Related papers: A simple and intuitive method to calculate $R_0$ i…
Stochastic epidemic models describe the dynamics of an epidemic as a disease spreads through a population. Typically, only a fraction of cases are observed at a set of discrete times. The absence of complete information about the time…
In this paper, we introduce a general numerical method to approximate the reproduction numbers of a large class of multi-group, age-structured, population models with a finite age span. To provide complete flexibility in the definition of…
While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details…
A key problem in modelling the evolution dynamics of infectious diseases is the mathematical representation of the mechanism of transmission of the contagion. Models with a finite number of subpopulations can be described via systems of…
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…
One of the most significant challenges in combating against the spread of infectious diseases was the difficulty in estimating the true magnitude of infections. Unreported infections could drive up disease spread, making it very hard to…
We construct a set of new epidemiological thresholds to address the general problem of spreading and containment of a disease with influx of infected individuals when the classic $\mathcal R_0$ is no longer meaningful. We provide analytical…
This paper is a survey paper on stochastic epidemic models. A simple stochastic epidemic model is defined and exact and asymptotic model properties (relying on a large community) are presented. The purpose of modelling is illustrated by…
This work provides a geometric version of the next-generation matrix method for obtaining the basic reproduction number of an epidemiological model. We exhibit a certain correspondence between any system of ODEs and Petri nets. We observe…
The dynamics of contact networks and epidemics of infectious diseases often occur on comparable time scales. Ignoring one of these time scales may provide an incomplete understanding of the population dynamics of the infection process. We…
We present a class of SEIR Markov chain models for infectious diseases observed over discrete time in a random human population living in a closed environment. The population changes over time through random births, deaths, and transitions…
When analysing new emerging infectious disease outbreaks one typically has observational data over a limited period of time and several parameters to estimate, such as growth rate, R0, serial or generation interval distribution, latent and…
Multidimensional continuous-time Markov jump processes $(Z(t))$ on $\mathbb{Z}^p$ form a usual set-up for modeling $SIR$-like epidemics. However, when facing incomplete epidemic data, inference based on $(Z(t))$ is not easy to be achieved.…
Structured epidemic models can be formulated as first-order hyperbolic PDEs, where the "spatial" variables represent individual traits, called structures. For models with two structures, we propose a numerical technique to approximate…
We develop a generalized group-based epidemic model (GgroupEM) framework for any compartmental epidemic model (for example; susceptible-infected-susceptible, susceptible-infected-recovered, susceptible-exposed-infected-recovered). Here, a…
We study the Suscectible-Infected-Recovered-Susceptible (SIRS) epidemic model on deterministic networks. For connected but otherwise general interaction patterns and heterogeneous recovery and loss-of-immunity rates, we identify a…
The interplay of biological, social, structural and random factors makes disease forecasting extraordinarily complex. The course of an epidemic exhibits average growth dynamics determined by features of the pathogen and the population, yet…
The effective reproduction number is an important descriptor of an infectious disease epidemic. In small populations, ideally we would estimate the effective reproduction number using a Markov Jump Process (MJP) model of the spread of…
An approach to estimate the influence of the treatment-type controls on the basic reproduction number, R 0 , is proposed and elaborated. The presented approach allows one to estimate the effect of a given treatment strategy or to compare a…
In infectious disease modelling, the expected time from endemicity to extinction (of infection) may be analysed via WKB approximation, a method with origins in mathematical physics. The method is very general, but its uptake to date may…