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Deep learning algorithms have been successfully adopted to extract meaningful information from digital images, yet many of them have been untapped in the semantic image segmentation of histopathology images. In this paper, we propose a deep convolutional neural network model that strengthens Atrous separable convolutions with a high rate within spatial pyramid pooling for histopathology image segmentation. A well-known model called DeepLabV3Plus was used for the encoder and decoder process. ResNet50 was adopted for the encoder block of the model which provides us the advantage of attenuating the problem of the increased depth of the network by using skip connections. Three Atrous separable convolutions with higher rates were added to the existing Atrous separable convolutions. We conducted a performance evaluation on three tissue types: tumor, tumor-infiltrating lymphocytes, and stroma for comparing the proposed model with the eight state-of-the-art deep learning models: DeepLabV3, DeepLabV3Plus, LinkNet, MANet, PAN, PSPnet, UNet, and UNet++. The performance results show that the proposed model outperforms the eight models on mIOU (0.8058/0.7792) and FSCR (0.8525/0.8328) for both tumor and tumor-infiltrating lymphocytes.