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Histopathological whole slide images (WSIs) are the gold standard for cancer diagnosis. In prognosis, WSIs can also help predict the overall survival (OS) time of cancer (such as glioblastoma (GBM) patients). However, current region of interest (ROI)-based supervised learning methods for GBM patients are unsatisfactory in accuracy and efficiency. To mitigate the issues, we propose a novel deep synergetic spiking neural (DSSN) P system to perform ROI-free prediction of OS time in GBM patients. Specifically, a dual-task attention network is designed by different synergistic firing mechanisms on new types of neurons to predict OS time and classify genotype simultaneously. The network can not only capture useful cell features but also enrich and share features between the two tasks to improve performance. Four triggering rules are also proposed to cluster pathological images into different phenotypes related to survival to implement ROI-free prediction. Since P systems are highly parallel, multiple preprocessing and ensemble learning of dual-task attention networks with different initial configurations are conducted to further improve OS time prediction accuracy and reduce time complexity. Experimental results show that the DSSN P system outperforms ten other state-of-the-art models, demonstrating the ability of the DSSN P system to predict OS time in GBM patients. • A novel deep synergetic spiking neural (DSSN) P system is proposed. • DSSN P system with dual-task attention network predicts OS time and genotype. • Four classes of synergistic neurons self-assemble into different function blocks. • Four triggering rules are provided to implement ROI-free prediction. • High parallelism of DSSN P system improves accuracy and saves time of computation. [ABSTRACT FROM AUTHOR]