Analysis of a Fractional-Order Mathematical Model of Gonorrhea Transmission with Control Measures

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Abstract Gonorrhea is a sexually transmitted infection caused by the bacterium Neisseria gonorrhoeae. It spreads primarily through sexual contact and can affect the genital tract, rectum, and throat. If left untreated, it may lead to serious health complications, including infertility and increased susceptibility to other infections. This study investigated the transmission dynamics of gonorrhea using a fractional-order mathematical model to evaluate the effects of treatment, vaccination, and contact rates on disease spread. The model established the existence and uniqueness of solutions within the fractional-order framework, confirming that it is well-posed. Stability analysis is conducted to better understand disease behavior, including the computation of the basic reproduction number. The results revealed that increasing treatment rates among infected individuals plays a crucial role in reducing the reproduction number below one, which is necessary for disease control. In contrast, higher contact rates contribute to increased transmission and help sustain the presence of the disease within the population. Simulation results further show that transmission-related parameters promote disease spread, while treatment-related parameters reduce infection levels, thereby lowering the overall disease burden. The dynamics of different population compartments under varying treatment and contact rates are examined using the fractional Adams–Bashforth–Moulton numerical scheme. The findings emphasized that effective treatment of infected individuals is essential for reducing the burden of gonorrhea. The study concludes that combining expanded treatment strategies with reduced transmission pathways is vital for controlling and potentially eradicating the disease in the population. Keywords: Gonorrhea, fractional-order model, Basic reproduction number, Stability analysis, Numerical simulation.

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