Rapid and accurate identification of COVID-19 and also other associated diseases is now crucial to limiting the disease's transmission, relaxing lockdown laws, and reducing the burden on public health infrastructures. Recently, several approaches and techniques have been proposed to identify the SARS-CoV-2 virus (COVID-19) using different clinical data and medical pictures. There are some limitations and shortcomings with the COVID-19 detection technologies that are currently available on the market. Because of this, it becomes essential to develop and study new diagnostic tools that have higher diagnostic accuracy while avoiding the shortcomings of existing tools. This study used the SARS-CoV-2 CT scan dataset to test non-linear SVM and Twin-SVM (TWSVM) classifiers in addition to textural characteristics such as GLCM, GLRLM, and ILMFD separately. There are a total of 2482 CT scan images in this database; 1252 of the scans show positive signs of SARS-CoV-2 infection (COVID-19), and 1230 show negative signs. Eight different models were developed in this work for the purpose of classifying and predicting COVID-19. We found that the GLCM + NLSVM model using RBF kernal, GLCM + TWSVM using linear kernal, GLRLM + NLSVM using RBF kernal, GLRLM + TWSVM using sigmoid, ILMFD + NLSVM using RBF kernal, ILMFD + TWSVM using polynomial kernal, Hybrid feature + NLSVM, and Hybrid feature + TWSVM all performed better in terms of evaluation done by performance metrics used in this work. For the given dataset, the Hybrid feature + NLSVM model with Linear Kernal yielded significantly better results out of eight models tested, including 100% accuracy, 100% recall, 100% precision, 100% F1-score, R-Squared = 1, and RMSE = 0. As a result, the high accuracy of this type of computer-aided screening method would significantly boost the speed and accuracy of COVID-19 diagnosis also encourage the study of other associated diseases with CT-scan images.