Book contents
- Frontmatter
- Contents
- Introduction
- Participants
- Non-Participant Contributors
- Part 1 Transmissible diseases with long development times and vaccination strategies
- Part 2 Dynamics of immunity (development of disease within individuals)
- Part 3 Population heterogeneity (mixing)
- Modeling heterogeneous mixing in infectious disease dynamics
- Behavior change and non-homogeneous mixing
- Sources and use of empirical observations to characterise networks of sexual behaviour
- Invited Discussion
- Invited Discussion
- Per-contact probabilities of heterosexual transmission of HIV, estimated from partner study data
- Heterosexual spread of HIV with biased sexual partner selection
- Dynamic simulation of sexual partner networks: which network properties are important in sexually transmitted disease (STD) epidemiology?
- The spread of an STD on a dynamic network of sexual contacts
- Network measures for epidemiology
- Spatial heterogeneity and the spread of infectious diseases
- Data analysis for estimating risk factor effects using transmission models
- Homosexual role behaviour and the spread of HIV
- Homogeneity tests for groupings of AIDS patient classifications
- Risk factors for heterosexual transmission of HIV
- The effect of behavioural change on the prediction of R0 in the transmission of AIDS
- The saturating contact rate in epidemic models
- A Liapunov function approach to computing R0
- Stochastic models for the eradication of poliomyelitis: minimum population size for polio virus persistence
- Part 4 Consequences of treatment interventions
- Part 5 Prediction
Invited Discussion
Published online by Cambridge University Press: 04 August 2010
- Frontmatter
- Contents
- Introduction
- Participants
- Non-Participant Contributors
- Part 1 Transmissible diseases with long development times and vaccination strategies
- Part 2 Dynamics of immunity (development of disease within individuals)
- Part 3 Population heterogeneity (mixing)
- Modeling heterogeneous mixing in infectious disease dynamics
- Behavior change and non-homogeneous mixing
- Sources and use of empirical observations to characterise networks of sexual behaviour
- Invited Discussion
- Invited Discussion
- Per-contact probabilities of heterosexual transmission of HIV, estimated from partner study data
- Heterosexual spread of HIV with biased sexual partner selection
- Dynamic simulation of sexual partner networks: which network properties are important in sexually transmitted disease (STD) epidemiology?
- The spread of an STD on a dynamic network of sexual contacts
- Network measures for epidemiology
- Spatial heterogeneity and the spread of infectious diseases
- Data analysis for estimating risk factor effects using transmission models
- Homosexual role behaviour and the spread of HIV
- Homogeneity tests for groupings of AIDS patient classifications
- Risk factors for heterosexual transmission of HIV
- The effect of behavioural change on the prediction of R0 in the transmission of AIDS
- The saturating contact rate in epidemic models
- A Liapunov function approach to computing R0
- Stochastic models for the eradication of poliomyelitis: minimum population size for polio virus persistence
- Part 4 Consequences of treatment interventions
- Part 5 Prediction
Summary
Comments on Heterogeneity Aspects in Mathematical Epidemiology
To begin with I remark generally upon two important aspects of communication in mathematical epidemiology, nomenclature and interpretation of formulae (Sections 1 and 2), and then upon the tension between simple and sophisticated models (Section 3). Finally possible quantitative and qualitative effects of heterogeneity on the basic reproduction ratio in epidemic models are discussed (Section 4).
Nomenclature
Mathematical epidemiology is a scientific field where interdisciplinary collaboration is essential and, as part of this, communication between mathematicians and non-mathematicians (biologists, epidemiologists, etc.) is most important. One prerequisite for efficient and fruitful communication – in particular with people who are not specialists in mathematical epidemiology – is a joint nomenclature which tries to avoid using verbal expressions in ambiguous or misleading ways. But unfortunately there seems to persist some confusion about this, not only between persons who are specialists in different scientific fields, but occasionally even within fields.
One example of expressions in epidemiology which are quite misleading, but can be easily avoided, is random mixing and non-random mixing. Both terms assume that an infection is transmitted through contacts which are made at random (even if the mathematical model does not contain explicitly a stochastic formulation, but some deterministic counterpart). But whereas the first of these two terms intends to express that the population mixes homogeneously, and thus even contacts between individuals of distinct subpopulations are made uniformly, the latter particularly expresses that this is not the case. Since both types of mixing patterns involve random contacts, these two inappropriate verbal expressions should not be used.
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- Information
- Models for Infectious Human DiseasesTheir Structure and Relation to Data, pp. 265 - 270Publisher: Cambridge University PressPrint publication year: 1996