Related papers: A new stochastic SIS-type modelling framework for …
In this article, we introduce an infinite-dimensional deterministic SIS model which takes into account the heterogeneity of the infections and the social network among a large population. We study the long-time behavior of the dynamic. We…
This review maps developments in stochastic modeling, highlighting non-standard approaches and their applications to biology and epidemiology. It brings together four strands: (1) core models for systems that evolve with randomness; (2)…
Motivated by the classical Susceptible-Infected-Recovered (SIR) epidemic models proposed by Kermack and Mckendrick, we consider a class of stochastic compartmental dynamical systems with a notion of partial ordering among the compartments.…
The transmission dynamics of an epidemic are rarely homogeneous. Super-spreading events and super-spreading individuals are two types of heterogeneous transmissibility. Inference of super-spreading is commonly carried out on secondary case…
Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…
We introduce a minimal multiscale framework that links within-host virus dynamics to population-level SIRS epidemiology through explicit, bidirectional coupling. At the microscopic layer, a two variant quasispecies (master and mutant…
Many real epidemics of an infectious disease are not straightforwardly super- or sub-critical, and the understanding of epidemic models that exhibit such complexity has been identified as a priority for theoretical work. We provide insights…
In this paper, we are concerned with the stochastic susceptible-infectious-susceptible (SIS) epidemic model on the complete graph with $n$ vertices. This model has two parameters, which are the infection rate and the recovery rate. By…
Infectious diseases are a threat for human health with tremendous impact on our society at large. The recent COVID-19 pandemic, caused by the SARS-CoV-2, is the latest example of a highly infectious disease ravaging the world, since late…
We predict the future course of ongoing susceptible-infected-susceptible (SIS) epidemics on regular, Erd\H{o}s-R\'{e}nyi and Barab\'asi-Albert networks. It is known that the contact network influences the spread of an epidemic within a…
We study the diffusion of epidemics on networks that are partitioned into local communities. The gross structure of hierarchical networks of this kind can be described by a quotient graph. The rationale of this approach is that individuals…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
Two simple agent based models are often employed in epidemic studies: the susceptible-infected (SI) and the susceptible-infected-susceptible (SIS). Both models describe the time evolution of infectious diseases in networks in which vertices…
We study a stochastic spatial epidemic model where the $N$ individuals carry two features: a position and an infection state, interact and move in $\R^d$. In this Markovian model, the evolution of the infection states are described with the…
Biological systems commonly exhibit complex spatiotemporal patterns whose underlying generative mechanisms pose a significant analytical challenge. Traditional approaches to spatiodynamic inference rely on dimensionality reduction through…
We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic…
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…
In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent p-coin tosses. Spatial variants of these models are proposed, in which finite…
The estimation from available data of parameters governing epidemics is a major challenge. In addition to usual issues (data often incomplete and noisy), epidemics of the same nature may be observed in several places or over different…
Mathematical models are formal and simplified representations of the knowledge related to a phenomenon. In classical epidemic models, a neglected aspect is the heterogeneity of disease transmission and progression linked to the viral load…