# American Institute of Mathematical Sciences

September  2009, 12(2): 279-304. doi: 10.3934/dcdsb.2009.12.279

## The impact of vaccination and coinfection on HPV and cervical cancer

 1 University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, United States, United States

Received  October 2008 Published  July 2009

Understanding the relationship between coinfection with 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 (strain 1, oncogenic) in order to investigate how multiple strains of HPV and vaccination may affect the number of cervical cancer cases and deaths due to infections with both types of HPV. We calculate the basic reproductive number $R_i$ for both strains independently as well as the basic reproductive number for the system based on $R_1$ and $R_2$. We also compute the invasion reproductive number Ř i for strain i when strain j is at endemic equilibrium ($i\ne j$). We show that the disease-free equilibrium is locally stable when $R_0=max\{R_1,R_2\}<1$ and each single strain endemic equilibrium $E_i$ exists when $R_i>1$. We determine stability of the single strain equilibria using the invasion reproductive numbers. The $R_1,R_2$ parameter space is partitioned into 4 regions by the curves $R_1=1, R_2=1,$ Ř 1 = 1, and Ř 2 = 1. In each region a different equilibrium is dominant. The presence of strain 2 can increase strain 1 related cancer deaths by more than 100 percent, but strain 2 prevalence 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.
Citation: Britnee Crawford, Christopher M. Kribs-Zaleta. The impact of vaccination and coinfection on HPV and cervical cancer. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 279-304. doi: 10.3934/dcdsb.2009.12.279
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