Results 1  10
of
28
The structure and function of complex networks
 SIAM REVIEW
, 2003
"... Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, ..."
Abstract

Cited by 1675 (7 self)
 Add to MetaCart
(Show Context)
Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the smallworld effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.
Drug abuse and HIV prevention research: Expanding paradigms and network contributions to risk reduction
 Connections
, 1995
"... This paper identifies an important paradigm shift in social research on HIV transmission, drug abuse, and risk reduction research. The article describes the key research trends and the institutional support for social network analysis in the HIV and drug risk field for the past decade. Key hypothese ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
This paper identifies an important paradigm shift in social research on HIV transmission, drug abuse, and risk reduction research. The article describes the key research trends and the institutional support for social network analysis in the HIV and drug risk field for the past decade. Key hypotheses and recommended areas for future research are identified.
Optimal immunisation of complex networks
, 2001
"... Complex networks such as the sexual partnership web or the Internet often show a high degree of redundancy and heterogeneity in their connectivity properties. This peculiar connectivity, however, provides an ideal environment for the spreading of biological or digital infective agents. Here we show ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
(Show Context)
Complex networks such as the sexual partnership web or the Internet often show a high degree of redundancy and heterogeneity in their connectivity properties. This peculiar connectivity, however, provides an ideal environment for the spreading of biological or digital infective agents. Here we show that the random uniform immunisation of individuals does not lead to the eradication of infections in all complex networks. Namely, networks with scalefree properties do not acquire global immunity from major epidemic outbreaks even in the presence of unrealistically high densities of randomly immunised individuals. The absence of any critical immunisation threshold is due to the unbounded connectivity fluctuations of scalefree networks. Successful immunisation strategies can be developed only by taking into account the inhomogeneous connectivity properties of scalefree networks. In particular, targeted immunisation programmes, based on the nodes’ connectivity hierarchy, sharply lower the network’s vulnerability to epidemic attacks.
Potential Impact of Antiretroviral Chemoprophylaxis on HIV1 Transmission in ResourceLimited Settings
"... Background. The potential impact of preexposure chemoprophylaxis (PrEP) on heterosexual transmission of HIV1 infection in resourcelimited settings is uncertain. Methodology/Principle Findings. A deterministic mathematical model was used to simulate the effects of antiretroviral PrEP on an HIV1 e ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Background. The potential impact of preexposure chemoprophylaxis (PrEP) on heterosexual transmission of HIV1 infection in resourcelimited settings is uncertain. Methodology/Principle Findings. A deterministic mathematical model was used to simulate the effects of antiretroviral PrEP on an HIV1 epidemic in subSaharan Africa under different scenarios (optimistic, neutral and pessimistic) both with and without sexual disinhibition. Sensitivity analyses were used to evaluate the effect of uncertainty in input parameters on model output and included calculation of partial rank correlations and standardized rank regressions. In the scenario without sexual disinhibition after PrEP initiation, key parameters influencing infections prevented were effectiveness of PrEP (partial rank correlation coefficient (PRCC) = 0.94), PrEP discontinuation rate (PRCC = 20.94), level of coverage (PRCC = 0.92), and time to achieve target coverage (PRCC = 20.82). In the scenario with sexual disinhibition, PrEP effectiveness and the extent of sexual disinhibition had the greatest impact on prevention. An optimistic scenario of PrEP with 90 % effectiveness and 75 % coverage of the general population predicted a 74 % decline in cumulative HIV1 infections after 10 years, and a 28.8 % decline with PrEP targeted to the highest risk groups (16 % of the population). Even with a 100 % increase in atrisk behavior from sexual disinhibition, a beneficial effect (23.4%–62.7 % decrease in infections) was seen with 90% effective PrEP across a broad range of coverage (25%–75%). Similar disinhibition led to a rise in infections with lower effectiveness of PrEP (#50%). Conclusions/Significance. Mathematical modeling supports the potential public health benefit of PrEP. Approximately 2.7 to 3.2 million new HIV1 infections could be averted in southern subSaharan Africa over 10
On the spread of epidemics in a closed heterogeneous population
, 802
"... Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptibleinfectiveremoved) model is formulated and analyzed for di ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
(Show Context)
Heterogeneity is an important property of any population experiencing a disease. Here we apply general methods of the theory of heterogeneous populations to the simplest mathematical models in epidemiology. In particular, an SIR (susceptibleinfectiveremoved) model is formulated and analyzed for different sources of heterogeneity. It is shown that a heterogeneous model can be reduced to a homogeneous model with a nonlinear transmission function, which is given in explicit form. The widely used power transmission function is deduced from a heterogeneous model with the initial gammadistribution of the disease parameters. Therefore, a mechanistic derivation of the phenomenological model, which mimics reality very well, is provided. The equation for the final size of an epidemic for an arbitrary initial distribution is found. The implications of population heterogeneity are discussed, in particular, it is pointed out that usual momentclosure methods can lead to erroneous conclusions if applied for the study of the longterm behavior of the model.
Preclinical Assessment of HIV Vaccines and Microbicides by Repeated LowDose Virus Challenges
"... have declared that no competing interests exist. Author Contributions: RRR performed the analysis. RRR, IML, MBF, and SIS designed the study and wrote the paper. ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
(Show Context)
have declared that no competing interests exist. Author Contributions: RRR performed the analysis. RRR, IML, MBF, and SIS designed the study and wrote the paper.
Model Validation and Assessment of Uncertainty in a Deterministic Model for Gonorrhea
, 1995
"... Deterministic mathematical models of disease transmission have been used to forecast the course of epidemics and to investigate how various hypothetical interventions or changes in assumptions would alter these predictions. The inputs for such models include parameters such as rates of partner chang ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Deterministic mathematical models of disease transmission have been used to forecast the course of epidemics and to investigate how various hypothetical interventions or changes in assumptions would alter these predictions. The inputs for such models include parameters such as rates of partner change and rates of disease transmission, and the model outputs are usually predicted incidence rates for the study population and for various subpopulations in each year of the simulation. Considerable uncertainty may exist about the correct values of both type of parameters. Model validation (adjusting parameters by fitting the model to real data) is often done in an iterative, adhoc fashion and relatively little work has been done on the difficult issue of attaching a measure of uncertainty to the predictions of these models. We describe a Bayesian approach to estimation, fitting and uncertainty analysis in complex, nonlinear deterministic models. The sampling importance resampling algorithm ...
Analysis of a RiskBased Model for the Growth of AIDS Infection*
, 1990
"... Several models for the spread of AIDS within a homosexual community have been proposed that incorporate biased mixing of different risk groups. A simple model is presented that captures many of the features of these more complex models. Analytical expressions are derived for the time to the state of ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Several models for the spread of AIDS within a homosexual community have been proposed that incorporate biased mixing of different risk groups. A simple model is presented that captures many of the features of these more complex models. Analytical expressions are derived for the time to the state of maximum infection (SMI) in a particular risk group, the proportion infected at SMI, and the number of infected individuals as the group approaches SMI. These results agree qualitatively with numerical simulations of the model. 1.