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During the COVID-19 pandemic, control measures, especially massive contact tracing following prompt quarantine and isolation, play an important role in mitigating the disease spread, and quantifying the dynamic contact rate and quarantine rate and estimate their impacts remain challenging. To precisely quantify the intensity of interventions, we develop the mechanism of physics-informed neural network (PINN) to propose the extended transmission-dynamics-informed neural network (TDINN) algorithm by combining scattered observational data with deep learning and epidemic models. The TDINN algorithm can not only avoid assuming the specific rate functions in advance but also make neural networks follow the rules of epidemic systems in the process of learning. We show that the proposed algorithm can fit the multi-source epidemic data in Xi'an, Guangzhou and Yangzhou cities well, and moreover reconstruct the epidemic development trend in Hainan and Xinjiang with incomplete reported data. We inferred the temporal evolution patterns of contact/quarantine rates, selected the best combination from the family of functions to accurately simulate the contact/quarantine time series learned by TDINN algorithm, and consequently reconstructed the epidemic process. The selected rate functions based on the time series inferred by deep learning have epidemiologically reasonable meanings. In addition, the proposed TDINN algorithm has also been verified by COVID-19 epidemic data with multiple waves in Liaoning province and shows good performance. We find the significant fluctuations in estimated contact/quarantine rates, and a feedback loop between the strengthening/relaxation of intervention strategies and the recurrence of the outbreaks. Moreover, the findings show that there is diversity in the shape of the temporal evolution curves of the inferred contact/quarantine rates in the considered regions, which indicates variation in the intensity of control strategies adopted in various regions. Author summary: When applying the compartment model to simulate the disease transmission dynamics, some parameters or particular functions are assumed to describe the intensity of the control interventions. However, these preset specific functions may not accurately quantify the intervention strategies, which brings great challenges to accurately make prediction and evaluation. In this study, we developed an extended transmission-dynamics-informed neural network algorithm by integrating deep neural network with epidemic model. Even for insufficient case data, the proposed algorithm can still help us reconstruct the temporal evolution trend of the epidemic and infer unknown parameters. We inferred the time series on contract rate and quarantine rate for six regions based on the case data, on which the reasonable and interpretable functions, describing the dynamic variation in the intensity of control strategies, can be successfully selected and determined. The inferred contact/quarantine rates in various regions show the diverse shapes and regional dependent, and hence the variation in the intensity of control measures. This suggests the dynamic zero-case policy exhibits the different efficacy in reducing contacts and increasing the quarantine and isolation. [ABSTRACT FROM AUTHOR]

Tumor heterogeneity is a large obstacle for cancer study and treatment. Different cancer patients may involve different combinations of gene mutations or the distinct regulatory pathways for inducing the progression of tumor. Investigating the pathways of gene mutations which can cause the formation of tumor can provide a basis for the personalized treatment of cancer. Studies suggested that KRAS, APC and TP53 are the most significant driver genes for colorectal cancer. However, it is still an open issue regarding the detailed mutation order of these genes in the development of colorectal cancer. For this purpose, we analyze the mathematical model considering all orders of mutations in oncogene, KRAS and tumor suppressor genes, APC and TP53, and fit it on data describing the incidence rates of colorectal cancer at different age from the Surveillance Epidemiology and End Results registry in the United States for the year 1973–2013. The specific orders that can induce the development of colorectal cancer are identified by the model fitting. The fitting results indicate that the mutation order with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53 explain the age–specific risk of colorectal cancer with very well. Furthermore, eleven pathways of gene mutations can be accepted for the mutation order of genes with KRAS → APC → TP53, APC → TP53 → KRAS and APC → KRAS → TP53, and the alternation of APC acts as the initiating or promoting event in the colorectal cancer. The estimated mutation rates of cells in the different pathways demonstrate that genetic instability must exist in colorectal cancer with alterations of genes, KRAS, APC and TP53. Author summary: Cumulative mutations in driver genes are the essential cause of cancer disease. For the colorectal cancer, KRAS, APC and TP53 are the common driver genes, and approximately 15% patients with colorectal cancer carry all mutations of the three genes. Exploring the pathway of mutations in these gene is extremely useful for the diagnosis and treatment of cancer. However, the mutation orders of these genes may vary in different patients due to the heterogeneity of tumor. Hence, we discuss all possible mutation orders in the genes, KRAS, APC and TP53 by using the model with five hits and find out the mutation pathways of genes that can effectively fit the incidence rate of colorectal cancer at different age in this article. In addition, we give the estimated values of mutation rates in each pathway that can explain the procession of colorectal cancer. The results obtained can offer guidelines to the treatment strategy of colorectal cancer. [ABSTRACT FROM AUTHOR]