makers to test and compare various strategies to limit disease transmission while mitigating collateral damage on the economy. Epidemic models…
We introduce a numerical method to solve epidemic models on the underlying topology of complex networks. The approach exploits the mean-field like rate equations describing the system and allows to work with very large system sizes, where…
Epidemic modelling on complex networks has been studied intensively all the time. The majority of relative research assumes that the time scale of the underlying network evolution is much larger compared to the propagation dynamics on it,…
Mathematical modeling is one of the key factors of the effective control of newly found infectious diseases, such as COVID-19. Our knowledge about the parameters and the course of the infection is highly limited in the beginning of the…
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…
We define the projected entropy S(T) at a given temperature T in the context of an Ising model transition matrix calculation as the entropy associated with the distribution of Markov chain realizations in energy-magnetization, E-H, space.…
We are interested in describing the infected size of the SIS Epidemic model using Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) model is defined within a population of constant size $M$; the size is kept constant by…
We study the Susceptible-Infected-Recovered model of epidemics in the vicinity of the threshold infectivity. We derive the distribution of total outbreak size in the limit of large population size $N$. This is accomplished by mapping the…
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…
Optimal designs minimize the number of experimental runs (samples) needed to accurately estimate model parameters, resulting in algorithms that, for instance, efficiently minimize parameter estimate variance. Governed by knowledge of past…
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…
In the infectious disease literature, significant effort has been devoted to studying dynamics at a single scale. For example, compartmental models describing population-level dynamics are often formulated using differential equations. In…
More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…
We consider a strictly substochastic matrix or an stochastic matrix with absorbing states. By using quasi-stationary distributions one shows there is a canonical associated stationary Markov chain. Based upon $2-$stringing representation of…
We test a Markov chain approximation to the segment description (Li, 2007) of chaos (and turbulence) on a tent map, the Minea system, the H\'enon map, and the Lorenz system. For the tent map, we compute the probability transition matrix of…
Transition Path Theory (TPT) provides a rigorous statistical characterization of the ensemble of trajectories connecting directly, i.e., without detours, two disconnected (sets of) states in a Markov chain, a stochastic process that…
Consider stochastic models for the spread of an infection in a structured community, where this structured community is itself described by a random network model. Some common network models and transmission models are defined and large…
We study epidemic processes using a metapopulation approach on the line featuring random transport rates between arbitrarily distant sites. An average transport network is found using a recently developed variant of the effective medium…
Motivated by fundamental issues in non-equilibrium statistical mechanics (NESM), we study the venerable susceptible-infected (SIS) model of disease spreading in an idealized, simple setting. Using Monte Carlo and analytic techniques, we…
Tensor network states are powerful variational ans\"atze for many-body ground states of quantum lattice models. The use of Monte Carlo sampling techniques in tensor network approaches significantly reduces the cost of tensor contractions,…