<p>In disease epidemiology, mathematical models are crucial for studying disease dynamics and developing, evaluating, and recommending the most effective disease control measures. In this study, we considered the fractional-order cattle skin disease model. Cattle skin diseases significantly challenge livestock health, productivity, and welfare. These conditions can range from minor irritations to severe, systemic infections that impact an entire herd. Addressing these diseases requires a comprehensive understanding of their causes, progression, and impacts. One effective approach to managing and mitigating cattle skin diseases is developing and applying disease models. The cattle skin disease model is a nonlinear coupled system of ordinary differential equations (SODEs). The Gegenbauer wavelet collocation method (GWCM) is used to solve the model. Using the Gegenbauer wavelets, we created the operational matrices of integration. Nonlinear SODEs are transformed into a system of algebraic equations using the characteristics of the Gegenbauer wavelet expansions and the operational matrix of integration, which speeds up processing. This system of algebraic equations is solved by the Newton-iterative technique to find the unknown coefficients and to obtain the approximate solution for this equation. We present numerical examples to show the efficacy and precision of the approach. The numerical results imply that the projected approach is reasonably close to the exact solution compared with the existing solutions available in the literature. These results show that the projected scheme is simple, reliable, and resilient.</p>