Related papers: A Computer Virus Propagation Model Using Delay Dif…
Diffusion processes pervade numerous areas of AI, abstractly modeling the dynamics of exchanging, oftentimes volatile, information in networks. A central question is how long the information remains in the network, known as survival time.…
We develop an extension of the Susceptible-Infected-Recovery (SIR) model to account for spatial variations in population as well as infection and recovery parameters. The equations are derived by taking the continuum limit of discrete…
In the standard SIR model, infected vertices infect their neighbors at rate $\lambda$ independently across each edge. They also recover at rate $\gamma$. In this work we consider the SIR-$\omega$ model where the graph structure itself…
In this paper, a susceptible-infected-susceptible (SIS) model with identical infectivity, where each node is assigned with the same capability of active contacts, $A$, at each time step, is presented. We found that on scale-free networks,…
In this paper we generalise a simple discrete time stochastic SIR type model defined by Tuckwell and Williams. The SIR model by Tuckwell and Williams assumes a homogeneous population, a fixed infectious period, and a strict transition from…
Time-varying network topologies can deeply influence dynamical processes mediated by them. Memory effects in the pattern of interactions among individuals are also known to affect how diffusive and spreading phenomena take place. In this…
The infections and fatalities due to SARS-CoV-2 virus for cases specific to India have been studied using a deterministic susceptible-exposed-infected-recovered-dead (SEIRD) compartmental model. One of the most significant epidemiological…
We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model. Through the use of a normal form coordinate transform, we are able to analytically derive the stochastic center manifold along with the…
We consider the spread of a Susceptible-Infected-Recovered (SIR) disease through finite populations and derive an expression for the final size distribution. Our derivation allows arbitrary distributions of the number of transmissions…
In this paper we study a discrete-time SIS (susceptible-infected-susceptible) model, where the infection and healing parameters and the underlying network may change over time. We provide conditions for the model to be well-defined and…
Individual-based models of contagious processes are useful for predicting epidemic trajectories and informing intervention strategies. In such models, the incorporation of contact network information can capture the non-randomness and…
Two simple agent based models are often employed in epidemic studies: the susceptible-infected (SI) and the susceptible-infected-susceptible (SIS). Both models describe the time evolution of infectious diseases in networks in which vertices…
The SIR pandemic model suffers from an unrealistic assumption: The rate of removal from the infectious class of individuals is assumed to be proportional to the number of infectious individuals. This means that a change in the rate of…
We introduce a new method to efficiently approximate the number of infections resulting from a given initially-infected node in a network of susceptible individuals. Our approach is based on counting the number of possible infection walks…
The transmission rate of many acute infectious diseases varies significantly in time, but the underlying mechanisms are usually uncertain. They may include seasonal changes in the environment, contact rate, immune system response, etc. The…
We investigate the evolution of epidemics over dynamical networks when nodes choose to interact with others in a selfish and decentralized manner. Specifically, we analyze the susceptible-asymptomatic-infected-recovered (SAIR) epidemic in…
The infection dynamics of a population under stationary isolation conditions is modeled. It is underlined that the stationary character of the isolation measures can be expected to imply that an effective SIR model with constant parameters…
Compartmental epidemic models, grounded in mass-action kinetics, often assume homogeneous mixing. Although this neglects network structure, recent results show that for Poisson random graphs, the classical SIR model, especially the…
Deterministic compartmental models are predominantly used in the modeling of infectious diseases, though stochastic models are considered more realistic, yet are complicated to estimate due to missing data. In this paper we present a novel…
This paper presents a novel time-space SIR (Susceptible-Infected-Recovered) model for simulating infectious disease dynamics in two interconnected regions. The model is formulated as a coupled reaction-diffusion system with boundary…