Category: Nevin Manimala

Math Biosci Eng. 2023 Jan 13;20(3):5949-5965. doi: 10.3934/mbe.2023257.

ABSTRACT

Utilizing statistical information from the Seventh National Population Census, statistical yearbook and sampling dynamic survey data, this study examines the distribution characteristics of the floating population in Beijing, Tianjin and Hebei Region as well as the growth trend of the floating population in each region. It also makes assessments using floating population concentration and The Moran Index Computing Methods. According to the study, the spatial distribution of the floating population has a clear clustering pattern in Beijing, Tianjin and Hebei region. Beijing, Tianjin and Hebei region’s mobile population growth patterns differ substantially, and the region’s inflow population is mostly made up of migrant inhabitants of domestic provinces and inflow of people from nearby regions. Most of the mobile population resides in Beijing and Tianjin, whereas the outflow of people originates in Hebei province. The diffusion impact and the spatial features of the floating population in the Beijing, Tianjin and Hebei area have a constant, positive association, according to the timeline between 2014 and 2020.

PMID:36896558 | DOI:10.3934/mbe.2023257

Math Biosci Eng. 2023 Jan 12;20(3):5379-5412. doi: 10.3934/mbe.2023249.

ABSTRACT

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been spreading worldwide for over two years, with millions of reported cases and deaths. The deployment of mathematical modeling in the fight against COVID-19 has recorded tremendous success. However, most of these models target the epidemic phase of the disease. The development of safe and effective vaccines against SARS-CoV-2 brought hope of safe reopening of schools and businesses and return to pre-COVID normalcy, until mutant strains like the Delta and Omicron variants, which are more infectious, emerged. A few months into the pandemic, reports of the possibility of both vaccine- and infection-induced immunity waning emerged, thereby indicating that COVID-19 may be with us for longer than earlier thought. As a result, to better understand the dynamics of COVID-19, it is essential to study the disease with an endemic model. In this regard, we developed and analyzed an endemic model of COVID-19 that incorporates the waning of both vaccine- and infection-induced immunities using distributed delay equations. Our modeling framework assumes that the waning of both immunities occurs gradually over time at the population level. We derived a nonlinear ODE system from the distributed delay model and showed that the model could exhibit either a forward or backward bifurcation depending on the immunity waning rates. Having a backward bifurcation implies that $ R_c < 1 $ is not sufficient to guarantee disease eradication, and that the immunity waning rates are critical factors in eradicating COVID-19. Our numerical simulations show that vaccinating a high percentage of the population with a safe and moderately effective vaccine could help in eradicating COVID-19.

PMID:36896550 | DOI:10.3934/mbe.2023249

Math Biosci Eng. 2023 Jan 11;20(3):5352-5378. doi: 10.3934/mbe.2023248.

ABSTRACT

Penalized Cox regression can efficiently be used for the determination of biomarkers in high-dimensional genomic data related to disease prognosis. However, results of Penalized Cox regression is influenced by the heterogeneity of the samples who have different dependent structure between survival time and covariates from most individuals. These observations are called influential observations or outliers. A robust penalized Cox model (Reweighted Elastic Net-type maximum trimmed partial likelihood estimator, Rwt MTPL-EN) is proposed to improve the prediction accuracy and identify influential observations. A new algorithm AR-Cstep to solve Rwt MTPL-EN model is also proposed. This method has been validated by simulation study and application to glioma microarray expression data. When there were no outliers, the results of Rwt MTPL-EN were close to the Elastic Net (EN). When outliers existed, the results of EN were impacted by outliers. And whenever the censored rate was large or low, the robust Rwt MTPL-EN performed better than EN. and could resist the outliers in both predictors and response. In terms of outliers detection accuracy, Rwt MTPL-EN was much higher than EN. The outliers who “lived too long” made EN perform worse, but were accurately detected by Rwt MTPL-EN. Through the analysis of glioma gene expression data, most of the outliers identified by EN were those “failed too early”, but most of them were not obvious outliers according to risk estimated from omics data or clinical variables. Most of the outliers identified by Rwt MTPL-EN were those who “lived too long”, and most of them were obvious outliers according to risk estimated from omics data or clinical variables. Rwt MTPL-EN can be adopted to detect influential observations in high-dimensional survival data.

PMID:36896549 | DOI:10.3934/mbe.2023248

Math Biosci Eng. 2023 Jan 11;20(3):5333-5351. doi: 10.3934/mbe.2023247.

ABSTRACT

As COVID-19 continues to spread across the world and causes hundreds of millions of infections and millions of deaths, medical institutions around the world keep facing a crisis of medical runs and shortages of medical resources. In order to study how to effectively predict whether there are risks of death in patients, a variety of machine learning models have been used to learn and predict the clinical demographics and physiological indicators of COVID-19 patients in the United States of America. The results show that the random forest model has the best performance in predicting the risk of death in hospitalized patients with COVID-19, as the COVID-19 patients’ mean arterial pressures, ages, C-reactive protein tests’ values, values of blood urea nitrogen and their clinical troponin values are the most important implications for their risk of death. Healthcare organizations can use the random forest model to predict the risks of death based on data from patients admitted to a hospital due to COVID-19, or to stratify patients admitted to a hospital due to COVID-19 based on the five key factors this can optimize the diagnosis and treatment process by appropriately arranging ventilators, the intensive care unit and doctors, thus promoting the efficient use of limited medical resources during the COVID-19 pandemic. Healthcare organizations can also establish databases of patient physiological indicators and use similar strategies to deal with other pandemics that may occur in the future, as well as save more lives threatened by infectious diseases. Governments and people also need to take action to prevent possible future pandemics.

PMID:36896548 | DOI:10.3934/mbe.2023247

Math Biosci Eng. 2023 Jan 9;20(3):5194-5222. doi: 10.3934/mbe.2023241.

ABSTRACT

Healthcare is the method of keeping or enhancing physical and mental well-being with its aid of illness and injury prevention, diagnosis, and treatment. The majority of conventional healthcare practices involve manual management and upkeep of client demographic information, case histories, diagnoses, medications, invoicing, and drug stock upkeep, which can result in human errors that have an impact on clients. By linking all the essential parameter monitoring equipment through a network with a decision-support system, digital health management based on Internet of Things (IoT) eliminates human errors and aids the doctor in making more accurate and timely diagnoses. The term “Internet of Medical Things” (IoMT) refers to medical devices that have the ability to communicate data over a network without requiring human-to-human or human-to-computer interaction. Meanwhile, more effective monitoring gadgets have been made due to the technology advancements, and these devices can typically record a few physiological signals simultaneously, including the electrocardiogram (ECG) signal, the electroglottography (EGG) signal, the electroencephalogram (EEG) signal, and the electrooculogram (EOG) signal. Yet, there has not been much research on the connection between digital health management and multi-modal signal monitoring. To bridge the gap, this article reviews the latest advancements in digital health management using multi-modal signal monitoring. Specifically, three digital health processes, namely, lower-limb data collection, statistical analysis of lower-limb data, and lower-limb rehabilitation via digital health management, are covered in this article, with the aim to fully review the current application of digital health technology in lower-limb symptom recovery.

PMID:36896542 | DOI:10.3934/mbe.2023241

Math Biosci Eng. 2023 Jan 6;20(3):5043-5065. doi: 10.3934/mbe.2023234.

ABSTRACT

The influence of residents’ income on mental health is complex, and there are heterogeneous effects of residents’ income on different types of mental health. Based on the annual panel data of 55 countries from 2007 to 2019, this paper divides residents’ income into three dimensions: absolute income, relative income and income gap. Mental health is divided into three aspects: subjective well-being, prevalence of depression and prevalence of anxiety. Panel Tobit model is used to study the heterogeneous impact of residents’ income on mental health. The results show that, on the one hand, different dimensions of residents’ income have a heterogeneous impact on mental health, specifically, absolute income has a positive impact on mental health, while relative income and income gap have no significant impact on mental health. On the other hand, the impact of different dimensions of residents’ income on different types of mental health is heterogeneous. Specifically, absolute income and income gap have heterogeneous effects on different types of mental health, while relative income has no significant impact on different types of mental health.

PMID:36896535 | DOI:10.3934/mbe.2023234

Math Biosci Eng. 2023 Jan 4;20(3):4816-4837. doi: 10.3934/mbe.2023223.

ABSTRACT

This paper is devoted to investigating the impact of vaccination on mitigating COVID-19 outbreaks. In this work, we propose a compartmental epidemic ordinary differential equation model, which extends the previous so-called SEIRD model ^[1,2,3,4] by incorporating the birth and death of the population, disease-induced mortality and waning immunity, and adding a vaccinated compartment to account for vaccination. Firstly, we perform a mathematical analysis for this model in a special case where the disease transmission is homogeneous and vaccination program is periodic in time. In particular, we define the basic reproduction number $ mathcal{R}_0 $ for this system and establish a threshold type of result on the global dynamics in terms of $ mathcal{R}_0 $. Secondly, we fit our model into multiple COVID-19 waves in four locations including Hong Kong, Singapore, Japan, and South Korea and then forecast the trend of COVID-19 by the end of 2022. Finally, we study the effects of vaccination again the ongoing pandemic by numerically computing the basic reproduction number $ mathcal{R}_0 $ under different vaccination programs. Our findings indicate that the fourth dose among the high-risk group is likely needed by the end of the year.

PMID:36896524 | DOI:10.3934/mbe.2023223

Math Biosci Eng. 2023 Jan;20(3):4714-4740. doi: 10.3934/mbe.2023218. Epub 2022 Dec 29.

ABSTRACT

The variation of nutrient supply not only leads to the differences in the phytoplankton biomass and primary productivity but also induces the long-term phenotypic evolution of phytoplankton. It is widely accepted that marine phytoplankton follows Bergmann’s Rule and becomes smaller with climate warming. Compared with the direct effect of increasing temperature, the indirect effect via nutrient supply is considered to be an important and dominant factor in the reduction of phytoplankton cell size. In this paper, a size-dependent nutrient-phytoplankton model is developed to explore the effects of nutrient supply on the evolutionary dynamics of functional traits associated with phytoplankton size. The ecological reproductive index is introduced to investigate the impacts of input nitrogen concentration and vertical mixing rate on the persistence of phytoplankton and the distribution of cell size. In addition, by applying the adaptive dynamics theory, we study the relationship between nutrient input and the evolutionary dynamics of phytoplankton. The results show that input nitrogen concentration and vertical mixing rate have significant effects on the cell size evolution of phytoplankton. Specifically, cell size tends to increase with the input nutrient concentration, as does the diversity of cell sizes. In addition, a single-peaked relationship between vertical mixing rate and cell size is observed. When the vertical mixing rate is too low or too high, only small individuals are dominant in the water column. When the vertical mixing rate is moderate, large individuals can coexist with small individuals, so the diversity of phytoplankton is elevated. We predict that reduced intensity of nutrient input due to climate warming will lead to a trend towards smaller cell size and will reduce the diversity of phytoplankton.

PMID:36896519 | DOI:10.3934/mbe.2023218

Math Biosci Eng. 2023 Jan;20(3):4673-4689. doi: 10.3934/mbe.2023216. Epub 2022 Dec 28.

ABSTRACT

The effective reproduction number, $ R_t $, is a vital epidemic parameter utilized to judge whether an epidemic is shrinking, growing, or holding steady. The main goal of this paper is to estimate the combined $ R_t $ and time-dependent vaccination rate for COVID-19 in the USA and India after the vaccination campaign started. Accounting for the impact of vaccination into a discrete-time stochastic augmented SVEIR (Susceptible-Vaccinated-Exposed-Infectious-Recovered) model, we estimate the time-dependent effective reproduction number $ (R_t) $ and vaccination rate $ (xi_t) $ for COVID-19 by using a low pass filter and the Extended Kalman Filter (EKF) approach for the period February 15, 2021 to August 22, 2022 in India and December 13, 2020 to August 16, 2022 in the USA. The estimated $ R_t $ and $ xi_t $ show spikes and serrations with the data. Our forecasting scenario represents the situation by December 31, 2022 that the new daily cases and deaths are decreasing for the USA and India. We also noticed that for the current vaccination rate, $ R_t $ would remain greater than one by December 31, 2022. Our results are beneficial for the policymakers to track the status of the effective reproduction number, whether it is greater or less than one. As restrictions in these countries ease, it is still important to maintain safety and preventive measures.

PMID:36896517 | DOI:10.3934/mbe.2023216

Math Biosci Eng. 2023 Jan;20(3):4437-4454. doi: 10.3934/mbe.2023206. Epub 2022 Dec 26.

ABSTRACT

This article presents the existence outcomes concerning a family of singular nonlinear differential equations containing Caputo’s fractional derivatives with nonlocal double integral boundary conditions. According to the nature of Caputo’s fractional calculus, the problem is converted into an equivalent integral equation, while two standard fixed theorems are employed to prove its uniqueness and existence results. An example is presented at the end of this paper to illustrate our obtained results.

PMID:36896507 | DOI:10.3934/mbe.2023206