Human Papillomavirus infection is the most common sexually transmitted infection, and causes serious complications such as cervical cancer in vulnerable female populations in regions such as East Africa. Due to the scarcity of empirical data about sexual relationships in varying demographics, computationally modelling the underlying sexual contact networks is important to understand Human Papillomavirus infection dynamics and prevention strategies. In this work we present SeCoNet, a heterosexual contact network growth model for Human Papillomavirus disease simulation. The growth model consists of three mechanisms that closely imitate real-world relationship forming and discontinuation processes in sexual contact networks. We demonstrate that the networks grown from this model are scale-free, as are the real world sexual contact networks, and we demonstrate that the model can be calibrated to fit different demographic contexts by using a range of parameters. We also undertake disease dynamics analysis of Human Papillomavirus infection using a compartmental epidemic model on the grown networks. The presented SeCoNet growth model is useful to computational epidemiologists who study sexually transmitted infections in general and Human Papillomavirus infection in particular.