A model to determinate the reproductive basic number, detonated R_o, for the case of population with heterogeneity in sexual activity and proportionate mixing is solved using computer algebra and SMT solvers. Specifically Maple and Z3 were used. The code for the solution of the model was written in Z3-Python, but it can also be played by Z3-SMT-Lib. R_o represents an algebraic synthesis of every epidemiological parameter. Numerical simulations were done to prove the effectiveness of the model and the code. The algebraic structure of R_o suggests the possible control measurements that should be implemented to avoid the propagation of the sexual transmitted diseases. The obtained results are important on the computational epidemiology field. As a future investigation, it is suggested to apply the STM solvers to analyze models for other kinds of epidemic diseases.