Abstract
A central aspect in the study of the dynamics of sexually transmitted diseases is that of mixing. The study of the effects of social structure in disease dynamics has received considerable attention over the last few years as a result of the AIDS epidemic. In this paper, we formulate a generalization of the Blythe and Castillo-Chavez social/sexual framework for human interactions through the incorporation of age structure, and derive an explicit expression in terms of a preference function for the general solution to this formulation. We emphasize the role played by proportionate mixing, the only separable solution to this mixing framework, through the discussion of several specific cases, and we formulate an age-structured epidemic model for a single sexually active homosexual population, stratified by risk and age, with arbitrary risk- and age-dependent mixing as well as variable infectivity. In the special case of proportionate mixing in age and risk, an explicit expression for the basic reproductive number is computed.
Keywords
Mixing (physics)GeneralizationPopulationBasic reproduction numberExpression (computer science)PreferenceSeparable spaceEpidemic modelMathematicsDemographyComputer scienceStatisticsSociologyMathematical analysisPhysics
Affiliated Institutions
Related Publications
A Preliminary Study of the Transmission Dynamics of the Human Immunodeficiency Virus (HIV), the Causative Agent of AIDS
The paper describes some preliminary attempts to formulate simple mathematical models of the transmission dynamics of HIV infection in homosexual communities. In conjunction wit...
The Social Organization of Sexuality-Reply
<h3>In Reply.</h3> —Drs Haverkos and Drotman assert in their second paragraph that our conclusion regarding the negligible likelihood of an epidemic spread of HIV in the heteros...
Stability and Bifurcation for a Multiple-Group Model for the Dynamics of HIV/AIDS Transmission
This paper examines a multigroup epidemic model with variable population size. It is shown that even in the case of proportionate mixing, multiple endemic equilibria are possibl...
The social organization of sexuality
To the Editor. —The National Health and Social Life Survey on adult sexual behavior in the United States was released recently. 1-3 The report is based on interviews of 3432 me...
Seroconversion, sexual activity, and condom use among 2915 HIV seronegative men followed for up to 2 years.
A cohort of 2915 HIV-1-seronegative men from the four centers of the Multicenter AIDS Cohort Study (MACS) was followed at 6 month intervals for 24 months to identify men who dev...
Publication Info
- Year
- 1991
- Type
- article
- Volume
- 8
- Issue
- 1
- Pages
- 1-29
- Citations
- 161
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
161
OpenAlex
Cite This
Stavros Busenberg,
Carlos Castillo‐Chávez
(1991).
A General Solution of the Problem of Mixing of Subpopulations and its Application to Risk- and Age-Structured Epidemic Models for the Spread of AIDS.
Mathematical Medicine and Biology A Journal of the IMA
, 8
(1)
, 1-29.
https://doi.org/10.1093/imammb/8.1.1
Identifiers
- DOI
- 10.1093/imammb/8.1.1