Related papers: An approximate diffusion process for environmental…
Infectious diseases that incorporate pre-symptomatic transmission are challenging to monitor, model, predict and contain. We address this scenario by studying a variant of a stochastic susceptible-exposed-infected-recovered model on…
The spread of infectious diseases crucially depends on the pattern of contacts among individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. Few empirical studies are however available that…
Many systems with propagation dynamics, such as spike propagation in neural networks and spreading of infectious diseases, can be approximated by autoregressive models. The estimation of model parameters can be complicated by the…
Even in large systems, the effect of noise arising from when populations are initially small can persist to be measurable on the macroscale. A deterministic approximation to a stochastic model will fail to capture this effect, but it can be…
We introduce a kinetic model that couples the movement of a population of individuals with the dynamics of a pathogen in the same population. We consider that transmission occurs when a susceptible and an infectious individual are…
The main aim to build models capable of simulating the spreading of infectious diseases is to control them. And along this way, the key to find the optimal strategy for disease control is to obtain a large number of simulations of disease…
The spreading of evolutionary novelties across populations is the central element of adaptation. Unless population are well-mixed (like bacteria in a shaken test tube), the spreading dynamics not only depends on fitness differences but also…
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…
Recent years have seen a large amount of interest in epidemics on networks as a way of representing the complex structure of contacts capable of spreading infections through the modern human population. The configuration model is a popular…
The COVID-19 pandemic provides new motivation for a classic problem in epidemiology: estimating the empirical rate of transmission during an outbreak (formally, the time-varying reproduction number) from case counts. While standard methods…
Motivated by recent epidemic outbreaks, including those of COVID-19, we solve the canonical problem of calculating the dynamics and likelihood of extensive outbreaks in a population within a large class of stochastic epidemic models with…
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…
The spread of an epidemic process is considered in the context of a spatial SIR stochastic model that includes a parameter $0\le p\le 1$ that assigns weights $p$ and $1- p$ to global and local infective contacts respectively. The model was…
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 two statistical models for space-time abundance data based on a stochastic underlying continuous individual movement. In contrast to current models for abundance in statistical ecology, our models exploit the explicit connection…
Many stochastic processes in the physical and biological sciences can be modelled as Brownian dynamics with multiplicative noise. However, numerical integrators for these processes can lose accuracy or even fail to converge when the…
The coronavirus pandemic has rapidly evolved into an unprecedented crisis. The susceptible-infectious-removed (SIR) model and its variants have been used for modeling the pandemic. However, time-independent parameters in the classical…
Stochastic epidemic models which incorporate interactions between space and human mobility are a key tool to inform prioritisation of outbreak control to appropriate locations. However, methods for fitting such models to national-level…
We study two simple mathematical models of the epidemic. At first, we study the repetitive infection spreading in a simplified SIRS model including the effect of the decay of the acquired immune. The model is an intermediate model of the…
Comparative biologists are often interested in inferring covariation between multiple biological traits sampled across numerous related taxa. To properly study these relationships, we must control for the shared evolutionary history of the…