Abdilundsgaard0262

In this paper, we modify the HBV model proposed in [1] to include the spatial variations of free antibody, virus-antibody complexes, and free virus. By using comparison arguments and theory of uniform persistence, we can show that the persistene/extinction of HBV can be determined by the reproduction number(s).Markovian model is widely used to study cardiac electrophysiology and drug screening. Due to the stiffness of Markov model for single-cell simulation, it is prone to induce instability by using large time-steps. Hybrid operator splitting (HOS) and uniformization (UNI) methods were devised to solve Markovian models with fixed time-step. Recently, it is shown that these two methods combined with Chen-Chen-Luo's quadratic adaptive algorithm (CCL) can save markedly computation cost with adaptive time-step. https://www.selleckchem.com/peptide/box5.html However, CCL determines the time-step size solely based on the membrane potential. The voltage changes slowly to increase the step size rapidly, while the values of state variables of Markov sodium channel model still change dramatically. As a result, the system is not stable and the errors of membrane potential and sodium current exceed 5%. To resolve this problem, we propose a multi-variable CCL method (MCCL) in which state occupancies of Markov model are included with membrane potential as the control quadratic parameters to determine the time-step adaptively. Using fixed time-step RK4 as a reference, MCCL combined with HOS solver has 17.2 times speedup performance with allowable errors 0.6% for Wild-Type Na+ channel with 9 states (WT-9) model, and it got 21.1 times speedup performance with allowable errors 3.2% for WildType Na+ channel with 8 states (WT-8) model. It is concluded that MCCL can improve the simulation instability problem induced by a large time-step made with CCL especially for high stiff Markov model under allowable speed tradeoff.Kidney tubules are lined with flow-sensing structures, yet information about the flow itself is not easily obtained. We aim to generate a multiscale biomechanical model for analyzing fluid flow and fluid-structure interactions within an elastic kidney tubule when the driving pressure is pulsatile. We developed a two-dimensional macroscopic mathematical model of a single fluid-filled tubule corresponding to a distal nephron segment and determined both flow dynamics and wall strains over a range of driving frequencies and wall compliances using finite-element analysis. The results presented here demonstrate good agreement with available analytical solutions and form a foundation for future inclusion of elastohydrodynamic coupling by neighboring tubules. Overall, we are interested in exploring the idea of dynamic pathology to better understand the progression of chronic kidney diseases such as Polycystic Kidney Disease.Prostate cancer (PCa) is one of the most common cancer in males. Previous studies indicated that MIR22HG was a tumor suppressor in various cancers. However, the expression pattern and functional roles of MIR22HG in PCa remained to be further investigated. In this study, we for the first time showed MIR22HG was down-regulated in PCa. Furthermore, we observed the lower expression levels of MIR22HG were significantly related to higher Gleason score and T stage. Of note, we found that higher MIR22HG expression was associated with better disease-free survival and overall survival time in PCa. Moreover, we constructed a MIR22HG mediated co-expression network. Bioinformatics analysis showed MIR22HG was associated with regulating inflammatory response, regulation of transcription, cellular response to tumor necrosis factor, neutrophil chemotaxis, cell-cell signaling, and TNF signaling pathway. These results showed that MIR22HG could serve as a novel biomarker for prostate cancer.The incubation period for Hepatitis B virus (HBV) within the human is epidemiologically significant because it is typically of long duration (1.5∼6 months) and the disease transmission possibility may be increased due to more contact from the patients in this period. In this paper, we investigate an SEICRV epidemic model with time delay to research the transmission dynamics of Hepatitis B disease. The basic reproductive number $\mathcal R_0$ is derived and can determine the dynamics of the model. The disease-free equilibrium is globally asymptotically stable if $\mathcal R_01$, the model admits a unique endemic equilibrium which is locally asymptotically stable. The endemic equilibrium is globally asymptotically stable when the vertical transmission is ignored. Numerically, we study the Hepatitis B transmission case in Xinjiang, China. Using the Hepatitis B data from Xinjiang, the basic reproductive number is estimated as 1.47 (95% CI 1.34-1.50). By the end of 2028, the cumulative number of Hepatitis B cases in Xinjiang will be estimated about 700,000 if there is no more effective preventive measures. The sensitivity analysis of $\mathcal R_0$ in terms of parameters indicates prevention and treatment for chronic patients are key measures in controlling the spread of Hepatitis B in Xinjiang.We consider a population dynamics model in investigating data from controlled experiments with aphids in broccoli patches surrounded by different margin types (bare or weedy ground) and three levels of insecticide spray (no, light, or heavy spray). The experimental data is clearly aggregate in nature. In previous efforts [1], the aggregate nature of the data was ignored. In this paper, we embrace this aspect of the experiment and correctly model the data as aggregate data, comparing the results to the previous approach. We discuss cases in which the approach may provide similar results as well as cases in which there is a clear difference in the resulting fit to the data.The relationship between conspecific density and the probability of emigrating from a patch can play an essential role in determining the population-dynamic consequences of an Allee effect. In this paper, we model a population that inside a patch is diffusing and growing according to a weak Allee effect per-capita growth rate, but the emigration probability is dependent on conspecific density. The habitat patch is one-dimensional and is surrounded by a tuneable hostile matrix. We consider five different forms of density dependent emigration (DDE) that have been noted in previous empirical studies. Our models predict that at the patch-level, DDE forms that have a positive slope will counteract Allee effects, whereas, DDE forms with a negative slope will enhance them. Also, DDE can have profound effects on the dynamics of a population, including producing very complicated population dynamics with multiple steady states whose density profile can be either symmetric or asymmetric about the center of the patch. Our results are obtained mathematically through the method of subsuper solutions, time map analysis, and numerical computations using Wolfram Mathematica.