Sex Partner Math II: the British Problem

We now consider the solution to the British Problem: What is the age difference between the British male and female onset of sex partner accumulation that will account for the difference in the survey data reported by ABC News?

The Model:

We assert a profile of sexual activity thus: sex partner accumulation begins at one age and continues at a constant rate until another age when subjects settle into monogamy until natural death. The age at which partner accumulation is different for males and females; however, both sexes accumulate the same number of partners at the same rate for the same length of time.

Simplifying assumptions:

We assume a uniform age distribution throughout the population. We will assume zero population growth (or decline). We will assume the average parameters actually apply to all members. (This probably isn’t a necessary assumption, but we state it anyway.)

Constants:

The survey reports that the average number of sexual partners of the female population is 9; we assume this survey included no women younger than the age of onset. The survey reports that the average number of sexual partners of the male population is 7; we assume that this includes those men with zero partners between the age of female onset and the age of male onset. We assume that men begin their accumulation of sexual partners at age 19 and cease accumulation at age 37. Men will remain monogamous from age 37 until their death at age 72. We assume that women begin their partner accumulation at some age 19 – Dy, cease accumulation at age 37 – Dy, and live monogamously until age 77.

Variables:

N: total number of lifetime sexual partners for both men and women.

T: partner period; as in the length of time (in years) between different partners. The rate of accumulation is therefore 1/T.

D: difference in age between male onset and female onset, measured in multiples of T. Thus, D*T = Dy in years.

Rm: length of male monogamy, measured in multiples of T.

Rf: length of female monogamy, measured in multiples of T.

Equations:

Men accumulate N sexual partners at rate 1/T in the 18 years between 19 and 37. Thus,

Men remain monogamous for the 35 years between age 37 and 72. As measured in T,

Women live five years longer than men, but they stop accumulating sexual partners D*T years earlier. Thus:

The last two equations are tricky. We must express the average number of sex partners for both men and women in terms of the other variables. Consider women first. Given the model and assumptions, the average number of sexual partners of women between age 19 – Dy and 37 – Dy would be:

But the average also includes women who have already accumulated their N partners, So the actual equation is:

We now consider the equation for the male average, which includes a number of young men with no sexual partners for D*T years. This equation is:

We now have 5 equations in 5 unknowns.

Solution:

Using algebra and Matlab, we can solve for the partner period T = 1.44 years and the onset age difference D = 3.9 multiples of T, or 5.6 years. Thus, women begin sexual partner accumulation at age 19 – 5.6 = 13.4 years of age. The total number of lifetime sexual partners for men and women is 12.5.

Conclusion:

Using this simple model, and a plausible set of parameters, we can account for the survey results merely with the age difference between men and women at which they become sexually active.