Transmission heterogeneity and autoinoculation in a multisite infection model of HPV

The human papillomavirus (HPV) is sexually transmitted and can infect oral, genital, and anal sites in the human epithelium. Here, we develop a multisite transmission model that includes autoinoculation to study HPV and other multisite diseases. Under a homogeneous-contacts assumption, we analyze the basic reproduction number R0, as well as type and target reproduction numbers, for a two-site model. In particular, we find that R0 occupies a space between taking the maximum of next generation matrix terms for same site transmission and taking the geometric average of cross-site transmission terms in such a way that heterogeneity in the same-site transmission rates increases R0 while heterogeneity in the cross-site transmission decreases it. Additionally, autoinoculation adds considerable complexity to the form of R0. We extend this analysis to a heterosexual population, which additionally yields dynamics analogous to those of vector-host models. We also examine how these issues of heterogeneity may affect disease control, using type and target reproduction numbers.