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.

S. Busenberg, C. Castillo-Chavez

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)1-29
Number of pages29
JournalIMA Journal of Mathematics Applied in Medicine and Biology
Volume8
Issue number1
StatePublished - 1991
Externally publishedYes

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Age-structured Model
Epidemic Model
acquired immune deficiency syndrome
subpopulation
General Solution
Acquired Immunodeficiency Syndrome
Sexually Transmitted Diseases
sexually transmitted disease
Basic Reproductive number
sexually transmitted diseases
Age Structure
Social Structure
infectivity
social structure
age structure
pathogenicity
Population
Formulation
Dependent
Arbitrary

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Mathematics (miscellaneous)

Cite this

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