Mathematics of STI Spread

(DISCLAIMER: This post is a little more technical, and hopefully will be enjoyed by my dear friends in math, engineering, or computer science).

Let:

R° = the average number of secondary cases infected by each person who has an STI (units: people)

β = the percentage probability that a person with an STI will spread the infection to a current susceptible sexual partner.

c = the average number of new sexual partners made (units: people/month)

D = the average duration of infectiousness for a particular STI (units: months)

M = the average number of people with an STI cured from infectiousness each month by medical intervention (units: people/month)

The change in prevalence of an STI in the population is determined by R°:
- If R° < 1, the STI is declining in prevalence
- If R° = 1, the STI is in equilibrium
- If R° > 1, the STI is becoming more prevalent 

R° can be expressed in terms of the other variables: 
     R° = βcD

Given a particular M, and noticing that β and D are constant for each STI, R° varies with c. Studies of sexual practices show that c follows a Poisson distribution that is heavily skewed towards the left. Thus:
- In most populations (the left-skew of the distribution), c is low enough that R° < 1
- There exist “core” populations (the right-sided tail of the distribution) where c is high enough that R° > 1. 
- Demonstrated core populations are: young people, sex-trade workers, and drug users.
- By estimating β and D, we can determine the threshold c for which R° = 1 (c = 1 / βD), and above which there is increasing prevalence of the STI. 

Some interesting research findings regarding core groups and epidemics:
- Like-with-like sexual activity (= within a core group) is a risk factor for a fast-developing, but limited STI epidemic.
- When core groups are small enough, there is self-limiting of the epidemic since sexual contacts become very likely to have previously contracted the infection
- Like-with-unlike sexual activity (= between a core group member and non-core group member) is a risk factor for a slow-developing, but ultimately more prevalent epidemic. 

STI prevention focuses on:
- Increasing M, which causes a decrease in D
- Advocating safe-sex and protective behaviours that reduce β
- Identifying core groups for focused medical attention and STI screening

Whoever said that mathematicians have no hope of ever becoming familiar with sex ? Course this isn’t quite the type of familiar I think they were hoping for…