Abstract
This study aims at investigating the dynamics of sexually transmitted infectious disease (STID), which is serious health concern. In so doing, the integer order STID model is progressed in to the time-delayed non-integer order STID model by introducing the Caputo fractional derivatives in place of integer order derivatives and including the delay factors in the susceptible and infectious compartments. Moreover, unique existence of the solution for the underlying model is ensured by establishing some benchmark results. Likewise, the positivity and boundedness of the solutions for the projected model is explored. The basic reproduction number is [Formula: see text] is found out for the model. The time-delayed non-integer order STID model holds two steady states, namely, the STID free and endemic steady state. The model stability is carried out at the steady states. The non-standard finite difference (NSFD) technique is hybridized with the Grunwald Letnikov (GL) approximation for finding the numerical solutions of the time-delayed non-integer order STID model. The boundedness and non-negativity of the numerical scheme is confirmed. The simulated graphs are presented with the help of an appropriate test example. These graphs show that the proposed numerical algorithm provides the positive bounded solutions. The article is ended with productive outcomes of the study.