Research

12 pages, 2240 KiB

Open AccessArticle

A Computational Approach to Individual Cell-Based Decision Algorithms Involved in Bone Remodeling

by Belén Serrano-Antón, Chloë Mian, Rocío Fuente, Federica Bertocchini, Miguel A. Herrero, José M. López, Gerardo E. Oleaga and Clemente F. Arias

Mathematics 2024, 12(3), 362; https://doi.org/10.3390/math12030362 - 23 Jan 2024

Viewed by 539

Abstract

This work is concerned with bone remodeling, an intriguing and efficient biological process that ensures the optimal compliance of the human skeleton by screening and replacing any single piece of it on a recursive basis. We propose here that a class of algorithms, [...] Read more.

This work is concerned with bone remodeling, an intriguing and efficient biological process that ensures the optimal compliance of the human skeleton by screening and replacing any single piece of it on a recursive basis. We propose here that a class of algorithms, which are simple enough to be implemented at an individual cell level, suffices to account for the two main features of such homeostatic process: thorough screening of the whole skeleton on the one hand and destruction and subsequent replacement of any single bone piece on the other. This last process is accomplished at a microscopic scale by special groups of cells, assembled for that purpose, called Bone Multicellular Units (BMUs). Moreover, it is shown that the algorithms proposed are robust, i.e, they remain functional in a wide range of biomechanical environments, thus allowing for different remodeling rates at different places. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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23 pages, 3692 KiB

Open AccessArticle

Periodic Behaviour of HIV Dynamics with Three Infection Routes

by Miled El Hajji and Rahmah Mohammed Alnjrani

Mathematics 2024, 12(1), 123; https://doi.org/10.3390/math12010123 - 29 Dec 2023

Cited by 1 | Viewed by 633

Abstract

In this study, we consider a system of nonlinear differential equations modeling the human immunodeficiency virus type-1 (HIV-1) in a variable environment. Infected cells were subdivided into two compartments describing both latently and productively infected cells. Thus, three routes of infection [...] Read more.

In this study, we consider a system of nonlinear differential equations modeling the human immunodeficiency virus type-1 (HIV-1) in a variable environment. Infected cells were subdivided into two compartments describing both latently and productively infected cells. Thus, three routes of infection were considered including the HIV-to-cell contact, latently infected cell-to-cell contact, and actively infected cell-to-cell contact. The nonnegativity and boundedness of the trajectories of the dynamics were proved. The basic reproduction number was determined through an integral operator. The global stability of steady states is then analyzed using the Lyapunov theory together with LaSalle’s invariance principle for the case of a fixed environment. Similarly, for the case of a variable environment, we showed that the virus-free periodic solution is globally asymptotically stable once

R_{0} \leq 1

, while the virus will persist once

R_{0} > 1

. Finally, some numerical examples are provided illustrating the theoretical investigations. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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39 pages, 1840 KiB

Open AccessArticle

Effect of Impaired B-Cell and CTL Functions on HIV-1 Dynamics

by Noura H. AlShamrani, Reham H. Halawani and Ahmed M. Elaiw

Mathematics 2023, 11(20), 4385; https://doi.org/10.3390/math11204385 - 22 Oct 2023

Viewed by 625

Abstract

This paper formulates and analyzes two mathematical models that describe the within-host dynamics of human immunodeficiency virus type 1 (HIV-1) with impairment of both cytotoxic T lymphocytes (CTLs) and B cells. Both viral transmission (VT) and cellular infection (CT) mechanisms are considered. The [...] Read more.

This paper formulates and analyzes two mathematical models that describe the within-host dynamics of human immunodeficiency virus type 1 (HIV-1) with impairment of both cytotoxic T lymphocytes (CTLs) and B cells. Both viral transmission (VT) and cellular infection (CT) mechanisms are considered. The second model is a generalization of the first model that includes distributed time delays. For the two models, we establish the non-negativity and boundedness of the solutions, find the basic reproductive numbers, determine all possible steady states and establish the global asymptotic stability properties of all steady states by means of the Lyapunov method. We confirm the theoretical results by conducting numerical simulations. We conduct a sensitivity analysis to show the effect of the values of the parameters on the basic reproductive number. We discuss the results, showing that impaired B cells and CTLs, time delay and latent CT have significant effects on the HIV-1 dynamics. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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24 pages, 1055 KiB

Open AccessArticle

A Richness Estimator Based on Integrated Data

by Chun-Huo Chiu

Mathematics 2023, 11(17), 3775; https://doi.org/10.3390/math11173775 - 02 Sep 2023

Viewed by 770

Abstract

Species richness is a widely used measure for assessing the diversity of a particular area. However, observed richness often underestimates the true richness due to resource limitations, particularly in a small-sized sample or highly heterogeneous assemblage. To estimate the number of different species [...] Read more.

Species richness is a widely used measure for assessing the diversity of a particular area. However, observed richness often underestimates the true richness due to resource limitations, particularly in a small-sized sample or highly heterogeneous assemblage. To estimate the number of different species (species richness) present across several different sites (communities), researchers often use a combined collection of data (an integrated dataset). This dataset is created by collecting samples from each site individually and independently. However, the pooled sample of integrated data is no longer a random sample from the entire area, and the use of different sampling schemes results in different collected data formats. Consequently, employing a single sampling distribution to model the pooled sample becomes unfeasible, rendering existing richness estimators inadequate. This study provides a theoretical explanation for the applicability of Chao’s lower bound estimator in assessing species richness across multiple sites based on the pooled sample. Additionally, a new non-parametric estimator is introduced, which adjusts the bias of Chao’s lower bound estimator by leveraging the Good–Turing frequency formula. This proposed estimator only utilizes the richness of singletons, doubletons, and tripletons in the pooled sample to estimate undetected richness. Simulated datasets across various models are employed to demonstrate the statistical performance of the estimator, showcasing its ability to reduce the bias of observed richness and provide accurate 95% confidence intervals. Real datasets are also utilized to illustrate the practical application of the proposed approach. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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26 pages, 1344 KiB

Open AccessArticle

Analyzing the Dynamics of a Periodic Typhoid Fever Transmission Model with Imperfect Vaccination

by Mohammed H. Alharbi, Fawaz K. Alalhareth and Mahmoud A. Ibrahim

Mathematics 2023, 11(15), 3298; https://doi.org/10.3390/math11153298 - 26 Jul 2023

Cited by 1 | Viewed by 1160

Abstract

We present a nonautonomous compartmental model that incorporates vaccination and accounts for the seasonal transmission of typhoid fever. The dynamics of the system are governed by the basic reproductive number

R_{0}

. This demonstrates the global stability of the disease-free solution if [...] Read more.

We present a nonautonomous compartmental model that incorporates vaccination and accounts for the seasonal transmission of typhoid fever. The dynamics of the system are governed by the basic reproductive number

R_{0}

. This demonstrates the global stability of the disease-free solution if

R_{0} < 1

. On the contrary, if

R_{0} > 1

, the disease persists and positive periodic solutions exist. Numerical simulations validate our theoretical findings. To accurately fit typhoid fever data in Taiwan from 2008 to 2023, we use the model and estimate its parameters using Latin hypercube sampling and least squares techniques. A sensitivity analysis reveals the significant influence of parameters such as infection rates on the reproduction number. Increasing vaccination coverage, despite challenges in developing countries, reduces typhoid cases. Accessible and highly effective vaccines play a critical role in suppressing the epidemic, outweighing concerns about the efficacy of the vaccine. Investigating possible parameter changes in Taiwan highlights the importance of monitoring and managing transmission rates to prevent recurring annual epidemics. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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18 pages, 3078 KiB

Open AccessArticle

Adapting Strategies for Effective Schistosomiasis Prevention: A Mathematical Modeling Approach

by Zadoki Tabo, Chester Kalinda, Lutz Breuer and Christian Albrecht

Mathematics 2023, 11(12), 2609; https://doi.org/10.3390/math11122609 - 07 Jun 2023

Cited by 2 | Viewed by 1232

Abstract

One of the most deadly neglected tropical diseases known to man is schistosomiasis. Understanding how the disease spreads and evaluating the relevant control strategies are key steps in predicting its spread. We propose a mathematical model to evaluate the potential impact of four [...] Read more.

One of the most deadly neglected tropical diseases known to man is schistosomiasis. Understanding how the disease spreads and evaluating the relevant control strategies are key steps in predicting its spread. We propose a mathematical model to evaluate the potential impact of four strategies: chemotherapy, awareness programs, the mechanical removal of snails and molluscicides, and the impact of a change in temperature on different molluscicide performances based on their half-lives and the length of time they persist in contact with target species. The results show that the recruitment rate of humans and the presence of cercaria and miracidia parasites are crucial factors in disease transmission. However, schistosomiasis can be entirely eradicated by combining all of the four strategies. In the face of climate change and molluscicide degradation, the results show that increasing the temperatures and the number of days a molluscicide persists in the environment before it completely degrades decreases the chemically induced mortality rate of snails while increasing the half-life of different molluscicides increases the death rate of snails. Therefore, eradicating schistosomiasis effectively necessitates a comprehensive integration of all preventative measures. Moreover, regions with different weather patterns and seasonal climates need strategies that have been adapted in terms of the appropriate molluscicide and time intervals for reapplication and effective schistosomiasis control. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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18 pages, 2956 KiB

Open AccessArticle

Machine-Learning Approach for Risk Estimation and Risk Prediction of the Effect of Climate on Bovine Respiratory Disease

by Joseph K. Gwaka, Marcy A. Demafo, Joel-Pascal N. N’konzi, Anton Pak, Jamiu Olumoh, Faiz Elfaki and Oyelola A. Adegboye

Mathematics 2023, 11(6), 1354; https://doi.org/10.3390/math11061354 - 10 Mar 2023

Viewed by 1720

Abstract

Bovine respiratory disease (BRD) is a major cause of illness and death in cattle; however, its global extent and distribution remain unclear. As climate change continues to impact the environment, it is important to understand the environmental factors contributing to BRD’s emergence and [...] Read more.

Bovine respiratory disease (BRD) is a major cause of illness and death in cattle; however, its global extent and distribution remain unclear. As climate change continues to impact the environment, it is important to understand the environmental factors contributing to BRD’s emergence and re-emergence. In this study, we used machine-learning models and remotely sensed climate data at 2.5 min (21 km²) resolution environmental layers to estimate the risk of BRD and predict its potential future distribution. We analysed 13,431 BRD cases from 1727 cities worldwide between 2005 and 2021 using two machine-learning models, maximum entropy (MaxEnt) and Boosted Regression Trees (BRT), to predict the risk and geographical distribution of the risk of BRD globally with varying model parameters. Different re-sampling regimes were used to visualise and measure various sources of uncertainty and prediction performance. The best-fitting model was assessed based on the area under the receiver operator curve (AUC-ROC), positive predictive power and Cohen’s Kappa. We found that BRT had better predictive power compared with MaxEnt. Our findings showed that favourable habitats for BRD occurrence were associated with the mean annual temperature, precipitation of the coldest quarter, mean diurnal range and minimum temperature of the coldest month. Similarly, we showed that the risk of BRD is not limited to the currently known suitable regions of Europe and west and central Africa but extends to other areas, such as Russia, China and Australia. This study highlights the need for global surveillance and early detection systems to prevent the spread of disease across borders. The findings also underscore the importance of bio-security surveillance and livestock sector interventions, such as policy-making and farmer education, to address the impact of climate change on animal diseases and prevent emergencies and the spread of BRD to new areas. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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21 pages, 564 KiB

Open AccessArticle

An Age of Infection Kernel, an

R

Formula, and Further Results for Arino–Brauer A, B Matrix Epidemic Models with Varying Populations, Waning Immunity, and Disease and Vaccination Fatalities

by Florin Avram, Rim Adenane, Lasko Basnarkov, Gianluca Bianchin, Dan Goreac and Andrei Halanay

Mathematics 2023, 11(6), 1307; https://doi.org/10.3390/math11061307 - 08 Mar 2023

Cited by 2 | Viewed by 1074

Abstract

In this work, we first introduce a class of deterministic epidemic models with varying populations inspired by Arino et al. (2007), the parameterization of two matrices, demography, the waning of immunity, and vaccination parameters. Similar models have been focused on by Julien Arino, [...] Read more.

In this work, we first introduce a class of deterministic epidemic models with varying populations inspired by Arino et al. (2007), the parameterization of two matrices, demography, the waning of immunity, and vaccination parameters. Similar models have been focused on by Julien Arino, Fred Brauer, Odo Diekmann, and their coauthors, but mostly in the case of “closed populations” (models with varying populations have been studied in the past only in particular cases, due to the difficulty of this endeavor). Our Arino–Brauer models contain SIR–PH models of Riano (2020), which are characterized by the phase-type distribution

(\vec{α}, A)

, modeling transitions in “disease/infectious compartments”. The A matrix is simply the Metzler/sub-generator matrix intervening in the linear system obtained by making all new infectious terms 0. The simplest way to define the probability row vector

\vec{α}

is to restrict it to the case where there is only one susceptible class

s

, and when matrix B (given by the part of the new infection matrix, with respect to

s

) is of rank one, with

B = b \vec{α}

. For this case, the first result we obtained was an explicit formula (12) for the replacement number (not surprisingly, accounting for varying demography, waning immunity and vaccinations led to several nontrivial modifications of the Arino et al. (2007) formula). The analysis of

(A, B)

Arino–Brauer models is very challenging. As obtaining further general results seems very hard, we propose studying them at three levels: (A) the exact model, where only a few results are available—see Proposition 2; and (B) a “first approximation” (FA) of our model, which is related to the usually closed population model often studied in the literature. Notably, for this approximation, an associated renewal function is obtained in (7); this is related to the previous works of Breda, Diekmann, Graaf, Pugliese, Vermiglio, Champredon, Dushoff, and Earn. (C) Finally, we propose studying a second heuristic “intermediate approximation” (IA). Perhaps our main contribution is to draw attention to the importance of

(A, B)

Arino–Brauer models and that the FA approximation is not the only way to tackle them. As for the practical importance of our results, this is evident, once we observe that the

(A, B)

Arino–Brauer models include a large number of epidemic models (COVID, ILI, influenza, illnesses, etc.). Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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26 pages, 1558 KiB

Open AccessArticle

Global Stability of a MERS-CoV Infection Model with CTL Immune Response and Intracellular Delay

by Tuersunjiang Keyoumu, Wanbiao Ma and Ke Guo

Mathematics 2023, 11(4), 1066; https://doi.org/10.3390/math11041066 - 20 Feb 2023

Cited by 3 | Viewed by 1106

Abstract

In this paper, we propose and study a Middle East respiratory syndrome coronavirus (MERS-CoV) infection model with cytotoxic T lymphocyte (CTL) immune response and intracellular delay. This model includes five compartments: uninfected cells, infected cells, viruses, dipeptidyl peptidase 4 (DPP4), and CTL immune [...] Read more.

In this paper, we propose and study a Middle East respiratory syndrome coronavirus (MERS-CoV) infection model with cytotoxic T lymphocyte (CTL) immune response and intracellular delay. This model includes five compartments: uninfected cells, infected cells, viruses, dipeptidyl peptidase 4 (DPP4), and CTL immune cells. We obtained an immunity-inactivated reproduction number

R_{0}

and an immunity-activated reproduction number

R_{1}

. By analyzing the distributions of roots of the corresponding characteristic equations, the local stability results of the infection-free equilibrium, the immunity-inactivated equilibrium, and the immunity-activated equilibrium were obtained. Moreover, by constructing suitable Lyapunov functionals and combining LaSalle’s invariance principle and Barbalat’s lemma, some sufficient conditions for the global stability of the three types of equilibria were obtained. It was found that the infection-free equilibrium is globally asymptotically stable if

R_{0} \leq 1

and unstable if

R_{0} > 1

; the immunity-inactivated equilibrium is locally asymptotically stable if

R_{0} > 1 > R_{1}

and globally asymptotically stable if

R_{0} > 1 > R_{1}

and condition (H1) holds, but unstable if

R_{1} > 1

; and the immunity-activated equilibrium is locally asymptotically stable if

R_{1} > 1

and is globally asymptotically stable if

R_{1} > 1

and condition (H1) holds. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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17 pages, 3023 KiB

Open AccessArticle

Mathematical Modelling of Combined Intervention Strategies for the Management and Control of Plasma Glucose of a Diabetes Mellitus Patient: A System Dynamic Modelling Approach

by Vincent O. Omwenga, Vaishnav Madhumati, Kumar Vinay, Sathyanarayan Srikanta and Navakanta Bhat

Mathematics 2023, 11(2), 306; https://doi.org/10.3390/math11020306 - 06 Jan 2023

Viewed by 1332

Abstract

With the rapid increase of diabetes mellitus cases in the world, management and control of the disease has become a complex and highly dynamic process. This challenge requires a multifaceted approach to manage and control the complications associated with the hyperglycaemia or hypoglycaemia [...] Read more.

With the rapid increase of diabetes mellitus cases in the world, management and control of the disease has become a complex and highly dynamic process. This challenge requires a multifaceted approach to manage and control the complications associated with the hyperglycaemia or hypoglycaemia conditions. This paper presents a mathematical model for determining the influence of combined intervention strategies in the management and control for the plasma glucose of the type II diabetes. System dynamics (SD) techniques were used in modelling the sub-compartments of biological systems of an Identifiable Patient (IP). The system dynamic model developed gave an illustration on how typical glucose-insulin dynamics occur at different intervention strategies involving varying amounts of carbohydrates taken, intensity of physical exercises, stress levels and the amount of exogenous insulin administered. The model was conceptualized within a semi-closed loop system representing the patient ecosystem by extending the Bergman Minimal Model. Stochastic differential equations (SDE) were used to capture the non-linear, continuous time varying interactions of the measurements associated with plasma glucose-insulin dynamics. The estimated results from the model showed combined intervention strategies of reduced amounts of carbohydrates intake, reduced stress levels and varying moderately high-to-low exercise intensity at a constant unit of exogenous insulin produced good plasma glucose levels control. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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31 pages, 2788 KiB

Open AccessArticle

Global Stability of a Reaction–Diffusion Malaria/COVID-19 Coinfection Dynamics Model

by Ahmed M. Elaiw and Afnan D. Al Agha

Mathematics 2022, 10(22), 4390; https://doi.org/10.3390/math10224390 - 21 Nov 2022

Cited by 11 | Viewed by 1808

Abstract

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a new virus which infects the respiratory system and causes the coronavirus disease 2019 (COVID-19). The coinfection between malaria and COVID-19 has been registered in many countries. This has risen an urgent need to understand [...] Read more.

Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a new virus which infects the respiratory system and causes the coronavirus disease 2019 (COVID-19). The coinfection between malaria and COVID-19 has been registered in many countries. This has risen an urgent need to understand the dynamics of coinfection. In this paper, we construct a reaction–diffusion in-host malaria/COVID-19 model. The model includes seven-dimensional partial differential equations that explore the interactions between seven compartments, healthy red blood cells (RBCs), infected RBCs, free merozoites, healthy epithelial cells (ECs), infected ECs, free SARS-CoV-2 particles, and antibodies. The biological validation of the model is confirmed by establishing the nonnegativity and boundedness of the model’s solutions. All equilibrium points with the corresponding existence conditions are calculated. The global stability of all equilibria is proved by picking up appropriate Lyapunov functionals. Numerical simulations are used to enhance and visualize the theoretical results. We found that the equilibrium points show the different cases when malaria and SARS-CoV-2 infections occur as mono-infection or coinfection. The shared antibody immune response decreases the concentrations of SARS-CoV-2 and malaria merozoites. This can have an important role in reducing the severity of SARS-CoV-2 if the immune response works effectively. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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11 pages, 909 KiB

Open AccessArticle

SCAFG: Classifying Single Cell Types Based on an Adaptive Threshold Fusion Graph Convolution Network

by Haonan Peng, Yuanyuan Li and Wei Zhang

Mathematics 2022, 10(18), 3407; https://doi.org/10.3390/math10183407 - 19 Sep 2022

Cited by 1 | Viewed by 1933

Abstract

Single-cell RNA sequencing (scRNA-seq) technology has been a significant direction for single-cell research due to its high accuracy and specificity, as it enables unbiased high-throughput studies with minimal sample sizes. The continuous improvement of scRNA-seq technology has promoted parallel research on single-cell multi-omics. [...] Read more.

Single-cell RNA sequencing (scRNA-seq) technology has been a significant direction for single-cell research due to its high accuracy and specificity, as it enables unbiased high-throughput studies with minimal sample sizes. The continuous improvement of scRNA-seq technology has promoted parallel research on single-cell multi-omics. Instead of sequencing bulk cells, analyzing single cells inspires greater discovery power for detecting novel genes without prior knowledge of sequence information and with greater sensitivity when quantifying rare variants and transcripts. However, current analyses of scRNA-seq data are usually carried out with unsupervised methods, which cannot take advantage of the prior distribution and structural features of the data. To solve this problem, we propose the SCAFG (Classifying Single Cell Types Based on an Adaptive Threshold Fusion Graph Convolution Network), a semi-supervised single-cell classification model that adaptively fuses cell-to-cell correlation matrices under various thresholds according to the distribution of cells. We tested the performance of the SCAFG in identifying cell types on diverse real scRNA-seq data; then, we compared the SCAFG with other commonly used semi-supervised algorithms, and it was shown that the SCAFG can classify single-cell data with a higher accuracy. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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25 pages, 5481 KiB

Open AccessArticle

An Attention-Preserving Network-Based Method for Assisted Segmentation of Osteosarcoma MRI Images

by Feng Liu, Fangfang Gou and Jia Wu

Mathematics 2022, 10(10), 1665; https://doi.org/10.3390/math10101665 - 12 May 2022

Cited by 28 | Viewed by 2066

Abstract

Osteosarcoma is a malignant bone tumor that is extremely dangerous to human health. Not only does it require a large amount of work, it is also a complicated task to outline the lesion area in an image manually, using traditional methods. With the [...] Read more.

Osteosarcoma is a malignant bone tumor that is extremely dangerous to human health. Not only does it require a large amount of work, it is also a complicated task to outline the lesion area in an image manually, using traditional methods. With the development of computer-aided diagnostic techniques, more and more researchers are focusing on automatic segmentation techniques for osteosarcoma analysis. However, existing methods ignore the size of osteosarcomas, making it difficult to identify and segment smaller tumors. This is very detrimental to the early diagnosis of osteosarcoma. Therefore, this paper proposes a Contextual Axial-Preserving Attention Network (CaPaN)-based MRI image-assisted segmentation method for osteosarcoma detection. Based on the use of Res2Net, a parallel decoder is added to aggregate high-level features which effectively combines the local and global features of osteosarcoma. In addition, channel feature pyramid (CFP) and axial attention (A-RA) mechanisms are used. A lightweight CFP can extract feature mapping and contextual information of different sizes. A-RA uses axial attention to distinguish tumor tissues by mining, which reduces computational costs and thus improves the generalization performance of the model. We conducted experiments using a real dataset provided by the Second Xiangya Affiliated Hospital and the results showed that our proposed method achieves better segmentation results than alternative models. In particular, our method shows significant advantages with respect to small target segmentation. Its precision is about 2% higher than the average values of other models. For the segmentation of small objects, the DSC value of CaPaN is 0.021 higher than that of the commonly used U-Net method. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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26 pages, 859 KiB

Open AccessArticle

Exploring HIV Dynamics and an Optimal Control Strategy

by Salah Alsahafi and Stephen Woodcock

Mathematics 2022, 10(5), 749; https://doi.org/10.3390/math10050749 - 26 Feb 2022

Cited by 5 | Viewed by 1287

Abstract

In this paper, we propose a six-dimensional nonlinear system of differential equations for the human immunodeficiency virus (HIV) including the B-cell functions with a general nonlinear incidence rate. The compartment of infected cells was subdivided into three classes representing the latently infected cells, [...] Read more.

In this paper, we propose a six-dimensional nonlinear system of differential equations for the human immunodeficiency virus (HIV) including the B-cell functions with a general nonlinear incidence rate. The compartment of infected cells was subdivided into three classes representing the latently infected cells, the short-lived productively infected cells, and the long-lived productively infected cells. The basic reproduction number was established, and the local and global stability of the equilibria of the model were studied. A sensitivity analysis with respect to the model parameters was undertaken. Based on this study, an optimal strategy is proposed to decrease the number of infected cells. Finally, some numerical simulations are presented to illustrate the theoretical findings. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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20 pages, 489 KiB

Open AccessArticle

Signal Folding for Efficient Classification of Near-Cyclostationary Biological Signals

by Tianxiang Zheng and Pavel Loskot

Mathematics 2022, 10(2), 192; https://doi.org/10.3390/math10020192 - 08 Jan 2022

Viewed by 1289

Abstract

The classification of biological signals is important in detecting abnormal conditions in observed biological subjects. The classifiers are trained on feature vectors, which often constitute the parameters of the observed time series data models. Since the feature extraction is usually the most time-consuming [...] Read more.

The classification of biological signals is important in detecting abnormal conditions in observed biological subjects. The classifiers are trained on feature vectors, which often constitute the parameters of the observed time series data models. Since the feature extraction is usually the most time-consuming step in training a classifier, in this paper, signal folding and the associated folding operator are introduced to reduce the variability in near-cyclostationary biological signals so that these signals can be represented by models that have a lower order. This leads to a substantial reduction in computational complexity, so the classifier can be learned an order of magnitude faster and still maintain its decision accuracy. The performance of different classifiers involving signal folding as a pre-processing step is studied for sleep apnea detection in one-lead ECG signals assuming ARIMA modeling of the time series data. It is shown that the R-peak-based folding of ECG segments has superior performance to other more general, similarity based signal folding methods. The folding order can be optimized for the best classification accuracy. However, signal folding requires precise scaling and alignment of the created signal fragments. Full article

(This article belongs to the Special Issue Mathematical Modeling and Analysis in Biology and Medicine, 2nd Edition)

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