Existing compartmental mathematical modelling methods for epidemics, such as SEIR
models, cannot accurately represent effects of contact tracing. This makes them …

Emerging epidemics and local infection clusters are initially prone to stochastic effects that
can substantially impact the early epidemic trajectory. While numerous studies are devoted …

We introduce an epidemic model with varying infectivity and general exposed and infectious
periods, where the infectivity of each individual is a random function of the elapsed time …

Starting from a stochastic individual-based description of an SIS epidemic spreading on a
random network, we study the dynamics when the size $ n $ of the network tends to infinity …

We study the Susceptible-Infected-Recovered (SIR) and the Susceptible-Exposed-Infected-
Recovered (SEIR) models of epidemics, with possibly time-varying rates, on a class of …

In this survey paper, we review the recent advances in individual based non--Markovian
epidemic models. They include epidemic models with a constant infectivity rate, varying …

We examine here the effects of recurrent vaccination and waning immunity on the
establishment of an endemic equilibrium in a population. An individual-based model that …

We study the stochastic SIR epidemic model with infection-age dependent infectivity for
which a measure-valued process is used to describe the ages of infection for each …

We study epidemic models where the infectivity of each individual is a random function of
the infection age (the elapsed time since infection). To describe the epidemic evolution …

This article introduces a novel hybrid mathematical modelling approach that effectively
couples partial differential equations (PDEs) with ordinary differential equations (ODEs) …