Dynamics and numerical analysis of a fractional-order toxoplasmosis model incorporating human and cat populations

Toxoplasmosis is a significant zoonotic disease that poses risks to public health and animal health, making the understanding of its transmission dynamics crucial. In this study, we present a novel fractional-order model that captures complex interactions among human, cat, and mouse populations, providing deeper insights into the disease spread and control. We utilize mathematical techniques to analyze the model properties, including the existence, uniqueness, positivity, and boundedness of solutions, along with stability analysis of the equilibrium states. The basic reproduction number R0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$R_{0}$\end{document} is derived, revealing the threshold for potential outbreaks. Our findings indicate that key parameters significantly influence the dynamics of toxoplasmosis, with implications for targeted intervention strategies. We propose the QLM-FONP numerical scheme for efficient resolution of the model and provide a comprehensive convergence analysis, demonstrating the reliability of the numerical solutions. The results confirm the effectiveness of our approach, illustrating that the proposed model not only offers accurate predictions but also extends beyond previous efforts in the literature by incorporating fractional-order dynamics, which better reflect real-world transmission processes. Overall, this study enhances the understanding of toxoplasmosis transmission and informs future research and control efforts.