This research is aimed to escalate Adaptive Neuro-Fuzzy Inference System (ANFIS) functioning in order to ensure the veracity of existing time-series modeling. The COVID-19 pandemic has been a global threat for the past three years. Therefore, advanced forecasting of confirmed infection cases is extremely essential to alleviate the crisis brought out by COVID-19. An adaptive neuro-fuzzy inference system-reptile search algorithm (ANFIS-RSA) is developed to effectively anticipate COVID-19 cases. The proposed model integrates a machine-learning model (ANFIS) with a nature-inspired Reptile Search Algorithm (RSA). The RSA technique is used to modulate the parameters in order to improve the ANFIS modeling. Since the performance of the ANFIS model is dependent on optimizing parameters, the statistics of infected cases in China and India were employed through data obtained from WHO reports. To ensure the accuracy of our estimations, corresponding error indicators such as RMSE, RMSRE, MAE, and MAPE were evaluated using the coefficient of determination (R2). The recommended approach employed on the China dataset was compared with other upgraded ANFIS methods to identify the best error metrics, resulting in anR2value of 0.9775. ANFIS-CEBAS and Flower Pollination Algorithm and Salp Swarm Algorithm (FPASSA-ANFIS) attained values of 0.9645 and 0.9763, respectively. Furthermore, the ANFIS-RSA technique was used on the India dataset to examine its efficiency and acquired the bestR2value (0.98). Consequently, the suggested technique was found to be more beneficial for high-precision forecasting of COVID-19 on time-series data.