Traveling wave speed and profile of a "go or grow" glioblastoma multiforme model.

Glioblastoma multiforme (GBM) is a fast-growing and deadly brain tumor due to its ability to aggressively invade the nearby brain tissue. A host of mathematical models in the form of reaction-diffusion equations have been formulated and studied in order to assist clinical assessment of GBM growth and its treatment prediction. To better understand the speed of GBM growth and form, we propose a two population reaction-diffusion GBM model based on the 'go or grow' hypothesis. Our model is validated by in vitro data and assumes that tumor cells are more likely to leave and search for better locations when resources are more limited at their current positions. Our findings indicate that the tumor progresses slower than the simpler Fisher model, which is known to overestimate GBM progression. Moreover, we obtain accurate estimations of the traveling wave solution profiles under several plausible GBM cell switching scenarios by applying the approximation method introduced by Canosa.

SARS-CoV-2 PCR-positive and PCR-negative cases of pneumonia admitted to the hospital during the peak of COVID-19 pandemic: analysis of in-hospital and post-hospital mortality.

BACKGROUND: During the spike of COVID-19 pandemic in Kazakhstan (June-2020), multiple SARS-CoV-2 PCR-test negative pneumonia cases with higher mortality were reported by media. We aimed to study the epidemiologic characteristics of hospitalized PCR-test positive and negative patients with analysis of in-hospital and post-hospital mortality. We also compare the respiratory disease characteristics between 2019 and 2020. METHODS: The study population consist of 17,691 (March-July-2020) and 4600 (March-July-2019) hospitalized patients with respiratory diseases (including COVID-19). The incidence rate, case-fatality rate and survival analysis for overall mortality (in-hospital and post-hospital) were assessed. RESULTS: The incidence and mortality rates for respiratory diseases were 4-fold and 11-fold higher in 2020 compared to 2019 (877.5 vs 228.2 and 11.2 vs 1.2 per 100,000 respectively). The PCR-positive cases (compared to PCR-negative) had 2-fold higher risk of overall mortality. We observed 24% higher risk of death in males compared to females and in older patients compared to younger ones. Patients residing in rural areas had 66% higher risk of death compared to city residents and being treated in a provisional hospital was associated with 1.9-fold increased mortality compared to those who were treated in infectious disease hospitals. CONCLUSION: This is the first study from the Central Asia and Eurasia regions, evaluating the mortality of SARS-CoV-2 PCR-positive and PCR-negative respiratory system diseases during the peak of COVID-19 pandemic. We describe a higher mortality rate for PCR-test positive cases compared to PCR-test negative cases, for males compared to females, for elder patients compared to younger ones and for patients living in rural areas compared to city residents.

Global finite-time stability of delayed quaternion-valued neural networks based on a class of extended Lyapunov-Razumikhin methods.

In this paper, a class of global finite-time stability problem for quaternion-valued neural networks with time-varying delays are investigated by adopting an extended modification Lyapunov-Razumikhin (L-R) method and a new upper bounds estimation of system solution in terms of convergence rate was obtained. Firstly, a new extended method of L-R is proposed to solve the general difficulty to find a proper Lyapunov functional. Then, a new suitable controller is designed, the new conditions of inequalities global finite-time stability are obtained via combining with the former proposed L-R method in the separated real-valued system. Finally, for purpose of verifying the availability of the theorem presented, two given illustrative examples are shown.

Saturated and asymmetric saturated control for projective synchronization of inertial neural networks with delays and discontinuous activations through matrix measure method.

The projective synchronization work presented in this article is focused on a class of nonlinear discontinuous coupled inertial neural networks with mixed time-varying delays and a cluster topological structure. The synchronization problem for discontinuous coupled inertial neural networks with clustering topology is examined in consideration with the mismatched parameters and the mutual influence among various clusters. To determine the required conditions for network convergence under the influence of an extensive range of impulses, the matrix measure technique and the average impulsive intervals are employed. To illustrate the effectiveness of the theoretical findings, graphical representation of varied impulsive ranges for multiple cases are provided using numerical simulations.

Prevalence of HIV in Kazakhstan 2010-2020 and Its Forecasting for the Next 10 Years.

Background: HIV is a growing public health burden that threatens thousands of people in Kazakhstan. Countries around the world, including Kazakhstan, are facing significant problems in predicting HIV infection prevalence. It is crucial to understand the epidemiological trends of infectious diseases and to monitor the prevalence of HIV in a long-term perspective. Thus, in this study, we aimed to forecast the prevalence of HIV in Kazakhstan for 10 years from 2020 to 2030 by using mathematical modeling and time series analysis. Methods: We use statistical Autoregressive Integrated Moving Average (ARIMA) models and a nonlinear epidemic Susceptible-Infected (SI) model to forecast the HIV infection prevalence rate in Kazakhstan. We estimated the parameters of the models using open data on the prevalence of HIV infection among women and men (aged 15-49 years) in Kazakhstan provided by the Kazakhstan Bureau of National Statistics. We also predict the effect of pre-exposure prophylaxis (PrEP) control measures on the prevalence rate. Results: The ARIMA (1,2,0) model suggests that the prevalence of HIV infection in Kazakhstan will increase from 0.29 in 2021 to 0.47 by 2030. On the other hand, the SI model suggests that this parameter will increase to 0.60 by 2030 based on the same data. Both models were statistically significant by Akaike Information Criterion corrected (AICc) score and by the goodness of fit. HIV prevention under the PrEP strategy on the SI model showed a significant effect on the reduction of the HIV prevalence rate. Conclusion: This study revealed that ARIMA (1,2,0) predicts a linear increasing trend, while SI forecasts a nonlinear increase with a higher prevalence of HIV. Therefore, it is recommended for healthcare providers and policymakers use this model to calculate the cost required for the regional allocation of healthcare resources. Moreover, this model can be used for planning effective healthcare treatments.

Predicting 1-year mortality of patients with diabetes mellitus in Kazakhstan based on administrative health data using machine learning.

Diabetes mellitus (DM) affects the quality of life and leads to disability, high morbidity, and premature mortality. DM is a risk factor for cardiovascular, neurological, and renal diseases, and places a major burden on healthcare systems globally. Predicting the one-year mortality of patients with DM can considerably help clinicians tailor treatments to patients at risk. In this study, we aimed to show the feasibility of predicting the one-year mortality of DM patients based on administrative health data. We use clinical data for 472,950 patients that were admitted to hospitals across Kazakhstan between mid-2014 to December 2019 and were diagnosed with DM. The data was divided into four yearly-specific cohorts (2016-, 2017-, 2018-, and 2019-cohorts) to predict mortality within a specific year based on clinical and demographic information collected up to the end of the preceding year. We then develop a comprehensive machine learning platform to construct a predictive model of one-year mortality for each year-specific cohort. In particular, the study implements and compares the performance of nine classification rules for predicting the one-year mortality of DM patients. The results show that gradient-boosting ensemble learning methods perform better than other algorithms across all year-specific cohorts while achieving an area under the curve (AUC) between 0.78 and 0.80 on independent test sets. The feature importance analysis conducted by calculating SHAP (SHapley Additive exPlanations) values shows that age, duration of diabetes, hypertension, and sex are the top four most important features for predicting one-year mortality. In conclusion, the results show that it is possible to use machine learning to build accurate predictive models of one-year mortality for DM patients based on administrative health data. In the future, integrating this information with laboratory data or patients' medical history could potentially boost the performance of the predictive models.

Global dynamics of tick-borne diseases.

A tick-borne disease model is considered with nonlinear incidence rate and piecewise constant delay of generalized type. It is known that the tick-borne diseases have their peak during certain periods due to the life cycle of ticks. Only adult ticks can bite and transmit disease. Thus, we use a piecewise constant delay to model this phenomena. The global asymptotic stability of the disease-free and endemic equilibrium is shown by constructing suitable Lyapunov functions and Lyapunov-LaSalle technique. The theoretical findings are illustrated through numerical simulations.

Existence of traveling wave solutions to data-driven glioblastoma multiforme growth models with density-dependent diffusion.

Mathematical modeling for cancerous disease has attracted increasing attention from the researchers around the world. Being an effective tool, it helps to describe the processes that happen to the tumour as the diverse treatment scenarios. In this paper, a density-dependent reaction-diffusion equation is applied to the most aggressive type of brain cancer, Glioblastoma multiforme. The model contains the terms responsible for the growth, migration and proliferation of the malignant tumour. The traveling wave solution used is justified by stability analysis. Numerical simulation of the model is provided and the results are compared with the experimental data obtained from the reference papers.