Related papers: How many outbreaks before an epidemic?
The correct evaluation of the reproductive number $R$ for COVID-19 -- which characterizes the average number of secondary cases generated by each typical primary case -- is central in the quantification of the potential scope of the…
Consider an epidemic model with a constant flux of susceptibles, in a situation where the corresponding deterministic epidemic model has a unique stable endemic equilibrium. For the associated stochastic model, whose law of large numbers…
A novel parametric regression model is proposed to fit incidence data typically collected during epidemics. The proposal is motivated by real-time monitoring and short-term forecasting of the main epidemiological indicators within the first…
We review epidemiological models for the propagation of the COVID-19 pandemic during the early months of the outbreak: from February to May 2020. The aim is to propose a methodological review that highlights the following characteristics:…
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…
We formulate a general SEIR epidemic model in a heterogenous population characterized by some trait in a discrete or continuous subset of a space R d. The incubation and recovery rates governing the evolution of each homogenous…
COVID-19 is highly transmissible and containing outbreaks requires a rapid and effective response. Because infection may be spread by people who are pre-symptomatic or asymptomatic, substantial undetected transmission is likely to occur…
We investigate final outcome properties of an SIR (susceptible $\to$ infective $\to$ recovered) epidemic model defined on a population of large sub-communities in which there is stronger disease transmission within the communities than…
When an infectious disease strikes a population, the number of newly reported cases is often the only available information that one can obtain during early stages of the outbreak. An important goal of early outbreak analysis is to obtain a…
In this work, we review the figures used to characterize an epidemic outbreak most. Particular attention is drawn to epidemic spreading at time-varying transition rates. A time-varying SIR-like model is used to describe the epidemic…
We study the classic Susceptible-Infected-Recovered (SIR) model for the spread of an infectious disease. In this stochastic process, there are two competing mechanism: infection and recovery. Susceptible individuals may contract the disease…
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…
Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible $S$, infected $I$, removed $R$ and dead people $D$. In order to have…
A Reed-Frost epidemic with inhomogeneous infection probabilities on a graph with prescribed degree distribution is studied. Each edge $(u,v)$ in the graph is equipped with two weights $W_{(u,v)}$ and $W_{(v,u)}$ that represent the…
We introduce a simple multiplicative model to describe the temporal behavior and the ultimate outcome of an epidemic. Our model accounts, in a minimalist way, for the competing influences of imposing public-health restrictions when the…
We propose a compartmental mathematical model for the spread of the COVID-19 disease, showing its usefulness with respect to the pandemic in Portugal, from the first recorded case in the country till the end of the three states of…
Many models of epidemic spread have a common qualitative structure. The numbers of infected individuals during the initial stages of an epidemic can be well approximated by a branching process, after which the proportion of individuals that…
This paper introduces a microscopic approach to model epidemics, which can explicitly consider the consequences of individual's decisions on the spread of the disease. We first formulate a microscopic multi-agent epidemic model where every…
It is of vital importance to understand and track the dynamics of rapidly unfolding epidemics. The health and economic consequences of the current COVID-19 pandemic provide a poignant case. Here we point out that since they are based on…
While COVID-19 is rapidly propagating around the globe, the need for providing real-time forecasts of the epidemics pushes fits of dynamical and statistical models to available data beyond their capabilities. Here we focus on statistical…