#### DMCA

## Mathematical Statistics (2008)

Citations: | 1 - 0 self |

### Citations

2553 | The structure and function of complex networks,” - Newman - 2003 |

735 |
Infectious Diseases of Humans: Dynamics and Control,
- Anderson, May
- 1991
(Show Context)
Citation Context ...tion Stochastic epidemic models have been studied intensely over the past decades, trying to capture the behaviour of a real epidemic spreading in a population, may it be human or bacterial (see e.g. =-=[3]-=- and [4]). Over time more general models have been analysed such as multitype epidemics models, and models allowing for individual heterogeneities and demographics in the monitored population. We focu... |

498 | A critical point for random graphs with a given degree sequence. - Molloy, Reed - 1995 |

371 |
The Mathematical Theory of Infectious Diseases and Its Applications,TheGriffin, London,UK, 2nd edition,
- Bailey
- 1975
(Show Context)
Citation Context ...chastic epidemic models have been studied intensely over the past decades, trying to capture the behaviour of a real epidemic spreading in a population, may it be human or bacterial (see e.g. [3] and =-=[4]-=-). Over time more general models have been analysed such as multitype epidemics models, and models allowing for individual heterogeneities and demographics in the monitored population. We focus on the... |

252 |
Brownian Motion and Stochastic Calculus, volume 113 of Graduate Texts in Mathematics
- Karatzas, Shreve
- 1991
(Show Context)
Citation Context ...the above equation, thereby ensuring the interpretation as a covariance matrix. Using this it is also possible to calculate the covariance function of Z according to ρ(t) = Σet(∂F ?)T (5.9) (see e.g. =-=[6]-=- Theorem 5.6.7). 10 5.3 Dynamics in the limit Using the results in the above section we are able to draw conclusions concerning the dynamics of the system when ν is large. It is possible to obtain an ... |

234 | Social network analysis: A handbook, 2nd edition - Scott - 2000 |

210 | Mathematical Epidemiology of Infectious Diseases. Model Building, Analysis and Interpretation. - Diekmann, Heesterbeek - 2000 |

181 | Epidemic Modeling: An Introduction - Daley, Gani - 2005 |

161 |
Stochastic Epidemic Models and Their Statistical Analysis. Volume 151.
- Andersson, Britton
- 2000
(Show Context)
Citation Context ...xing, i.e. that all pairs of individuals have the same probability of meeting and infecting each other. A thorough treatment of stochastic epidemic models and the standard assumptions can be found in =-=[1]-=-. The rest of the paper is organised as follows: Section 2 describes the model and the assumptions made in detail. In Section 3 the basic reproduction number is derived. In Section 4 an approximation ... |

117 | Introduction to probability and mathematical statistics”, - Bain, Engelhardt - 1992 |

98 |
Approximation of Population Processes
- Kurtz
- 1987
(Show Context)
Citation Context ...habited area of the model grow large. To emphasise the dependence on ν we will denote the process {(S(t), I(t)), t ≥ 0} with parameter ν by {(S(ν)(t), I(ν)(t)), t ≥ 0}. We will rely on the results in =-=[7]-=- and in particular Theorems 8.1 and 8.2 therein. 5.1 Law of large numbers Our approximations will depend on the fact that (S(ν)(t), I(ν)(t)) is a so called density dependent Markov process, i.e. the t... |

84 |
Markov Chains (Cambridge U.
- Norris
- 1998
(Show Context)
Citation Context ...ing the rate of partnership change in the population, and underestimating the absolute gap length. Consequently, in section 2.2., we define an alternative gap measure based on the queueing modelM/M/∞ =-=[33]-=-: the gap length is the difference between ”the inter-arrival time” - the time between the starting points of two successive partnerships - and ”the service time” - the partnership duration. This allo... |

54 | Modern infectious disease epidemiology - Giesecke - 1994 |

38 |
Homogeheous models for sexually transmitted diseases.
- Hadeler, Ngoma
- 1990
(Show Context)
Citation Context ... They have mainly been formalized by means of dynamic systems - systems of differential equations - that specify rates of pair formation and dissolution, as well as rates of infection and recovery [9]=-=[11]-=-[27][28]. The dynamic system approach extends the state space of the basic version of the SIR model (appendix B). Individuals are either single or paired, which enables evaluation of relative threshol... |

37 |
Introduction to Probability Models, 9th ed.,
- Ross
- 2007
(Show Context)
Citation Context ...non decreasing, and the third since w ≤D w′|z′. This last fact follows since the birth intensity of w′ is larger than that of w, which is seen by examining the last two lines of Table 3. According to =-=[12]-=- p. 377 it holds that z ′ and w ′|z′(t) are geometrically distributed with second moments 2−q1 q21 and 2−q2 q22 respectively, where q1 := β exp{− exp{(µ − δ)t}t} and q2 := (z ′ + )(γ + 2µ)t. Thus E[z... |

25 |
Susceptible^infectious^recovered epidemic models with dynamic partnerships
- Altmann
- 1995
(Show Context)
Citation Context ...asic reproduction number. 4 In section 2.3., with the aim of evaluating threshold effects of gap lengths, we describe a stochastic epidemic model with partnership dynamics for a homogenous population =-=[1]-=-. We cite a formula for the basic reproduction number R0 that takes partnership and infection dynamics into account, i.e. rates of partnership formation and dissolution, as well as rates of infection ... |

24 | Branching processes with biological applications. Wiley-Interscience - Jagers - 1975 |

24 | Realistic distributions of infectious periods in epidemic models - Lloyd |

21 | The Mathematical Theory of Infectious Diseases, 2nd edition - Bailey - 1975 |

20 |
Realistic Distributions of Infectious Periods in Epidemic Models: Changing
- AL
- 2001
(Show Context)
Citation Context ...re research is needed to validate or refute a queueing model of gaps and corresponding stochastic models. For example, we should consider and evaluate different distributions than the exponential one =-=[30]-=-. More research is also needed to understand and explain the partnership dynamics and the threshold effects in heterogenous populations and over time [13]. In this study, we have kept the analysis of ... |

20 |
M: The contribution of steady and casual partnerships to the incidence of HIV infection among homosexual men in Amsterdam
- Xiridou, Geskus, et al.
(Show Context)
Citation Context ...nfections (STI). It is considered an important risk factor [19][24][29] and a hallmark of core groups, i.e. individuals with high rates of partnership change and high levels of sexual activity [4][22]=-=[36]-=-. With concurrent partners, infections can spread to a greater number of individuals. Two studies of sexual behavior point to the more general risk of ”time gaps” for the spread of STIs [18][26], i.e.... |

18 |
The effect of pair formation and variable infectivity on the spread of an infection without recovery
- Kretzschmar, Dietz
- 1998
(Show Context)
Citation Context ...ve mainly been formalized by means of dynamic systems - systems of differential equations - that specify rates of pair formation and dissolution, as well as rates of infection and recovery [9][11][27]=-=[28]-=-. The dynamic system approach extends the state space of the basic version of the SIR model (appendix B). Individuals are either single or paired, which enables evaluation of relative threshold effect... |

14 |
An introduction to mathematical models in sexually transmitted disease epidemiology, Sex
- GP
- 2002
(Show Context)
Citation Context ...that does not always allow for explicit calculations of R0 [1]. Nor is the approach well suited to deal with concurrency, except when assuming severe restrictions on the number of concurrent partners =-=[20]-=-. An argument has been made that the dynamic system approach does allow for unlimited concurrency: ”rapidly changing monogamous interactions” [15]. However, concurrency covers different types of overl... |

13 |
The impact of HIV epidemic phases on the effectiveness of core group interventions: insights from mathematical models. Sex Transm Infect.
- MC, Lowndes, et al.
- 2002
(Show Context)
Citation Context ...ed being unfaithful and faithful respectively. This division reflects core and non-core group behavior. First, unfaithfulness implies concurrency, multiple partners. This is a hallmark of core groups =-=[6]-=-. Second, unfaithfulness implies nondisclosure of information to sexual partners [14], which is also a central feature of core group behavior, where multiple sexual contacts are ignorant of each other... |

12 |
A threshold limit theorem for the stochastic logistic epidemic
- Andersson, Djehiche
- 1998
(Show Context)
Citation Context ...at only susceptibles reproduce and no recovery from infection is possible, in the latter, immigration is assumed instead of, as in our model, reproduction from within the process itself. Both [8] and =-=[2]-=- address the question of time to disease extinction, but where [8] is concerned with an open population model with immigration whereas [2] studies a closed population model. In the present paper the t... |

10 |
The geographical and temporal evolution of sexually transmitted disease epidemics. Sex Transm Infect 2002;78 Suppl 1:i14–9
- GP
(Show Context)
Citation Context ...arch has been conducted on the risks of concurrency, i.e. multiple and simultaneous sexual partners, for the spread of sexually transmitted infections (STI). It is considered an important risk factor =-=[19]-=-[24][29] and a hallmark of core groups, i.e. individuals with high rates of partnership change and high levels of sexual activity [4][22][36]. With concurrent partners, infections can spread to a grea... |

10 |
Chlamydia transmission: Concurrency, reproduction number, and the epidemic trajectory
- JJ, Zimmerman-Rogers, et al.
- 1999
(Show Context)
Citation Context ...t: an infected individual makes occasional sexual contact with susceptible individuals at a regular rate. These models cannot account for the function of partnership in the spread of STIs [23][24][29]=-=[34]-=-[36]. (See Appendix B for a short introduction to epidemic modeling). Some deterministic models do take partnership dynamics into account. They have mainly been formalized by means of dynamic systems ... |

8 | concurrency: comparing individual and partnership-level analyses of new partnerships of young adults at risk of sexually transmitted infections. Sex Transm Dis - Discord |

7 | Adimora AA, Padian NS. Sexual bridging socially and over time: a simulation model exploring the relative effects ofmixing and concurrency on viral sexually transmitted infection transmission. Sex Transm Dis - IA, Shiboski, et al. |

7 |
KK, Aral SO. Measures of sexual partnerships: lengths, gaps, overlaps, and sexually transmitted infection. Sex Transm Dis 2006
- Foxman, Newman, et al.
(Show Context)
Citation Context ...ty [4][22][36]. With concurrent partners, infections can spread to a greater number of individuals. Two studies of sexual behavior point to the more general risk of ”time gaps” for the spread of STIs =-=[18]-=-[26], i.e. the time between sexual partners. In this study, we restrict the definition of ”gap” to the time between the first sexual contact with the current or most recent sexual partner and the last... |

7 |
Gap length: an important factor in sexually transmitted disease transmission. Sex Transm Dis 2003
- JR, SO
(Show Context)
Citation Context ...4][22][36]. With concurrent partners, infections can spread to a greater number of individuals. Two studies of sexual behavior point to the more general risk of ”time gaps” for the spread of STIs [18]=-=[26]-=-, i.e. the time between sexual partners. In this study, we restrict the definition of ”gap” to the time between the first sexual contact with the current or most recent sexual partner and the last sex... |

6 | Inference for an epidemic when susceptibility varies - O’Neill, Becker - 2001 |

6 |
Sex partner concurrency, geographic context, and adolescent sexually transmitted infections. Sexually Transmitted Diseases
- Jennings, Glass, et al.
- 2004
(Show Context)
Citation Context ... has been conducted on the risks of concurrency, i.e. multiple and simultaneous sexual partners, for the spread of sexually transmitted infections (STI). It is considered an important risk factor [19]=-=[24]-=-[29] and a hallmark of core groups, i.e. individuals with high rates of partnership change and high levels of sexual activity [4][22][36]. With concurrent partners, infections can spread to a greater ... |

5 | The estimation of latent and infectious periods - Gough - 1977 |

5 |
Do people really know their sex partners? Concurrency, knowledge of partner behavior, and sexually transmitted infections within partnerships. Sex Transm Dis
- LN, PM, et al.
(Show Context)
Citation Context ...ore group behavior. First, unfaithfulness implies concurrency, multiple partners. This is a hallmark of core groups [6]. Second, unfaithfulness implies nondisclosure of information to sexual partners =-=[14]-=-, which is also a central feature of core group behavior, where multiple sexual contacts are ignorant of each other. Together, concurrency and non-disclosure of information neutralize the regulating f... |

5 | Number of sexual encounters involving intercourse and the transmission of sexually transmitted infections. Sexually Transmitted Diseases - Nordvik, Liljeros |

5 | Approximations for the long-term behaviour of an open-population epidemic model. Methodology and Computing
- Clancy, O’Neill, et al.
- 2001
(Show Context)
Citation Context ...o disease extinction given that the process is started in the quasi-stationary state. That is, the complete dynamics from introduction to extinction. Similar models have been analysed by e.g. [9] and =-=[5]-=-. In the first, it is assumed that only susceptibles reproduce and no recovery from infection is possible, in the latter, immigration is assumed instead of, as in our model, reproduction from within t... |

4 |
Deterministic and stochastic pair formation models for the spread of sexually transmitted diseases
- Kretzschmar
- 1995
(Show Context)
Citation Context ...y have mainly been formalized by means of dynamic systems - systems of differential equations - that specify rates of pair formation and dissolution, as well as rates of infection and recovery [9][11]=-=[27]-=-[28]. The dynamic system approach extends the state space of the basic version of the SIR model (appendix B). Individuals are either single or paired, which enables evaluation of relative threshold ef... |

3 | Britton T: Stochastic Epidemic Models - Andersson - 2000 |

3 | The final size and severity of a generalized stochastic multitype epidemic model. Adv Appl Probab 25: 721–736 - Ball, Clancy - 1993 |

3 |
Analysis and simulation of a stochastic, discrete-individual model of STD transmission Ž .with partnership concurrency
- SE, Adams, et al.
(Show Context)
Citation Context ...nt. They have mainly been formalized by means of dynamic systems - systems of differential equations - that specify rates of pair formation and dissolution, as well as rates of infection and recovery =-=[9]-=-[11][27][28]. The dynamic system approach extends the state space of the basic version of the SIR model (appendix B). Individuals are either single or paired, which enables evaluation of relative thre... |

3 |
Sexual behaviour related to the spread of sexually transmitted diseases: a population-based survey
- Giesecke, Scalia-Tomba, et al.
- 1992
(Show Context)
Citation Context ...ed infections (STI). It is considered an important risk factor [19][24][29] and a hallmark of core groups, i.e. individuals with high rates of partnership change and high levels of sexual activity [4]=-=[22]-=-[36]. With concurrent partners, infections can spread to a greater number of individuals. Two studies of sexual behavior point to the more general risk of ”time gaps” for the spread of STIs [18][26], ... |

3 |
Bakketeig LS. Frequency of sexual partner change in a Norwegian population. Data distribution and covariates
- Stigum, Magnus, et al.
- 1997
(Show Context)
Citation Context ... and methodological issues. 8 First, there are generational shifts in partnership dynamics. For example, during the last two decades, rates of partnership change have gone up in Sweden and Norway [17]=-=[35]-=-. If gaps are collapsed over time, we cannot account for these changes. Second, partnership sampling over longer time periods may result in higher sample losses among younger subjects with less sexual... |

3 |
Strong Approximations for Some Open Population Epidemic Models
- O’Neill
- 1996
(Show Context)
Citation Context ... outbreak occurs, p, when a single infected individual is introduced into a large susceptible population. We will show that our process can be approximated arbitrarily well by the process analysed in =-=[10]-=-, here denoted {(S̃, Ĩ)}, for which the outbreak probability is known. This process describes the spread of an epidemic in a open population, different to ours in that no recovery or reproduction is ... |

3 | On a Model for Interference Between Searching Insect Parasites - Pollet - 1990 |

2 | Social networks, epidemics and vaccination through contact tracing - Mbare, Britton, et al. - 2007 |

2 | Modelling sexually transmitted infections: the effect of partnership activity and number of partners on R0 - Britton, Nordvik, et al. - 2007 |

2 |
Concurrent partnerships among adolescents in a Latino community: the Mission District of
- Doherty, Minnis, et al.
- 2007
(Show Context)
Citation Context ...rences could be discerned for income, marital status, gender, age at first sex, and having same-sex partners. Other studies have demonstrated sex differences, men reporting more partners and overlaps =-=[12]-=-[24][29][31]. The absence of sex differences may be due to the detailed survey questions. It forces the respondents to think carefully about their sexual partners, instead of giving general answers, f... |

1 | Deijfen M., Martin-Löf A.: Generating random graphs with prescribed degree distribution - Britton |

1 | Appropriate Methods for the - Wearing, Rohani, et al. - 2005 |

1 |
Sexual risk behavior and infection: epidemiological considerations
- Aral
(Show Context)
Citation Context ...itted infections (STI). It is considered an important risk factor [19][24][29] and a hallmark of core groups, i.e. individuals with high rates of partnership change and high levels of sexual activity =-=[4]-=-[22][36]. With concurrent partners, infections can spread to a greater number of individuals. Two studies of sexual behavior point to the more general risk of ”time gaps” for the spread of STIs [18][2... |

1 | Measuring Concurrency. Sexually Transmitted Diseases - DD, RB |

1 |
Partnership dynamics and strain competition
- D
(Show Context)
Citation Context ...ere restrictions on the number of concurrent partners [20]. An argument has been made that the dynamic system approach does allow for unlimited concurrency: ”rapidly changing monogamous interactions” =-=[15]-=-. However, concurrency covers different types of overlapping partnerships, including concurrency with one steady and one causal partner, which cannot be equated with high rates of partnership formatio... |

1 |
AM McManus S and Erens B. Measuring sexual behavior: methodological challenges in survey research. Sexually Transmitted Infections
- KA, Johnson
(Show Context)
Citation Context ...e of sexual behaviors and STIs at a particular time. A measure that collapses data over time is not suited as a parameter. Fifth, the generalized gap measure introduces a potential bias in gap recall =-=[16]-=-. Recall is probably better for the most recent partners, whereas missing information on gaps increases with time. Thus, longer gaps may be underestimated. The authors do not discuss these issues, but... |

1 | Modeling infection transmission Annual Revue Public Health - Koopman |

1 |
and Susheela Singh Sexual Partnership Patterns as a Behavioral Risk Factor For Sexually Transmitted Diseases Family Planning Perspectives
- Finer, Darroch
- 1999
(Show Context)
Citation Context ... been conducted on the risks of concurrency, i.e. multiple and simultaneous sexual partners, for the spread of sexually transmitted infections (STI). It is considered an important risk factor [19][24]=-=[29]-=- and a hallmark of core groups, i.e. individuals with high rates of partnership change and high levels of sexual activity [4][22][36]. With concurrent partners, infections can spread to a greater numb... |