1. Modeling the Spread of Gonorrhea Talitha Washington University of Evansville MathFest 2006

2. Background Ranks high among reportable communicable diseases Caused by a bacterium, Neisseria gonorrhoeae In US, highest reported rates of infection are among sexually active teenagers and young adults Spread by sexual contact Can result in blindness, sterility, arthritis, heart failure and possible death Short incubation time (3-7 days) and not immune For males, causes burning and itching and often asymptomatic in females

3. Model Assumptions Sexually active heterosexual population with 1000 females and 1000 males Cure rates (or treatment rates) for infective females and males are proportional to the infective populations New infective females are added to the population at a rate proportional to the number of infective males and susceptible females (a similar term adds infective males to the male population)

4. Mathematical Model Infective females: x = x(t) Infective males: y = y(t) Time t is in months x' = -a 1 x + b 1 (1000 - x)y y' = -a 2 y + b 2 (1000 - y)x x(0) = 20, y(0) = 20 a 1 = 0.33, a 2 = 0.53, b 1 = 0.00052, b 2 = 0.00047 Use pplane to approximate the solution

5. x(100) ≈ 174 y(100) ≈ 134 Males seek more treatment Simulate for 100 months

6. Scenario 1 Because AIDS is such a problem in today’s society, the sexually active population is taking more precautions Lower infective rates for time 100 to 150 months b 1 = 0.00042 (versus 0.00052) b 2 = 0.00037 (versus 0.00047) Use original values of a 1 and a 2 x(150) = 20, y(150) = 15

7. Scenario 2 People fearing the more dangerous disease AIDS may seek medical treatment earlier Increase treatment rate for time 100 to 150 months a 1 = 0.43 (versus 0.33) a 2 = 0.63 (versus 0.53) Use original values of b 1 and b 2 x(150) = 15, y(150) = 12 Conclusion: Scare people

8. Learning Outcomes Learn how mathematics can be used to make predictions Understand the strengths of model for discussing public policy Learn to analyze weaknesses in model See mathematics as a useful tool Connects differential equations to an issue that affects young people Rationalize that “Sex Can Wait”

9. References Based on project by Joseph M. Mahaffy, San Diego State University Gonorrhea, Center for Disease Control Fact Sheet Sexually Transmitted Disease Surveillance 2004 Supplement: Gonococcal Isolate Surveillance Project (GISP) Annual Report – 2004. CDC pplane http://math.rice.edu/~dfield Copyrighted in the name of John Polking, Rice University Available free for use in educational institution

10. Contact Washington tw65@evansville.edu http://faculty.evansville.edu/tw65 www.myspace.com/dr_washington