<p>Nowadays, controlling the epidemic of infectious diseases is a major concern in the entire world. Since inaccurate testing can turn a susceptible person into an infected person, doing tests correctly is one of the most important steps in stopping the spread of infectious diseases. In this study, a three-dimensional childhood disease model is presented using the Caputo operators to investigate the effectiveness and efficiency of the obtained solution. Our analysis focuses on determining the existence and uniqueness of solutions under certain conditions, demonstrating that the model offers unique solutions based on these criteria. Further, we investigate the fixed points and show the stability of the proposed model. We also explain the Lyapunov stability of the fractional order system of this model. Additionally, we use the Lyapunov exponent to examine the chaotic behavior of the system. Using derivative orders and varying parameters, we analyze the solutions of the fractional order childhood disease model using bifurcation diagrams, time series diagrams, and phase diagrams. The Toufik-Atangana numerical scheme is used for numerical simulation. Furthermore, the findings demonstrate how several non-integer operator substitutes for this model provide a variety of dynamic behaviors. These findings highlight the impact of fractional calculus in enhancing the understanding of epidemic models and offer new insights into the dynamical properties of childhood disease spread.</p>