Unraveling the dynamics of trichomoniasis transmission: modeling reinfection and asymptomatic spread with optimal control strategies based on United States demographics

Abstract Trichomoniasis is one of the sexually transmitted infections caused by the parasite Trichomonas vaginalis . Although it can be prevented, its tendency to remain asymptomatic contributes significantly to its worldwide impact. This study builds a deterministic model aimed at reducing transmission by introducing three time-dependent control measures: promoting safe sex practices, strengthening treatment efforts, and providing counseling after recovery. The model divides the population into susceptible, asymptomatic infected, symptomatic infected, under treatment, and recovered individuals. The solution of the model possesses key qualitative properties, specifically nonnegativity and boundedness. The basic reproduction number ( R 0 ) is computed using the next-generation matrix method. Both local and global stability of the disease-free equilibrium point are analyzed. The sensitivity analysis pinpoints the most influential parameters affecting R 0 . The primary objective is to minimize both the number of infections and the costs associated with control measures. The optimal control problem is defined using the principles of control theory. With the aid of Hamiltonian function and through Pontryagin’s minimum principle, the necessary conditions of the optimality system are derived. Using the Runge-Kutta forward-backward sweep method, numerical simulations are calibrated based on demographic data from the United States. The obtained results indicate that implementing all three control measures simultaneously yields a significant reduction in both asymptomatic and symptomatic infections, underscoring the effectiveness of a comprehensive approach for controlling trichomoniasis.