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How Effective is the HPV Vaccine?

How Effective is the HPV Vaccine?. Aaron Steinberg 10 April 2008 Math Comps. Overview. HPV, the genital HPV infection, and Gardasil Previous models Markov Models My previous work New Markov model Results and discussion of new model. What is HPV?.

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How Effective is the HPV Vaccine?

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  1. How Effective is the HPV Vaccine? Aaron Steinberg 10 April 2008 Math Comps

  2. Overview • HPV, the genital HPV infection, and Gardasil • Previous models • Markov Models • My previous work • New Markov model • Results and discussion of new model

  3. What is HPV? • HPV (Human papillomavirus) is the name of a group of viruses, 30 of those types are sexually transmitted • The “high-risk” types of HPV are responsible for 90 percent of genital warts and 70 percent of cervical cancers • The genital HPV infection is thought to be the most common sexually transmitted disease in the world • To combat this infection a vaccine called Gardasil was created by Merck Pharmaceuticals

  4. Previous Models • Models by R.V. Barnabus et al. and E.J. Dasbach et al. explore the affects of Gardasil on HPV

  5. Markov Models • A Markov model is a discrete-time stochastic process • In such a process, future states are independent of past states • At each time step the model may transition into another state or remain in the same state according to a given probability distribution and transition diagram • Transition probabilities pij= probability of moving from state i to state j

  6. My Previous Work • A simple Markov model with three states • Concerned with HPV and Cervical Cancer • Population is 101 million women

  7. Transition Matrices for Previous Model

  8. Graphed Results of Previous Model

  9. Issues Leading to New Model • People naturally cure HPV infection so proportion ending in HPV state is too large • Three dose structure of HPV vaccine is not taken into account in previous models

  10. New Markov Model

  11. New Model Assumptions • Since humans naturally cure the HPV infection it is possible to return from any of the further states to the susceptible population • Population includes all sexually active females • Since there are three doses of the vaccine there are four susceptible states • Each iterative step is one year

  12. New Assumptions Cont. • The probability for returning to the different susceptible states is the probability for returning to one susceptible state given by Barnabus et al. but divided four ways where 4/10 was for returning to S0, 3/10 for S1, 2/10 for S2, and 1/10 for S3 • One can not acquire cancer or pre-cancer without getting HPV first, thus disregarding cases of cervical cancer not from HPV • Curing cervical cancer leads directly back to the susceptible population

  13. Transition Probability Matrix

  14. Variable Probabilities x y

  15. Cases Considered • No Vaccine • One Dose Vaccine • Variable Probabilities

  16. Is the Model Accurate? • Although steady states are small my population is on the scale of hundreds of millions so even these fractions of a percent are significant • In the unvaccinated case there was a steady state for HPV of 0.1144 meaning 11.44 percent of the population would be in the HPV state in the long run.

  17. One-Dose Vaccine Discussion • All cases with any vaccine end with a steady state for cervical cancer of zero. Leaves us with HPV as the useful result • For the case with a one-dose vaccine structure the steady state for HPV is 0.0153, corresponding to an 87 percent decrease in HPV • In the model with the one-dose vaccine structure there is an approximate average of a 60 percent decrease in pre-cancer

  18. Three-Dose vs. One-Dose Vaccines • For the case of the three-dose vaccine with the base indices, the steady state for HPV is 0.0173; in the one-dose case the HPV steady state is 0.0153

  19. Why Do the Steady States Increase Faster when Varying Y? • Mathematically speaking, only one row of the transition matrix is varied at each case • I put forth that the cause of this phenomenon is possibly that pS0S1 < pS1S2

  20. Hypothesis Test • To test this hypothesis I set pS0S1=pS1S2=0.5, the original value for pS0S1 → ΠHPV=0.0178. • To further test my hypothesis I set pS0S1=pS1S2=0.9 → ΠHPV=0.0169.

  21. What Do the Results of the Hypothesis Test Mean?

  22. Conclusion • The model is a good representation of real life • Implementing a vaccine, especially in a one-dose form, should heavily curtail cases of HPV • It is advisable to refrain from sexual activity during the vaccination period because we see that HPV cases in the long term are variable with unknown transition probabilities in between doses • Vaccinating more women in the beginning, and ensuring that more women, who begin the series, complete it, results in a reduction of overall HPV cases and greatly decreases variance in unknown transition probabilities in between doses

  23. Further Research • More attention to which S state people return to after CC • More elaborate model tracking cervical cancer • Make a model for genital warts caused by HPV

  24. Thank You • The entire Math Department, faculty and students…and of course everyone who came to watch • Professor Tamas Lengyel • Professor Mickey McDonald • Professor Ron Buckmire • Last, but definitely not least, Professor Angela Gallegos

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