Mathematical analysis of fractional Chlamydia pandemic model

In this study, we developed a Caputo-Fractional Chlamydia pandemic model to describe the disease's spread. We demonstrated the model's positivity and boundedness, ensuring biological relevance. The existence and uniqueness of the model's solution were established, and we investigated the stability of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha$$\end{document}-fractional order model. Our analysis proved that the disease-free equilibrium point is locally asymptotically stable. Additionally, we showed that the model has a single endemic equilibrium point, which is globally asymptotically stable when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0$$\end{document} exceeds 1. Using Latin Hypercube sampling and partial rank correlation coefficients (PRCCs), sensitivity analysis identified key parameters influencing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr {R}}_0$$\end{document}. Numerical simulations further illustrated the impact of parameter variations on disease dynamics.