Deshun Sun

In this paper, we propose a new fractional-order differential equation model with latent and vaccinated population to describe the dynamics of COVID-19. Firstly, the theoretical mathematical model is established based on the transmission mechanism of COVID-19 in the population. Then, the data of the infected, the recovered and the death are collected from big data report of Baidu’s epidemic situation, and the parameters are estimated by piecewise fitting and nonlinear least square method based on collected data. The correlation coefficients between the infected and model simulation, between the recovered and model simulation, between the death and model simulation are 0.9868, 0.9948 and 0.9994, respectively and the accuracy of prediction are 96.05%, 99.33% and 99.88%, respectively. Additionally, the accuracy of prediction is compared between fractional-order differential equation model and integer-order differential equation model, and the results show fractional-order differential equation model can better predict the development trend of COVID-19. Finally, we analyze the sensitivity of the parameters through numerical simulations, and put forward the corresponding strategies to control the epidemic development according to the screened sensitive parameters.

Introduction: Mathematical model can be used to model complex biological processes, and have shown potential in describing apoptosis in chondrocytes.Method: In order to investigate the regulatory mechanisms of TNF signaling pathway in regulating chondrocyte apoptosis, a fractional-order differential equation model is proposed to describe the dynamic behavior and mutual interaction of apoptosis-related genes under the activation of TNF signaling pathway. Compared with the traditional molecular biology techniques, the proposed mathematical modeling has advantages to providing a more comprehensive understanding of the regulatory mechanisms of TNF signaling pathway in chondrocyte apoptosis.Result: In this paper, differentially expressed genes induced by IL-1β in human chondrocyte apoptosis are screened using high-throughput sequencing. It is found that they were significantly enriched in the TNF signaling pathway. Therefore, a mathematical model of the TNF signaling pathway is built. Using real-time PCR experiments, mRNA data is measured and used to identify the model parameters, as well as the correlation coefficient. Finally, the sensitivity of the model parameters is discussed by using numerical simulation methods, which can be used to predict the effects of different interventions and explore the optimal intervention strategies for regulating chondrocyte apoptosis.Discussion: Therefore, fractional-order differential equation modeling plays an important role in understanding the regulatory mechanisms of TNF signaling pathway in chondrocyte apoptosis and its potential clinical applications.

In this paper, an online apparatus was developed for isothermal thermogravimetric measurement of silicide coatings within a wide temperature range (from −180 °C to 2300 °C) based on thermogravimetric analysis. Firstly, the measuring principle and method regarding silicide coatings of this apparatus were studied. Secondly, on the basis of oxidation kinetics analysis, the intrinsic mechanism and kinetic parameters of three stages (oxidation, diffusion, and fall-off) of silicide coatings were studied, and the oxidation kinetics features were also analyzed. In addition, according to mathematical physics methods, a kinetics model of silicide coatings in different stages of oxidation was established, including parameters such as weight change, oxidation rate, oxidation time, etc. Finally, online isothermal experiments from −180 °C to 2300 °C werecarried out and analyzed. The results showed that the kinetic model established in this paper was in good agreement with the oxidation process of silicide coatings. In this paper, a complete kinetics model including different oxidation stages is proposed for the entire oxidation process of a silicide coating, revealing its oxidation mechanism. The research will play a significant role in the study of preparation technology improvement and high-temperature environment application. This paper studied two measuring methods: weight gain and weight loss measuring methods. Also, an experiment was carried out on the silicide coatings to explore the physical oxidation process between −180 °C and 2300 °C. The results proved the perfect consistency of the kinetics model proposed by this paper and the oxidation process of silicide coatings. This paper will play a significant role in the study of preparation technology enhancement and high-temperature environment application. It also provides a theoretical foundation for accelerated aging and life evaluation methods.

In this article, a fractional-order differential equation model of HBV infection was proposed with a Caputo derivative, delayed immune response, and logistic proliferation. Initially, infection-free and infection equilibriums and the basic reproduction number were computed. Thereafter, the stability of the two equilibriums was analyzed based on the fractional Routh–Hurwitz stability criterion, and the results indicated that the stability will change if the time delay or fractional order changes. In addition, the sensitivity of the basic reproduction number was analyzed to find out the most sensitive parameter. Lastly, the theoretical analysis was verified by numerical simulations. The results showed that the time delay of immune response and fractional order can significantly affect the dynamic behavior in the HBV infection process. Therefore, it is necessary to consider time delay and fractional order in modeling HBV infection and studying its dynamics.

As of January 19, 2021, the cumulative number of people infected with coronavirus disease-2019 (COVID-19) in the United States has reached 24,433,486, and the number is still rising. The outbreak of the COVID-19 epidemic has not only affected the development of the global economy but also seriously threatened the lives and health of human beings around the world. According to the transmission characteristics of COVID-19 in the population, this study established a theoretical differential equation mathematical model, estimated model parameters through epidemiological data, obtained accurate mathematical models, and adopted global sensitivity analysis methods to screen sensitive parameters that significantly affect the development of the epidemic. Based on the established precise mathematical model, we calculate the basic reproductive number of the epidemic, evaluate the transmission capacity of the COVID-19 epidemic, and predict the development trend of the epidemic. By analyzing the sensitivity of parameters and finding sensitive parameters, we can provide effective control strategies for epidemic prevention and control. After appropriate modifications, the model can also be used for mathematical modeling of epidemics in other countries or other infectious diseases.

To develop and validate a mathematical model for predicting intracranial pressure (ICP) noninvasively using phase-contrast cine MRI (PC-MRI). We performed a retrospective analysis of PC-MRI from patients with communicating hydrocephalus (n = 138). The patients were recruited from Shenzhen Second People’s Hospital between November 2017 and April 2020, and randomly allocated into training (n = 97) and independent validation (n = 41) groups. All participants underwent lumbar puncture and PC-MRI in order to evaluate ICP and cerebrospinal fluid (CSF) parameters (i.e., aqueduct diameter and flow velocity), respectively. A novel ICP-predicting model was then developed based on the nonlinear relationships between the CSF parameters, using the Levenberg–Marquardt and general global optimisation methods. There was no significant difference in baseline demographic characteristics between the training and independent validation groups. The accuracy of the model for predicting ICP was 0.899 in the training cohort (n = 97) and 0.861 in the independent validation cohort (n = 41). We obtained an ICP-predicting model that showed excellent performance in the noninvasive diagnosis of clinically significant communicating hydrocephalus.

In this paper, an improved fractional-order model of boundary formation in the Drosophila large intestine dependent on Delta-Notch pathway is proposed for the first time. The uniqueness, nonnegativity, and boundedness of solutions are studied. In a two cells model, there are two equilibriums (no-expression of Delta and normal expression of Delta). Local asymptotic stability is proved for both cases. Stability analysis shows that the orders of the fractional-order differential equation model can significantly affect the equilibriums in the two cells model. Numerical simulations are presented to illustrate the conclusions. Next, the sensitivity of model parameters is calculated, and the calculation results show that different parameters have different sensitivities. The most and least sensitive parameters in the two cells model and the 60 cells model are verified by numerical simulations. What is more, we compare the fractional-order model with the integer-order model by simulations, and the results show that the orders can significantly affect the dynamic and the phenotypes.

We propose a comprehensive delayed HBV model, which not only considers the immune response to both infected cells and viruses and a time delay for the immune system to clear viruses but also incorporates an exposed state and the proliferation of hepatocytes. We prove the positivity and boundedness of solutions and analyze the global stability of two boundary equilibria and then study the local asymptotic stability and Hopf bifurcation of the positive (infection) equilibrium and also the stability of the bifurcating periodic solutions. Moreover, we illustrate how the factors such as the time delay, the immune response to infected cells and viruses, and the proliferation of hepatocytes affect the dynamics of the model by numerical simulation.

The boundary formation in the Drosophila large intestine is widely studied as an important biological problem. It has been shown that the Delta-Notch signaling pathway plays an essential role in the formation of boundary cells. In this paper, we propose a mathematical model for the Delta-Notch dependent boundary formation in the Drosophila large intestine in order to better interpret related experimental findings of this biological phenomenon. To achieve this, we not only perform stability analysis on the model from a theoretical point of view, but also perform numerical simulations to analyze the model with and without noises, the phenotype change with the change of Delta or Notch expression, and the perturbation influences of binding and inhibition parameters on the boundary formation. By doing all these work, we can assure that our model can better interpret the biological findings related to the boundary formation in the Drosophila large intestine.