Epidemiological models for sexually transmitted diseases

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.

Patterns in the effects of infectious diseases on population growth

“…by including a very crude description of pair formation. (For a discussion of pair formation models see [4,7,18].) A pair can be formed by two susceptibles, a susceptible and an infective, or two infectives.…”

“…Some authors dealing with models for STD's (sexually transmitted diseases) or worm diseases have introduced homogeneous models, i.e. models in which the total population size is but a scaling variable (see [7,8,9]). Such models allow for exponential solutions, as we will see in detail below.…”

Stochastic and deterministic models in epidemiology

“…The work of Lubkin and Castilla-Chavez on pair formation models provides an alternative to the early approach (10,17,18,26,27,28] and its later extensions to epidemiology (8,9,11,12,13,30]. In the next section we introduce a stochastic analog to the model presented by Lubkin and Castilla-Chavez.…”

“…The properties of such stochastic model are also explored in the next section. The approach of Dietz and Hadeler (8,9,11,12] is based on the use of a nonlinear function 't/J to model the process (rate) of pair formation. This mixing/pair-formation function is assumed to satisfy the Fredrickson/McFarland (10,26] properties, which are discussed in more detail in the contribution by Lubkin and Castilla-Chavez.…”

A pair formation approach to modeling inheritance of social traits

“…mathematically valid and biologically relevant. The first answer known to us is provided by the classical demographic pair-formation model [5,6,9]. The approach is based on the use of a nonlinear function 1/J to model the process (rate) of pair formation.…”