The impact of vaccination and coinfection on HPV and cervical cancer

Abstract

Understanding the relationship between coinfection with multiplestrains of human papillomavirus and cervical cancer may play a keyrole in vaccination strategies for the virus. In this article weformulate a model with two strains of infection and vaccination forone of the strains (strain 1, oncogenic) in order to investigate howmultiple strains of HPV and vaccination may affect the number ofcervical cancer cases and deaths due to infections with both typesof HPV. We calculate the basic reproductive number $R_i$ for bothstrains independently as well as the basic reproductive number forthe system based on $R_1$ and $R_2$. We also compute theinvasion reproductive number Ř i for straini when strain j is at endemic equilibrium ($i\nej$). We show that the disease-free equilibrium is locally stablewhen $R_0=max\{R_1,R_2\}1$. We determine stability ofthe single strain equilibria using the invasion reproductivenumbers. The $R_1,R_2$ parameter space is partitioned into 4 regionsby 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 ofstrain 2 can increase strain 1 related cancer deaths by more than100 percent, but strain 2 prevalence can be reduced by more than 90percent with 50 percent vaccination coverage. Under certainconditions, we show that vaccination against strain 1 can actuallyeradicate strain 2.