Especially, the method may also be used in countries with the first confirmed case is imported.Intra-tumor and inter-patient heterogeneity are two challenges in developing mathematical models for precision medicine diagnostics. Here we review several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data. These techniques include virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning. We create simulated virtual populations in this study and then apply the four remaining methods to these datasets to highlight the strengths and weak-nesses of each technique. We provide all code used in this review at https//github.com/jtnardin/Tumor-Heterogeneity/ so that this study may serve as a tutorial for the mathematical modelling community. This review article was a product of a Tumor Heterogeneity Working Group as part of the 2018-2019 Program on Statistical, Mathematical, and Computational Methods for Precision Medicine which took place at the Statistical and Applied Mathematical Sciences Institute.Energies and spectrum of graphs associated to different linear operators play a significant role in molecular chemistry, polymerisation, pharmacy, computer networking and communication systems. In current article, we compute closed forms of signless Laplacian and Laplacian spectra and energies of multi-step wheel networks W n,m . These wheel networks are useful in networking and communication, as every node is one hoop neighbour to other. We also present our results for wheel graphs as particular cases. In the end, correlation of these energies on the involved parameters m ≥ 3 and n is given graphically. Present results are the natural generalizations of the already available results in the literature.Based on the reported data from February 16, 2020 to March 9, 2020 in South Korea including confirmed cases, death cases and recovery cases, the control reproduction number was estimated respectively at different control measure phases using Markov chain Monte Carlo method and presented using the resulting posterior mean and 95% credible interval (CrI). At the early phase from February 16 to February 24, we estimate the basic reproduction number R0 of COVID-19 to be 4.79(95% CrI 4.38 - 5.2). The estimated control reproduction number dropped rapidly to R c ≈ 0.32(95% CrI 0.19 - 0.47) at the second phase from February 25 to March 2 because of the voluntary lockdown measures. At the third phase from March 3 to March 9, we estimate R c to be 0.27 (95% CrI 0.14 - 0.42). We predict that the final size of the COVID-19 outbreak in South Korea is 9661 (95% CrI 8660 - 11100) and the whole epidemic will be over by late April. It is found that reducing contact rate and enhancing the testing speed will have the impact on the peak value and the peak time.A new COVID-19 epidemic model with media coverage and quarantine is constructed. The model allows for the susceptibles to the unconscious and conscious susceptible compartment. First, mathematical analyses establish that the global dynamics of the spread of the COVID-19 infectious disease are completely determined by the basic reproduction number R0. If R0 ≤ 1, then the disease free equilibrium is globally asymptotically stable. If R0 > 1, the endemic equilibrium is globally asymptotically stable. Second, the unknown parameters of model are estimated by the MCMC algorithm on the basis of the total confirmed new cases from February 1, 2020 to March 23, 2020 in the UK. We also estimate that the basic reproduction number is R0 = 4.2816(95%CI (3.8882, 4.6750)). Without the most restrictive measures, we forecast that the COVID-19 epidemic will peak on June 2 (95%CI (May 23, June 13)) (Figure 3a) and the number of infected individuals is more than 70% of UK population. In order to determine the key parameters of the model, sensitivity analysis are also explored. Finally, our results show reducing contact is effective against the spread of the disease. We suggest that the stringent containment strategies should be adopted in the UK.Vaccination strategy is considered as the most cost-effective intervention measure for controlling diseases.  https://www.selleckchem.com/products/baxdrostat.html  It will strengthen the immunity and reduce the risks of infections. In this paper, a new delayed epidemic model with interim-immune and mixed vaccination strategy is studied. The diseasefree periodic solution is obtained by twice stroboscopic mapping and the corresponding dynamical behavior is analyzed. We determine a threshold parameter R1, the disease-free periodic solution is proved to be global attractive if R1 1, the infectious disease will exist persistently. Then, we provide numerical simulations to illustrate our theoretical results intuitively. In particular, a practical application for newtype TB vaccine under mixed vaccination strategy is presented, based on the proposed theory and the data reported by NBSC. The mixed vaccination strategy can achieve the End TB goal formulated by WHO in limited time. Our study will help public health agency to design mixed control strategy which can reduce the burden of infectious diseases.Most current automatic summarization methods are for English texts. The distinction between words in Chinese text is large, the types of parts of speech are many and complex, and polysemy or ambiguous words appear frequently. Therefore, compared with English text, Chinese text is more difficult to extract useful feature words. Due to the complex syntax of Chinese, there are currently relatively few automatic summarization methods for Chinese text. In the past, only the important sentences in the original text can be selected and simply arranged to obtain a summary with chaotic sentences and insufficient coherence. Meanwhile, because Chinese short text usually contains more redundant information and the sentence structure is not neat, we propose a topic-based automatic summary method for Chinese short text. Firstly, a key sentence selection method is proposed combining topic words and TF-IDF to obtain the score of each text corresponding to the topic in the original text data. Then the sentence with the highest score as the topic sentence of the topic is selected.