In this study, we present a novel intelligent computing framework based on unsupervised random projection neural networks for analyzing the within-host transmission dynamics of the Chikungunya virus with an adaptive immune response. In addition to the fundamental analysis of the model, we perform comprehensive simulations under varying initial conditions to explore the dynamics in both the virus-free and endemic states. The proposed method is compared with existing numerical techniques in terms of absolute errors for different cases, considering different suitable initial values of the state variables. Numerical simulations demonstrated the effectiveness of the stochastic neural network, achieving minimal residual errors in the least amount of time compared to conventional methods, thereby validating the accuracy and robustness of the proposed approach. Moreover, these results demonstrate that a random projection neural networks approach is adept at managing complex dynamics, enhancing our comprehension of disease behavior. Furthermore, this study emphasizes the adaptability and reliability of machine learning techniques in analyzing and predicting epidemiological dynamics, as well as in transmission modeling.