On the Dynamics of Sexually Transmitted Diseases Under Awareness and Treatment

In this paper, we develop and extend the work of Jia and Qin on sexually transmitted disease models with a novel class of non-linear incidence. Awareness plays a central role both in the susceptible and the infectious classes. The Existence, uniqueness, boundedness, and positivity of solutions are systematically established. Concavity arguments and the occurrence of a vertical asymptote are essential in the proof of the existence of a unique endemic equilibrium. Conditions for the stability of all steady states are investigated. In particular, numerical simulations are performed in order to capture the asymptotic behavior of solutions.