Transmission heterogeneity and autoinoculation in a multisite infection model of HPV

• We analyze the basic reproduction number R0 of a multisite infection model.
• Heterogeneity between same site transmission rates increases R0.
• Heterogeneity between cross site transmission rates decreases R0.
• Neglecting autoinoculation may result in severe misestimation of R0.

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.