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
Stochastic models for the eradication of poliomyelitis: minimum population size for polio virus persistence
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
Introduction
In small communities there are usually only few infectious individuals. If they contact too few susceptibles, this might lead to local extinction. On the other hand, if they contact too many susceptibles, they give rise to too many secondary infections. This reduces the number of susceptibles, which may eventually also lead to extinction. In order for long term persistence of the infection to be likely, the population must exceed a minimum size. If there is a long infectious period (e.g. for leprosy, tuberculosis and HIV it lasts for years), the infection can persist even in small populations. High contact rates cause a better ‘exploitation’ of the population, but they also bear the risk of causing large epidemics which in turn can cause local extinction. Human birth and death rates define the population turnover and therefore also influence the persistence of infectious diseases. It is the aim of this study to determine the minimum population size that is necessary for the persistence of polio virus infection by using stochastic simulations.
Methods
The computer models are stochastic. The sequence of epidemiological events is generated by a Markov process. The type of the event (birth, death of a susceptible, infection, loss of infectivity) is assigned according to a multinomial distribution which depends on the state of the population (number of susceptible and infectious individuals; see Appendix for details). If the event is a birth, the number of susceptibles is increased by one. If it is an infection, the number of susceptibles is decreased by one and the number of infectives is increased by one.
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- Chapter
- Information
- Models for Infectious Human DiseasesTheir Structure and Relation to Data, pp. 315 - 328Publisher: Cambridge University PressPrint publication year: 1996
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