Effects of immunization in small-world epidemics (original) (raw)

Epidemics in Interconnected Small-World Networks

PLOS ONE, 2015

Networks can be used to describe the interconnections among individuals, which play an important role in the spread of disease. Although the small-world effect has been found to have a significant impact on epidemics in single networks, the small-world effect on epidemics in interconnected networks has rarely been considered. Here, we study the susceptibleinfected-susceptible (SIS) model of epidemic spreading in a system comprising two interconnected small-world networks. We find that the epidemic threshold in such networks decreases when the rewiring probability of the component small-world networks increases. When the infection rate is low, the rewiring probability affects the global steady-state infection density, whereas when the infection rate is high, the infection density is insensitive to the rewiring probability. Moreover, epidemics in interconnected small-world networks are found to spread at different velocities that depend on the rewiring probability.

Effect of Small-World Networks on Epidemic Propagation and Intervention

Geographical Analysis, 2009

The small-world network, characterized by special structural properties of high connectivity and clustering, is one of the highlights in recent advances in network science and has the potential to model a variety of social contact networks. In an attempt to better understand how these structural properties of small-world networks affect epidemic propagation and intervention, this article uses an agent-based approach to investigate the interplay between an epidemic process and its underlying network structure. Small-world networks are derived from a network ''rewiring'' process, which readjusts edges in a completely regular two-dimensional network by different rewiring probabilities (0-1) to produce a spectrum of modified networks on which an agent-based simulation of epidemic propagation can be conducted. A comparison of simulated epidemics discloses the effect of small-world networks on epidemic propagation as well as the effectiveness of different intervention strategies, including mass vaccination, acquaintance vaccination, targeted vaccination, and contact tracing. Epidemics taking place on small-world networks tend to reach large-scale epidemic peaks within a short time period. Among the four intervention strategies tested, only one strategy-the targeted vaccination-proves to be effective for containing epidemics, a finding supported by a simulation of the severe acute respiratory syndrome epidemic in a large-scale realistic social contact network in Portland, OR.

Optimising control of disease spread on networks

Acta Physica Polonica B, 2005

We consider models for control of epidemics on local, global, small-world and scale-free networks, with only partial information accessible about the status of individuals and their connections. The effectiveness of local (e.g. ring vaccination or culling) vs global (e.g. random vaccination) control measures is evaluated, with the aim of minimising the total cost of an epidemic. The costs include direct costs of treating infected individuals as well as costs of treatment. We first consider a random (global) vaccination strategy designed to stop any potential outbreak. We show that if the costs of the preventive vaccination are ignored, the optimal strategy is to vaccinate the whole population, although most of the resources are wasted on preventing a small number of cases. If the vaccination costs are included, or if a local strategy (within a certain neighbourhood of a symptomatic individual) is chosen, there is an optimum number of treated individuals. Inclusion of non-local contacts ('small-worlds' or scale-free networks) increases the levels of preventive (random) vaccination and radius of local treatment necessary for stopping the outbreak at a minimal cost. The number of initial foci also influences our choice of optimal strategy. The size of epidemics and the number of treated individuals increase for outbreaks that are initiated from a larger number of initial foci, but the optimal radius of local control actually decreases. The results are important for designing control strategies based on cost effectiveness.

An Epidemic Model on Small-World Networks and Ring Vaccination

2001

A modified version of susceptible-infected-recovered-susceptible (SIRS) model for the outbreaks of foot-and-mouth disease (FMD) is introduced. The model is defined on small-world networks, and a ring vaccination programme is included. This model can be a theoretical explanation for the nonlocal interactions in epidemic spreading. Ring vaccination is capable of eradicating FMD provided that the probability of infection is high enough. Also an analytical approximation for this model is studied.

The analysis of an epidemic model on networks

The paper consider an epidemic model with birth and death on networks. We derive the epidemic threshold R 0 dependent on birth rate b, death rate d (natural death) and l from the infectious disease and natural death, and cure rate c. And the stability of the equilibriums (the disease-free equilibrium and endemic equilibrium) are analysed. Finally, the effects of various immunization schemes are studied and compared. We show that both targeted, and acquaintance immunization strategies compare favorably to a proportional scheme in terms of effectiveness. For active immunization, the threshold is easier to apply practically. To illustrate our theoretical analysis, some numerical simulations are also included.

Impact of network assortativity on epidemic and vaccination

Chaos, Solitons and Fractals, 2020

The resurgence of measles is largely attributed to the decline in vaccine adoption and the increase in mobility. Although the vaccine for measles is readily available and highly successful, its current adoption is not adequate to prevent epidemics. Vaccine adoption is directly affected by individual vaccination de- cisions, and has a complex interplay with the spatial spread of disease shaped by an underlying mobility (travelling) network. In this paper, we model the travelling connectivity as a scale-free network, and in- vestigate dependencies between the network’s assortativity and the resultant epidemic and vaccination dynamics. In doing so we extend an SIR-network model with game-theoretic components, capturing the imitation dynamics under a voluntary vaccination scheme. Our results show a correlation between the epidemic dynamics and the network’s assortativity, highlighting that networks with high assortativity tend to suppress epidemics under certain conditions. In highly assortative networks, the suppression is sustained producing an early convergence to equilibrium. In highly disassortative networks, however, the suppression effect diminishes over time due to scattering of non-vaccinating nodes, and frequent switch- ing between the predominantly vaccinating and non-vaccinating phases of the dynamics.

Review of Epidemics with Pathogen Mutation on Small World Networks and testing of control strategies

2010

We model the outbreak of a mutating pathogen on a small-world social-spacial network, and study the time-dependent dynamics. We examine the influence of the immunity duration, τ i, crossimmunity threshold, h thr , and system size, N, on epidemic dynamics. With the inclusion of a population at risk, one which is more susceptible to infection and experiences more severe symptoms, we explore various vaccination schemes and analyze their effectiveness. We find that the size of the population at risk is directly related to the severity of an outbreak, and that targeted vaccination of the population at risk was the most effective immunization strategy. The outbreak of a contagious novel virus is a major concern to both public health and safety, causing economic havoc and the deaths of large numbers of people. Recent outbreaks of diseases such as SARS and the recent H1N1 flu outbreak indicate how rapidly a potentially deadly virus can spread around the world and infect many millions of people.

Infection dynamics on small-world networks

2006

The use of network models to describe the impact of local spatial structure on the spread of infections is discussed. In particular, we focus on small-world networks, within which the pattern of interactions can be varied from being entirely local to being entirely global as a single parameter is changed. Analysis approaches from graph theory, statistical physics and mathematical epidemiology are discussed. Simulation results are presented that highlight the surprising findings of Watts and Strogatz [58], namely that a small number of long-range interactions in an otherwise locally structured population can markedly enhance the ability of an infection to spread and the rate at which the spread occurs. We also discuss some of the implications of such spatial structure on the dynamics and persistence of endemic infections.

Local immunization program for susceptible-infected-recovered network epidemic model

Chaos (Woodbury, N.Y.), 2016

The immunization strategies through contact tracing on the susceptible-infected-recovered framework in social networks are modelled to evaluate the cost-effectiveness of information-based vaccination programs with particular focus on the scenario where individuals belonging to a specific set can get vaccinated due to the vaccine shortages and other economic or humanity constraints. By using the block heterogeneous mean-field approach, a series of discrete-time dynamical models is formulated and the condition for epidemic outbreaks can be established which is shown to be not only dependent on the network structure but also closely related to the immunization control parameters. Results show that increasing the immunization strength can effectively raise the epidemic threshold, which is different from the predictions obtained through the susceptible-infected-susceptible network framework, where epidemic threshold is independent of the vaccination strength. Furthermore, a significant d...