Mathematical Modelling for the Role of CD4+T Cells in Tumor-Immune InteractionsRead the full article
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Mathematical Analysis of the Effects of Controls on the Transmission Dynamics of Anthrax in Both Animal and Human Populations
A nonlinear differential equation model is proposed to study the impact of vaccination on the transmission dynamics of anthrax in both livestock and human populations. The model is shown to exhibit only two equilibria, namely, the disease-free and the endemic equilibrium points, which are proven to be locally stable if the basic reproduction number () is less than unity and greater than unity, respectively. Local sensitivity analysis shows that the infection rate, pathogen-shedding rate, and rate of vaccination of livestock are parameters with the most positive impact on disease spread, whereas the rate of disinfection followed by the rate of vaccination are the parameters with the most negative impact on disease spread. Numerical simulation shows that implementing all control measures (i.e., vaccination, education, disinfection, and treatment) is a most effective strategy to curb disease spread.
3D Simulation Analysis of Central Shunt in Patient-Specific Hemodynamics: Effects of Varying Degree of Pulmonary Artery Stenosis and Shunt Diameters
The objective of this study was to compare the effects of different shunt diameters and pulmonary artery (PA) stenosis grades on the hemodynamics of central shunts to determine an optimal surgical plan and improve the long-term outcomes of the operation. A 3D anatomical model was reconstructed based on the patient’s clinical CT data. 3D computational fluid dynamics models were built with varying degrees of stenosis (the stenosis ratio α was represented by the ratio of blood flow through the main pulmonary artery to cardiac output, ranging from 0 to 30%; the smaller the value of α, the more severe the pulmonary artery stenosis) and varying shunt diameters (3, 3.5, 4, 4.5, and 5 mm). Our results show that the asymmetry of pulmonary artery flow increased with increasing shunt diameter and α, which will be more conducive to the development of the left pulmonary artery. Additionally, the pulmonary-to-systemic flow ratio (QP/QS) increases with the shunt diameter and α, and all the values exceed 1. When the shunt diameter is 3 mm and α = 0%, QP/QS reaches the minimum value of 1.01, and the oxygen delivery reaches the maximum value of 205.19 ml/min. However, increasing shunt diameter and α is beneficial to reduced power loss and smoother PA flow. In short, for patients with severe PA stenosis (α is small), a larger-diameter shunt may be preferred. Conversely, when the degree of PA stenosis is moderate, a smaller shunt diameter can be considered.
Logarithmic Fuzzy Entropy Function for Similarity Measurement in Multimodal Medical Images Registration
Multimodal medical images are useful for observing tissue structure clearly in clinical practice. To integrate multimodal information, multimodal registration is significant. The entropy-based registration applies a structure descriptor set to replace the original multimodal image and compute similarity to express the correlation of images. The accuracy and converging rate of the registration depend on this set. We propose a new method, logarithmic fuzzy entropy function, to compute the descriptor set. It is obvious that the proposed method can increase the upper bound value from log(r) to log(r) + ∆(r) so that a more representative structural descriptor set is formed. The experiment results show that our method has faster converging rate and wider quantified range in multimodal medical images registration.
Multiple Linear Regression Model of Meningococcal Disease in Ukraine: 1992–2015
Estimating the rates of invasive meningococcal disease (IMD) from epidemiologic data remains critical for making public health decisions. In Ukraine, such estimations have not been performed. We used epidemiological data to develop a national database. These data were used to estimate the population susceptible to IMD and identify the prevalence of asymptomatic carriers of N. meningitidis using simple epidemiological models of meningococcal disease that may be used by the national policy makers. The goal was to create simple, easily understood analysis of patterns of the infection within Ukraine that would capture the major features of the infection dynamics. Studies used nationally reported data during 1992–2015. A logic model identified the prevalence of carriage and the proportion of the population susceptible to IMD as key drivers of IMD incidence. Multiple linear regression models for all ages (total population) and for children ≤14 years old were fit to national-level data. Linear models with the incidence of IMD as an outcome were highly associated with carriage and estimated susceptible population in both total population and children (R2 = 0.994 and R2 = 0.978, respectively). The susceptibility rate to IMD in the study total population averaged 0.0034 ± 0.0009% annually. At the national level, IMD can be characterized by the simple interaction between the prevalence of asymptomatic carriage and the proportion of the susceptible population. IMD association with prevalence rates of carriage and the proportion of susceptible population is sufficiently strong for national-level planning of intervention strategies for IMD.
Bayesian and Frequentist Analytical Approaches Using Log-Normal and Gamma Frailty Parametric Models for Breast Cancer Mortality
One of the major causes of death among females in Saudi Arabia is breast cancer. Newly diagnosed cases of breast cancer among the female population in Saudi Arabia is 19.5%. With this high incidence, it is crucial that we explore the determinants associated with breast cancer among the Saudi Arabia populace—the focus of this current study. The total sample size for this study is 8312 (8172 females and about 140 representing 1.68% males) patients that were diagnosed with advanced breast cancer. These are facility-based cross-sectional data collected over a 9-year period (2004 to 2013) from a routine health information system database. The data were obtained from the Saudi Cancer Registry (SCR). Both descriptive and inferential (Cox with log-normal and gamma frailties) statistics were conducted. The deviance information criterion (DIC), Watanabe–Akaike information criterion (WAIC), Bayesian information criterion (BIC), and Akaike information criterion were used to evaluate or discriminate between models. For all the six models fitted, the models which combined the fixed and random effects performed better than those with only the fixed effects. This is so because those models had smaller AIC and BIC values. The analyses were done using R and the INLA statistical software. There are evident disparities by regions with Riyadh, Makkah, and Eastern Province having the highest number of cancer patients at 28%, 26%, and 20% respectively. Grade II (46%) and Grade III (45%) are the most common cancer grades. Left paired site laterality (51%) and regional extent (52%) were also most common characteristics. Overall marital status, grade, and cancer extent increased the risk of a cancer patient dying. Those that were married had a hazard ratio of 1.36 (95% CI: 1.03–1.80) while widowed had a hazard ratio of 1.57 (95% CI: 1.14–2.18). Both the married and widowed were at higher risk of dying with cancer relative to respondents who had divorced. For grade, the risk was higher for all the levels, that is, Grade I (Well diff) (HR = 7.11, 95% CI: 3.32–15.23), Grade II (Mod diff) (HR = 7.89, 95% CI: 3.88–16.06), Grade III (Poor diff) (HR = 5.90, 95% CI (2.91–11.96), and Grade IV (Undiff) (HR = 5.44, 95% (2.48–11.9), relative to B-cell. These findings provide empirical evidence that information about individual patients and their region of residence is an important contributor in understanding the inequalities in cancer mortalities and that the application of robust statistical methodologies is also needed to better understand these issues well.
Group Guided Fused Laplacian Sparse Group Lasso for Modeling Alzheimer’s Disease Progression
As the largest cause of dementia, Alzheimer’s disease (AD) has brought serious burdens to patients and their families, mostly in the financial, psychological, and emotional aspects. In order to assess the progression of AD and develop new treatment methods for the disease, it is essential to infer the trajectories of patients’ cognitive performance over time to identify biomarkers that connect the patterns of brain atrophy and AD progression. In this article, a structured regularized regression approach termed group guided fused Laplacian sparse group Lasso (GFL-SGL) is proposed to infer disease progression by considering multiple prediction of the same cognitive scores at different time points (longitudinal analysis). The proposed GFL-SGL simultaneously exploits the interrelated structures within the MRI features and among the tasks with sparse group Lasso (SGL) norm and presents a novel group guided fused Laplacian (GFL) regularization. This combination effectively incorporates both the relatedness among multiple longitudinal time points with a general weighted (undirected) dependency graphs and useful inherent group structure in features. Furthermore, an alternating direction method of multipliers- (ADMM-) based algorithm is also derived to optimize the nonsmooth objective function of the proposed approach. Experiments on the dataset from Alzheimer’s Disease Neuroimaging Initiative (ADNI) show that the proposed GFL-SGL outperformed some other state-of-the-art algorithms and effectively fused the multimodality data. The compact sets of cognition-relevant imaging biomarkers identified by our approach are consistent with the results of clinical studies.