Related papers: Exact solution for a discrete-time SIR model

Modeling epidemic dynamics plays an important role in studying how diseases spread, predicting their future course, and designing strategies to control them. In this letter, we introduce a model of SIR (susceptible-infected-removed) type…

In this paper we present the discrete-time networked SIR and SEIR models and present assumptions under which they are well defined. We analyze the limiting behavior of the models and present necessary and sufficient conditions for…

Social distancing strategies have been adopted by governments to manage the COVID-19 pandemic, since the first outbreak began. However, further epidemic waves keep out the return of economic and social activities to their standard levels of…

In this paper, we propose a modified susceptible-infected-recovered (SIR) model, in which each node is assigned with an identical capability of active contacts, $A$, at each time step. In contrast to the previous studies, we find that on…

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 networks that are locally tree-like, which includes sparse…

The Susceptible-Infectious-Recovered (SIR) equations and their extensions comprise a commonly utilized set of models for understanding and predicting the course of an epidemic. In practice, it is of substantial interest to estimate the…

In the Staged Progression (SP) epidemic models, infected individuals are classified into a suitable number of states. The goal of these models is to describe as closely as possible the effect of differences in infectiousness exhibited by…

We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an…

The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common…

This paper studies algorithmic strategies to effectively reduce the number of infections in susceptible-infected-recovered (SIR) epidemic models. We consider a Markov chain SIR model and its two instantiations in the deterministic SIR…

We analyse the infection-age-dependent SIR model from a numerical point of view. First, we present an algorithm for calculating the solution the infection-age-structured SIR model without demography of the background host. Second, we…

This paper presents a time discretization of the robust exact filtering differentiator, a sliding mode differentiator coupled to filter, which provides a suitable approximation to the derivatives of some noisy signals. This proposal takes…

We propose a stochastic SIR model, specified as a system of stochastic differential equations, to analyse the data of the Italian COVID-19 epidemic, taking also into account the under-detection of infected and recovered individuals in the…

Over the years numerous models of SIS (susceptible - infected - susceptible) disease dynamics unfolding on networks have been proposed. Here, we discuss the links between many of these models and how they can be viewed as more general…

Many algorithms have been proposed in prior literature to guarantee resilient multi-agent consensus in the presence of adversarial attacks or faults. The majority of prior work present excellent results that focus on discrete-time or…

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…

Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been…

We consider a susceptible, infected, removed (SIR) system where the transmission rate may be temporarily reduced for a fixed amount of time. We show that in order to minimize the total number of fatalities, the transmission rate should be…

This paper investigates asymptotic behavior of a stochastic SIR epidemic model, which is a system with degenerate diffusion. It gives sufficient conditions that are very close to the necessary conditions for the permanence. In addition,…

This paper revisits a longstanding problem of interest concerning the distributed control of an epidemic process on human contact networks. Due to the stochastic nature and combinatorial complexity of the problem, finding optimal policies…