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  • 1
    Electronic Resource
    Electronic Resource
    Pair formation models with maturation period (1993)
    Springer
    Journal of mathematical biology 32 (1993), S. 1-15 
    Details
    ISSN: 1432-1416
    Keywords: Demography ; Two-sex problem ; Age structure ; Pair formation ; Delay equation ; Homogeneous equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The standard model for pair formation is generalized to include a maturation period. This model in the form of three coupled delay equations is a special case of the general age-structured model for a two-sex population. The exact conditions for the existence of an exponential (persistent) two-sex solution are derived. It is shown that this solution is unique and locally stable. In order to achieve these results the theory of homogeneous differential equations is extended to a class of homogeneous delay equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00160370
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  • 2
    Electronic Resource
    Electronic Resource
    Epidemiological models for sexually transmitted diseases (1988)
    Springer
    Journal of mathematical biology 26 (1988), S. 1-25 
    Details
    ISSN: 1432-1416
    Keywords: Epidemiological models ; Basic reproduction rate ; Sexually transmitted infections ; Thresholds ; Pair formation ; Gonorrhea ; AIDS
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract The classical models for sexually transmitted infections assume homogeneous mixing either between all males and females or between certain subgroups of males and females with heterogeneous contact rates. This implies that everybody is all the time at risk of acquiring an infection. These models ignore the fact that the formation of a pair of two susceptibles renders them in a sense temporarily immune to infection as long as the partners do not separate and have no contacts with other partners. The present paper takes into account the phenomenon of pair formation by introducing explicitly a pairing rate and a separation rate. The infection transmission dynamics depends on the contact rate within a pair and the duration of a partnership. It turns out that endemic equilibria can only exist if the separation rate is sufficiently large in order to ensure the necessary number of sexual partners. The classical models are recovered if one lets the separation rate tend to infinity.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00280169
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  • 3
    Electronic Resource
    Electronic Resource
    Models for pair formation in bisexual populations (1988)
    Springer
    Journal of mathematical biology 26 (1988), S. 635-649 
    Details
    ISSN: 1432-1416
    Keywords: Pair formation ; Two-sex population ; Homogeneous evolution equation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Birth, death, pair formation, and separation are described by a system of three nonlinear homogeneous ordinary differential equations. The qualitative properties of the system are investigated, in particular the conditions for existence and global stability of the bisexual state.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00276145
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