Graduation Semester and Year




Document Type


Degree Name

Master of Science in Mathematics



First Advisor

Christopher Kribs


Understanding the relationship between multiple strains of human papillomavirus and cervical cancer may play a key role in vaccination strategies for the virus. In this article we formulate a model with two strains of infection and vaccination for one of the strains in order to investigate how multiple strains of HPV and vaccination may aect the number of cervical cancer cases and deaths due to infections with both types of HPV. We calculate the basic reproductive number for both strains independently as well as the basic reproductive number for the system based on R1 and R2. We also compute the invasion reproductive number R~i for strain i when strain j is at equilibrium (i 6= j). We show that the disease-free equilibrium is locally stable when R0 = maxfR1;R2g < 1 and each single strain endemic equilibrium Ei exists when Ri > 1. We determine stability of the single strain equilibrium using the invasion reproductive numbers. The R1;R2 parameter space is partitioned into 4 regions by the curves R1 = 1;R2 = 1;R~1 = 1, and R~2 = 1. In each region a dierent equilibrium is dominant. The presence of strain 2 can increase strain 1 related cancer deaths by more than 100 percent, but can be reduced by more than 90 percent with 50 percent vaccination coverage. Under certain conditions, we show that vaccination against strain 1 can actually eradicate strain 2.


Mathematics | Physical Sciences and Mathematics


Degree granted by The University of Texas at Arlington

Included in

Mathematics Commons