Related papers: Computing the extinction path for epidemic models
Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterize…
We develop a theory of first passage processes in stochastic non-equilibrium systems of birth-death type using two closely related epidemiological models as examples. Our method employs the probability generating function technique in…
We study the extinction of epidemics in a generalized susceptible-infected-susceptible model, where a susceptible individual becomes infected with the rate $\lambda$ when contacting $m$ infective individual(s) simultaneously, and an…
We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic Susceptible-Infected-Susceptible model, we predict the distribution of large…
Stochastic effects may cause fade-out of an infectious disease in a population immediately after an epidemic outbreak. We develop WKB theory to determine the most probable path of the system toward epidemic fade-out and to evaluate the…
The non-equilibrium phase transition in models for epidemic spreading with long-range infections in combination with incubation times is investigated by field-theoretical and numerical methods. Here the spreading process is modelled by…
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…
This study aims to estimate the parameters of a stochastic exposed-infected epidemiological model for the transmission dynamics of notifiable infectious diseases, based on observations related to isolated cases counts only. We use the…
The emergence and spread of deadly pandemics has repeatedly occurred throughout history, causing widespread infections and loss of life. The rapid spread of pandemics have made governments across the world adopt a range of actions,…
Infectious diseases are caused by pathogenic microorganisms and can spread through different ways. Mathematical models and computational simulation have been used extensively to investigate the transmission and spread of infectious…
Mathematical models of infectious diseases, which are in principle analytically tractable, use two general approaches. The first approach, generally known as compartmental modeling, addresses the time evolution of disease propagation at the…
Mathematical models in epidemiology are an indispensable tool to determine the dynamics and important characteristics of infectious diseases. Apart from their scientific merit, these models are often used to inform political decisions and…
We consider the propagation of a contagion process (epidemic) on a network and study the problem of dynamically allocating a fixed curing budget to the nodes of the graph, at each time instant. For bounded degree graphs, we provide a lower…
We propose a model for epidemic spreading on a finite complex network with a restriction to at most one contamination per time step. Because of a highly discrete character of the process, the analysis cannot use the continous approximation,…
Deterministic evolutionary game dynamics can lead to stable coexistences of different types. Stochasticity, however, drives the loss of such coexistences. This extinction is usually accompanied by population size fluctuations. We…
We investigate the expected time to extinction in the susceptible-infectious-susceptible (SIS) model of disease spreading. Rather than using stochastic simulations, or asymptotic calculations in network models, we solve the extinction time…
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time…
We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the…
We consider compartmental models in epidemiology. For the study of the divergence of the stochastic model from its corresponding deterministic limit (i.e., the solution of an ODE) for long time horizon, a large deviations principle suggests…
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…