Mathematical model weighs control strategies for HPV spread through sexual and non-sexual routes

A new mathematical modelling study examines how human papillomavirus (HPV) spreads through both sexual and non-sexual transmission routes, and uses optimal control theory to compare intervention strategies. The work, published in Advances in Continuous and Discrete Models, builds a dynamic transmission model that explicitly incorporates these two pathways of infection.

The researchers, Peng Qin, Junxia Wang and Wenhui Hao, first derive the basic reproduction number, R0, for their model using the next-generation matrix method. This threshold quantity determines the long-term behaviour of the epidemic: according to the analysis, when R0 is below 1, the disease-free equilibrium is globally asymptotically stable, meaning the infection dies out. When R0 exceeds 1, an endemic equilibrium exists, indicating persistent transmission.

Numerical simulations form a central part of the study. The authors report that vaccination strategies targeting susceptible populations proved more effective in their simulations than input measures applied to vaccinated populations. This distinction matters for programme design, because it concerns how vaccine-related interventions are represented and applied within the model rather than a direct clinical trial comparison.

The team also performed a sensitivity analysis on the threshold R0 and formulated a corresponding optimal control problem. Among single measures implemented on their own, the model results indicate that sexual contact control is the most effective, followed by non-sexual contact control. The authors additionally conclude that vaccination measures should not be ignored when designing combined strategies.

As a theoretical study, the analysis rests on the assumptions built into the dynamic model and the parameter choices used in the simulations, and the findings describe model behaviour rather than outcomes measured in a real-world vaccination or control programme. The article was published on 9 October 2026 and is available as open access.

Subject of Research: Optimal control analysis of a dynamic model of HPV transmission via sexual and non-sexual routes

Article Title: Optimal control of human papillomavirus transmission models integrating sexual and non-sexual routes

Article References: Qin, P., Wang, J., & Hao, W. (2026). Optimal control of human papillomavirus transmission models integrating sexual and non-sexual routes. Advances in Continuous and Discrete Models. https://doi.org/10.1186/s13662-026-04140-w

Image Credits: AI Generated

DOI: 10.1186/s13662-026-04140-w

Keywords: HPV, mathematical modelling, optimal control, basic reproduction number, vaccination strategy, sensitivity analysis, transmission dynamics, sexual transmission, non-sexual transmission, disease-free equilibrium, Optimal, control