An assessment on the effectiveness of condom use in reducing the incidence of chlamydia through mathematical modelling

OBJECTIVE: To determine the relationship between the rate of condom use and incidence of Chlamydia amongst commercial sex worker using a mathematical model. METHODS: Assuming that p(%) is the rate of condom use by female sex workers and r(%) is the incidence of Chlamydia. If the use of condom increases by delta p then the incidence of Chlamydia will decrease by delta r. k is the relative rate of change. Then the mathematical model established becomes dr/dp = -kr. RESULTS: The solution of the differential equation is r (p) = r (P0) exp [-k (p - p0)]. Using the surveillance data gathered from 100% Condom Use Program in Wuhan City the k value is calculated to be 4.36. If k indicates the contribution coefficient of reducing Chlamydia after condom use when the rate of condom use increases by 16% then the incidence of Chlamydia will decrease by 50%. The average difference between the actual incidence and the incidence calculated from the mathematical model is only 6.2%. This result demonstrates a good fit. The predicted result of using this mathematical model shows that at the time of lower levels of condom use a small increment on the rate of condom use would considerably reduce the infection rate of Chlamydia. CONCLUSION: When k remains constant this mathematical model reflects the qualitative relationship between the rate of condom use and the incidence of Chlamydia.