Related papers: Approximating time to extinction for endemic infec…
Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between…
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…
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.…
We study the extinction of epidemics in a simplicial susceptible-infected-susceptible model, where each susceptible individual becomes infected either by two-body interactions ($S+I \to 2I$) with a rate $\beta$ or by three-body interactions…
Characterizing the spatial extent of epidemics at the outbreak stage is key to controlling the evolution of the disease. At the outbreak, the number of infected individuals is typically small, so that fluctuations around their average are…
Traditional disease transmission models assume that the infectious period is exponentially distributed with a recovery rate fixed in time and across individuals. This assumption provides analytical and computational advantages, however it…
We study the Susceptible-Infected-Recovered model of epidemics in the vicinity of the threshold infectivity. We derive the distribution of total outbreak size in the limit of large population size $N$. This is accomplished by mapping the…
In this study, a new and natural way of constructing a stochastic Susceptible-Infected-Susceptible (SIS) model is proposed. This approach is natural in the sense that the disease transmission rate, $\beta$, is substituted with a generic,…
This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set…
Changing environmental conditions can significantly affect the dynamics of disease spread. These changes may arise naturally or result from human interventions; in the latter case, lockdown measures that lead to abrupt but temporary…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
Errors of approximations of the quasi-stationary distribution (the QSD) of the logistic SIS model are evaluated numerically. The results are used to derive asymptotic approximations of the approximation errors for large populations. We show…
The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…
We present a stochastic model for two successive SIR (Susceptible, Infectious, Recovered) epidemics in the same network structured population. Individuals infected during the first epidemic might have (partial) immunity for the second one.…
Infectious disease epidemiologists routinely fit stochastic epidemic models to time series data to elucidate infectious disease dynamics, evaluate interventions, and forecast epidemic trajectories. To improve computational tractability,…
This paper considers a stochastic SIR (susceptible$\to$infective$\to$removed) epidemic model in which individuals may make infectious contacts in two ways, both within `households' (which for ease of exposition are assumed to have equal…
In this paper we consider a model for the spread of a stochastic SIR (Susceptible $\to$ Infectious $\to$ Recovered) epidemic on a network of individuals described by a random intersection graph. Individuals belong to a random number of…
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…
The quasi-deterministic limit of the generic extinction transition is considered within the framework of standard epidemiological models. The susceptible-infected-susceptible (SIS) model is known to exhibit a transition from extinction to…
The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action Susceptible-Infected-Recovered model of Kermack and McKendrick. Its usefulness derives largely from its conceptual and mathematical…