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

Based on the transmission mechanism of HPV, this paper establishes a dynamic model that includes sexual and non-sexual transmission. First, the threshold \(R_{0} \) of the model is obtained using the next-generation matrix method. It is found that when \(R_{0} < 1 \) , the disease-free equilibrium is globally asymptotically stable, while when \(R_{0} > 1 \) , the endemic equilibrium exists. Subsequently, numerical simulations verify that vaccination strategies targeting susceptible populations are more effective than input measures for vaccinated populations. Furthermore, sensitivity analysis is conducted on threshold \(R_{0} \) , and the corresponding optimal control problem is considered. It is found that when implementing a single measure, sexual contact control is the most effective, followed by non-sexual contact control. In addition, vaccination measures should not be ignored.