<p>Cough is a normal indication of various respiratory infections, in which type as well as the sound of the cough the significant characteristics while diagnosing cough-based diseases, like Pneumonia. Existing methods in automatic cough sound detection utilize several signal transformations, often resulting in a loss of signal characteristics, impacting the detection performance. Hence, this research emphasizes developing a model for effective cough sound detection with the modified two-tier training based Search Hunt optimized Deep CNN (SHO-DCNN), where the training algorithm named search-hunt optimization (SHO) is established to tune the hyperparameters of the proposed model to improve the detection accuracy. Specifically, the proposed model extracts the Mel-Frequency Cepstral Coefficients (MFCCs) features and other spectral features in order to differentiate pneumonia from other acute respiratory diseases. A two-tier training module enabled DCNN to improve the prediction accuracy and speed up the training time, as well as minimize the overfitting problems. The proposed method addresses the challenges that commonly occur in cough-related disease detection methods, such as inaccurate classification, failure to distinguish coughs, and high misclassification rates. The proposed model aims to overcome these challenges, promising more reliable results. Extensive experiments demonstrate that the accuracy of this proposed cough sounds analysis is achieved as 93.23% using the COVID-19 cough sounds datasets, regarding the training percentage, and 92.09% by the Respiratory Sound dataset, regarding the training percentage.</p>