Chlamydia trachomatis infection, a major sexually transmitted disease, affects millions of people worldwide. A key public health challenge in managing such a transmitted disease is identifying infected but asymptomatic individuals so that they can be treated with antibiotics. Effectively resolving such a challenge will benefit both treated individuals (by improving quality of life) and the entire population (through reduced transmission). We adapt a well-established SEIRS (susceptible-exposed-infected-recovered-susceptible) model to evaluate the cost and effectiveness of different coverage levels of screening. To find the optimal screening rate, we formulate the question as a parameter optimization problem of ordinary differential equations and then apply a line search method which exhibits fast convergence. The numerical results as well as sensitivity analysis are presented in the paper.