Interaction, pair formation and force of infection terms in sexually transmitted diseases

A central question in the study of the dynamics of sexually-transmitted diseases — one emphasized by the AIDS epidemic — is that of mixing. In this note 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 for the general solution to this formulation. An age-structured epidemic model for a single sexually-active homosexual population, stratified by risk and age, with arbitrary risk and age-dependent mixing and variable infectivity is formulated. In the special case of proportionate mixing in age and risk, an explicit expression for the basic reproductive number is given.

[1]  D. Kendall.  Stochastic Processes and Population Growth , 1949 .

[2]  Roland Waldstätter,et al.  Pair Formation in Sexually-Transmitted Diseases , 1989 .

[3]  Carlos Castillo-Chavez,et al.  Some Applications of Structured Models in Population Dynamics , 1989 .

[4]  S. A. Levin,et al.  On the role of long incubation periods in the dynamics of acquired immunodeficiency syndrome (AIDS) , 1989, Journal of mathematical biology.

[5]  Carlos Castillo-Chavez,et al.  On the role of long incubation periods in the dynamics of Acquired Immunodeficiency Syndrome (AIDS). Part 2: multiple group models , 1990 .

[6]  Arak M. Mathai,et al.  Constructing the sunflower head , 1974 .

[7]  S. Levin,et al.  Epidemiological models with age structure, proportionate mixing, and cross-immunity , 1989, Journal of mathematical biology.

[8]  K Dietz,et al.  Epidemiological models for sexually transmitted diseases , 1988, Journal of mathematical biology.

[9]  Lisa Sattenspiel,et al.  Modeling and analyzing HIV transmission: the effect of contact patterns , 1988 .

[10]  A. Nold.  Heterogeneity in disease-transmission modeling , 1980 .

[11]  Roy M. Anderson,et al.  Transmission dynamics of HIV infection , 1987, Nature.

[12]  L Sattenspiel.  Epidemics in nonrandomly mixing populations: a simulation. , 1987, American journal of physical anthropology.

[13]  L. Sattenspiel,et al.  Population structure and the spread of disease. , 1987, Human biology.

[14]  Carlos Castillo-Chavez,et al.  The Role of Long Periods of Infectiousness in the Dynamics of Acquired Immunodeficiency Syndrome (AIDS) , 1989 .

[15]  Horst R. Thieme,et al.  Demographic change and persistence of HIV/AIDS in heterogeneous population , 1991 .

[16]  J. Hyman,et al.  Using mathematical models to understand the AIDS epidemic , 1988 .

[17]  C. Castillo-Chavez,et al.  Mixing framework for social/sexual behavior , 1989 .

[18]  Carlos Castillo-Chavez,et al.  On the role of variable infectivity in the dynamics of the human immunodeficiency virus epidemic , 1989 .

[19]  K. Hadeler.  Pair formation in age-structured populations. , 1989, Acta applicandae mathematicae.

[20]  C. Castillo-Chavez,et al.  On the possible effects of infection-age-dependent infectivity in the dynamics of HIV/AIDS. , 1990 .

[21]  Roy M. Anderson,et al.  The Transmission Dynamics of Human Immunodeficiency Virus (HIV) , 1988 .

[22]  C. Castillo-Chavez,et al.  Like-with-like preference and sexual mixing models. , 1989, Mathematical biosciences.

[23]  O. Diekmann,et al.  On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations , 1990, Journal of mathematical biology.

[24]  Klaus Dietz,et al.  On the transmission dynamics of HIV , 1988 .

[25]  A. G. Fredrickson,et al.  A mathematical theory of age structure in sexual populations: random mating and monogamous marriage models , 1971 .

[26]  L. Sattenspiel,et al.  The spread and persistence of infectious diseases in structured populations , 1988 .

[27]  Carlos Castillo-Chavez,et al.  Results on the dynamics for models for the sexual transmission of the human immunodeficiency virus , 1989 .