Numerical Solution of Fractional order Chlamydia Model Via the Generalized Fractional Adams-Bashforth-Moulton Approach

In this study we examine the epidemiological features of chlamydia infection using a fractional-order mathematical model, evaluating the impact of vaccine and therapy on the dynamics of disease transmission. In the fractional-order framework, the study determines the existence and uniqueness of solutions and uses the Lyapunov function approach to examine the stability of the endemic equilibrium. Numerical simulations that employ the fractional Adams–Bashforth–Moulton approach show how fractional-order values and model parameters impact the control and spread of the disease. More simulations, such as surface and contour plots, show that a higher prevalence of chlamydia is a result of increased contact rates and decreased treatment effectiveness. The results highlight how the infection's spread within the community can be successfully stopped by improving vaccine and treatment plans.