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Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition
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Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Biology".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 33720

Special Issue Editor

Prof. Dr. Ricardo Lopez-Ruiz

E-Mail Website
Guest Editor
Department of Computer Science and Systems Engineering, Faculty of Science, University of Zaragoza, 50009 Zaragoza, Spain
Interests: complexity and chaos; econophysics; nonlinear models; multiagent systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Mathematical biology has been an area of wide interest in recent decades, since the modeling of complicated biological processes became able to create analytical and computational approaches to many different bio-inspired problems, coming from different branches such as population dynamics, molecular dynamics in cells, neuronal and heart diseases, the cardiovascular system, genetics, etc. Mathematical and computer science have come to work interactively to contribute to the better understanding of the biological phenomena.

   We seek papers on insightful approaches to treat the basic relationships between species in population dynamics and implementations of many species interactions in complex networks to model natural ecosystems. Further, any other kind of models and their applications in neuroscience, genetics, cellular and molecular dynamics, heart diseases, etc. and where the fusion of mathematics and computation help in the progress in biological problems are welcome.

Prof. Dr. Ricardo Lopez-Ruiz
Guest Editor

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Keywords

  • bio-inspired modeling
  • population dynamics
  • cellular and molecular dynamics
  • computational neuroscience
  • heart disease modeling

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Published Papers (18 papers)

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Research

10 pages, 1093 KiB  
Article
Diffusion Simulation on Mammograms: A Technique for Analyzing and Monitoring Breast Tumors
by Jonas Borjas, Kay Tucci, Orlando Alvarez-Llamoza and Carlos Echeverria
Mathematics 2023, 11(24), 4988; https://doi.org/10.3390/math11244988 - 18 Dec 2023
Viewed by 1058
Abstract
We have developed an imaging biomarker for quantitatively monitoring the response to clinical treatment in cancer patients. Similar to other diffusion-weighted imaging DWI techniques, our method allows for the monitoring of breast cancer progression based on the diffusion coefficient values in the affected [...] Read more.
We have developed an imaging biomarker for quantitatively monitoring the response to clinical treatment in cancer patients. Similar to other diffusion-weighted imaging DWI techniques, our method allows for the monitoring of breast cancer progression based on the diffusion coefficient values in the affected area. Our technique has the advantage of using images from mammograms and mesoscopic multiparticle collision MPC simulation, making it more affordable and easier to implement compared to other DWI techniques, such as diffusion-weighted MRI. To create our simulation, we start with the region of interest from a mammogram where the lesion is located and build a flat simulation box with impenetrable cylindrical obstacles of varying diameters to represent the tissue’s heterogeneity. The volume of each obstacle is based on the intensity of the mammogram pixels, and the diffusion coefficient is calculated by simulating the behavior of a point particle fluid inside the box using MPC. We tested our technique on two mammograms of a male patient with a moderately differentiated breast ductal carcinoma lesion, taken before and after the first cycle of four chemotherapy sessions. As seen in other DWI studies, our technique demonstrated significant changes in the fluid concentration map of the tumor lesion, and the relative values of the diffusion coefficient showed a clear difference before and after chemotherapy. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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15 pages, 488 KiB  
Article
Modelling of Interaction Dynamics of a Pathogen and Bio-Markers (Matrix Metalloproteinases) of Tissue Destruction in Pulmonary Tuberculosis
by Anastasia I. Lavrova, Dilyara S. Esmedljaeva and Eugene B. Postnikov
Mathematics 2023, 11(21), 4522; https://doi.org/10.3390/math11214522 - 2 Nov 2023
Viewed by 891
Abstract
Tuberculosis (TB) has a long history as a serious disease induced by its causative agent Mycobacterium tuberculosis. This pathogen manipulates the host’s immune response, thereby stimulating inflammatory processes, which leads to an even greater imbalance of specific enzymes/inhibitors that contribute to tissue [...] Read more.
Tuberculosis (TB) has a long history as a serious disease induced by its causative agent Mycobacterium tuberculosis. This pathogen manipulates the host’s immune response, thereby stimulating inflammatory processes, which leads to an even greater imbalance of specific enzymes/inhibitors that contribute to tissue destruction. This work addresses a model consisting of two ordinary differential equations obtained by reducing a previously developed large-scale model describing lung damage, taking into account key metabolic pathways controlled by bacteria. The resulting system is explored as a dynamical system simulating the interaction between bio-markers (matrix metalloproteinases) of tissue destruction and the pathogen. In addition to the analysis of the mathematical model’s features, we qualitatively compared the model dynamics with real clinical data and discussed their mutual correspondence. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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29 pages, 1437 KiB  
Article
Global Properties of HIV-1 Dynamics Models with CTL Immune Impairment and Latent Cell-to-Cell Spread
by Noura H. AlShamrani, Reham H. Halawani, Wafa Shammakh and Ahmed M. Elaiw
Mathematics 2023, 11(17), 3743; https://doi.org/10.3390/math11173743 - 31 Aug 2023
Cited by 2 | Viewed by 1234
Abstract
This paper presents and analyzes two mathematical models for the human immunodeficiency virus type-1 (HIV-1) infection with Cytotoxic T Lymphocyte cell (CTL) immune impairment. These models describe the interactions between healthy CD4+T cells, latently and actively infected cells, HIV-1 particles, [...] Read more.
This paper presents and analyzes two mathematical models for the human immunodeficiency virus type-1 (HIV-1) infection with Cytotoxic T Lymphocyte cell (CTL) immune impairment. These models describe the interactions between healthy CD4+T cells, latently and actively infected cells, HIV-1 particles, and CTLs. The healthy CD4+T cells might be infected when they make contact with: (i) HIV-1 particles due to virus-to-cell (VTC) contact; (ii) latently infected cells due to latent cell-to-cell (CTC) contact; and (iii) actively infected cells due to active CTC contact. Distributed time delays are considered in the second model. We show the nonnegativity and boundedness of the solutions of the systems. Further, we derive basic reproduction numbers ℜ0 and ℜ˜0, that determine the existence and stability of equilibria of our proposed systems. We establish the global asymptotic stability of all equilibria by using the Lyapunov method together with LaSalle’s invariance principle. We confirm the theoretical results by numerical simulations. The effect of immune impairment, time delay and CTC transmission on the HIV-1 dynamics are discussed. It is found that weak immunity contributes significantly to the development of the disease. Further, we have established that the presence of time delay can significantly decrease the basic reproduction number and then suppress the HIV-1 replication. On the other hand, the presence of latent CTC spread increases the basic reproduction number and then enhances the viral progression. Thus, neglecting the latent CTC spread in the HIV-1 infection model will lead to an underestimation of the basic reproduction number. Consequently, the designed drug therapies will not be accurate or sufficient to eradicate the viruses from the body. These findings may help to improve the understanding of the dynamics of HIV-1 within a host. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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12 pages, 1032 KiB  
Article
Cross-Diffusion-Induced Turing Instability in a Two-Prey One-Predator System
by Ying Yu, Yahui Chen and You Zhou
Mathematics 2023, 11(11), 2411; https://doi.org/10.3390/math11112411 - 23 May 2023
Cited by 1 | Viewed by 1283
Abstract
This paper focuses on a strongly coupled specific ecological system consisting of two prey species and one predator. We explore a unique positive equilibrium solution of the system that is globally asymptotically stable. Additionally, we show that this equilibrium solution remains locally linearly [...] Read more.
This paper focuses on a strongly coupled specific ecological system consisting of two prey species and one predator. We explore a unique positive equilibrium solution of the system that is globally asymptotically stable. Additionally, we show that this equilibrium solution remains locally linearly stable, even in the presence of diffusion. This means that the system does not follow classical Turing instability. However, it becomes linearly unstable only when cross-diffusion also plays a role in the system, which is called a cross-diffusion-induced instability. The corresponding numerical simulations are also demonstrated and we obtain the spatial patterns. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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17 pages, 14480 KiB  
Article
Targeting Monoamine Oxidase B for the Treatment of Alzheimer’s and Parkinson’s Diseases Using Novel Inhibitors Identified Using an Integrated Approach of Machine Learning and Computer-Aided Drug Design
by Arif Jamal Siddiqui, Sadaf Jahan, Maqsood Ahmed Siddiqui, Andleeb Khan, Mohammed Merae Alshahrani, Riadh Badraoui and Mohd Adnan
Mathematics 2023, 11(6), 1464; https://doi.org/10.3390/math11061464 - 17 Mar 2023
Cited by 6 | Viewed by 2370
Abstract
Neurological disorders are disorders characterized by progressive loss of neurons leading to disability. Neurotransmitters such as nor-adrenaline, dopamine, and serotonin are partially regulated by the enzyme monoamine oxidase (MAO). Treatments for conditions like Alzheimer’s, Parkinson’s, anxiety, and depression involve the use of MAOIs. [...] Read more.
Neurological disorders are disorders characterized by progressive loss of neurons leading to disability. Neurotransmitters such as nor-adrenaline, dopamine, and serotonin are partially regulated by the enzyme monoamine oxidase (MAO). Treatments for conditions like Alzheimer’s, Parkinson’s, anxiety, and depression involve the use of MAOIs. To target MAO enzyme inhibition, various scaffolds are prepared and evaluated, including modified coumarins, chromone carboxylic acid substituents, pyridazine derivatives, and indolylmethylamine. The research presented here focuses on combining different computational tools to find new inhibitors of the MAO-B protein. We discovered 5 possible chemical inhibitors using the above computational techniques. We found five molecular inhibitors with high binding affinity using computational methods. These five molecules showed a high binding affinity; they are −10.917, −10.154, −10.223, −10.858, and −9.629 Kcal/mol, respectively. Additionally, the selected inhibitors were further examined by in vitro activity, and their binding affinity was confirmed using an enzyme-based assay. In summary, the computational studies performed here using molecular dynamics and free energy calculations can also be used to design and predict highly potent derivatives as MAO-B inhibitors, and these top inhibitors help in the development of novel drugs for neurological diseases such as Alzheimer’s and Parkinson’s. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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15 pages, 509 KiB  
Article
Parameter Estimation for a Kinetic Model of a Cellular System Using Model Order Reduction Method
by Neveen Ali Eshtewy, Lena Scholz and Andreas Kremling
Mathematics 2023, 11(3), 699; https://doi.org/10.3390/math11030699 - 30 Jan 2023
Cited by 1 | Viewed by 1808
Abstract
Order reduction methods are important tools for systems engineering and can be used, for example, for parameter estimation of kinetic models for systems biology applications. In particular, the Proper Orthogonal Decomposition (POD) method produces a reduced-order model of a system that is used [...] Read more.
Order reduction methods are important tools for systems engineering and can be used, for example, for parameter estimation of kinetic models for systems biology applications. In particular, the Proper Orthogonal Decomposition (POD) method produces a reduced-order model of a system that is used for solving inverse problems (parameter estimation). POD is an intrusive model order reduction method that is aimed to obtain a lower-dimensional system for a high-dimensional system while preserving the main features of the original system. We use a singular value decomposition (SVD) to compute a reduced basis as it is usually numerically more robust to compute the singular values of the snapshot matrix instead of the eigenvalues of the corresponding correlation matrix. The reduced basis functions are then used to construct a data-fitting function that fits a known experimental data set of system substance concentrations. The method is applied to calibrate a kinetic model of carbon catabolite repression (CCR) in Escherichia coli, where the regulatory mechanisms on the molecular side are well understood and experimental data for a number of state variables is available. In particular, we show that the method can be used to estimate the uptake rate constants and other kinetic parameters of the CCR model. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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22 pages, 1094 KiB  
Article
A Pell–Lucas Collocation Approach for an SIR Model on the Spread of the Novel Coronavirus (SARS CoV-2) Pandemic: The Case of Turkey
by Şuayip Yüzbaşı and Gamze Yıldırım
Mathematics 2023, 11(3), 697; https://doi.org/10.3390/math11030697 - 30 Jan 2023
Cited by 5 | Viewed by 1953
Abstract
In this article, we present a study about the evolution of the COVID-19 pandemic in Turkey. The modelling of a new virus named SARS-CoV-2 is considered by an SIR model consisting of a nonlinear system of differential equations. A collocation approach based on [...] Read more.
In this article, we present a study about the evolution of the COVID-19 pandemic in Turkey. The modelling of a new virus named SARS-CoV-2 is considered by an SIR model consisting of a nonlinear system of differential equations. A collocation approach based on the Pell–Lucas polynomials is studied to get the approximate solutions of this model. First, the approximate solution in forms of the truncated Pell–Lucas polynomials are written in matrix forms. By utilizing the collocation points and the matrix relations, the considered model is converted to a system of the nonlinear algebraic equations. By solving this system, the unknown coefficients of the assumed Pell–Lucas polynomial solutions are determined, and so the approximate solutions are obtained. Secondly, two theorems about the error analysis are given and proved. The applications of the methods are made by using a code written in MATLAB. The parameters and the initial conditions of the model are determined according to the reported data from the Turkey Ministry of Health. Finally, the approximate solutions and the absolute error functions are visualized. To demonstrate the effectiveness of the method, our approximate solutions are compared with the approximate solutions obtained by the Runge–Kutta method. The reliable results are obtained from numerical results and comparisons. Thanks to this study, the tendencies of the pandemic can be estimated. In addition, the method can be applied to other countries after some necessary arrangements. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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12 pages, 1315 KiB  
Article
Mathematical Modeling: Cisplatin Binding to Deoxyribonucleic Acid
by Mansoor H. Alshehri
Mathematics 2023, 11(1), 235; https://doi.org/10.3390/math11010235 - 3 Jan 2023
Viewed by 1529
Abstract
The discovery of the cisplatin drug attracted considerable research attention as scientists strove to understand the drug’s mechanism in the human body that is responsible for destroying cancer cells, particularly the coordination between the cisplatin drug and deoxyribonucleic acid. Here, the binding energies [...] Read more.
The discovery of the cisplatin drug attracted considerable research attention as scientists strove to understand the drug’s mechanism in the human body that is responsible for destroying cancer cells, particularly the coordination between the cisplatin drug and deoxyribonucleic acid. Here, the binding energies of a cisplatin molecule relative to double-stranded deoxyribonucleic acid are obtained. The interactions of the system are determined by performing double integrals, and the analytical expressions are derived from the Lennard–Jones function and the continuum approximation; here, it is assumed that a discrete atomic structure might be replaced by surfaces with a constant average atomic density. The results observed that the cisplatin molecule is binding to the double-stranded deoxyribonucleic acid at either the minor or major grooves. By minimizing the interaction energies between the cisplatin molecule and the minor and major grooves, for arbitrary distances λ and arbitrary tilt angles φ from the axis of the helix of the double-stranded deoxyribonucleic acid, the binding energies are determined, and their values are ≈−6 and ≈−12.5 (kcal/mol), respectively. Thus, we may deduce that the major groove in double-stranded deoxyribonucleic acid is the most preferred groove for linking with the cisplatin molecule. The current analysis might help in the equivalent continuum modeling of deoxyribonucleic acids and nanocomposites. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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35 pages, 1664 KiB  
Article
Global Stability of Delayed SARS-CoV-2 and HTLV-I Coinfection Models within a Host
by Ahmed M. Elaiw, Abdulsalam S. Shflot and Aatef D. Hobiny
Mathematics 2022, 10(24), 4756; https://doi.org/10.3390/math10244756 - 14 Dec 2022
Cited by 4 | Viewed by 1311
Abstract
The aim of the present paper is to formulate two new mathematical models to describe the co-dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and human T-cell lymphotropic virus type-I (HTLV-I) in a host. The models characterizes the interplaying between seven compartments, [...] Read more.
The aim of the present paper is to formulate two new mathematical models to describe the co-dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and human T-cell lymphotropic virus type-I (HTLV-I) in a host. The models characterizes the interplaying between seven compartments, uninfected ECs, latently SARS-CoV-2-infected ECs, actively SARS-CoV-2-infected ECs, free SARS-CoV-2 particles, uninfected CD4+T cells, latently HTLV-I-infected CD4+T cells and actively HTLV-I-infected CD4+T cells. The models incorporate five intracellular time delays: (i) two delays in the formation of latently SARS-CoV-2-infected ECs and latently HTLV-I-infected CD4+T cells, (ii) two delays in the reactivation of latently SARS-CoV-2-infected ECs and latently HTLV-I-infected CD4+T cells, and (iii) maturation delay of new SARS-CoV-2 virions. We consider discrete-time delays and distributed-time delays in the first and second models, respectively. We first investigate the properties of the model’s solutions, then we calculate all equilibria and study their global stability. The global asymptotic stability is examined by constructing Lyapunov functionals. The analytical findings are supported via numerical simulation. The impact of time delays on the coinfection progression is discussed. We found that, increasing time delays values can have an antiviral treatment-like impact. Our developed coinfection model can contribute to understand the SARS-CoV-2 and HTLV-I co-dynamics and help to select suitable treatment strategies for COVID-19 patients with HTLV-I. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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16 pages, 1431 KiB  
Article
Entropy-Based Informational Study of the COVID-19 Series of Data
by Andres M. Kowalski, Mariela Portesi, Victoria Vampa, Marcelo Losada and Federico Holik
Mathematics 2022, 10(23), 4590; https://doi.org/10.3390/math10234590 - 4 Dec 2022
Cited by 4 | Viewed by 1437
Abstract
Since the appearance in China of the first cases, the entire world has been deeply affected by the flagellum of the Coronavirus Disease (COVID-19) pandemic. There have been many mathematical approaches trying to characterize the data collected about this serious issue. One of [...] Read more.
Since the appearance in China of the first cases, the entire world has been deeply affected by the flagellum of the Coronavirus Disease (COVID-19) pandemic. There have been many mathematical approaches trying to characterize the data collected about this serious issue. One of the most important aspects for attacking a problem is knowing what information is really available. We investigate here the information contained in the COVID-19 data of infected and deceased people in all countries, using informational quantifiers such as entropy and statistical complexity. For the evaluation of these quantities, we use the Bandt–Pompe permutation methodology, as well as the wavelet transform, to obtain the corresponding probability distributions from the available series of data. The period analyzed covers from the appearance of the disease up to the massive use of anti-COVID vaccines. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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22 pages, 1957 KiB  
Article
Why Is Aedes aegypti Moving South in South America?
by Lucas Ernesto Alonso, Victoria Romeo Aznar and Hernán Gustavo Solari
Mathematics 2022, 10(23), 4510; https://doi.org/10.3390/math10234510 - 29 Nov 2022
Cited by 2 | Viewed by 1466
Abstract
Colonies of Aedes aegypti have been reported at increasingly southern locations. Is this feature a manifestation of climate change or the result of the mosquito’s adaptation? Answering the question requires the testing and comparison of results produced under different, competing, hypotheses. We address [...] Read more.
Colonies of Aedes aegypti have been reported at increasingly southern locations. Is this feature a manifestation of climate change or the result of the mosquito’s adaptation? Answering the question requires the testing and comparison of results produced under different, competing, hypotheses. We address the problem using “AedesBA”, a detailed model of the mosquito Aedes aegypti that has been under development for about 20 years. The aim of the model is to promote understanding. We incorporate the recently discovered biological behavior of this mosquito: diapause. Namely, this is the laying of resistance eggs when the day light shortens, entering into the unfavorable season for reproduction in temperate climates, as described from laboratory experiments. When the model is challenged to answer the questions posed, it suggests that climate change, as experienced during the time of the field records, does not explain the observations. Furthermore, the standard climate change argument does not support a detailed analysis. In contrast, we find that while diapause is not expected to be a trait that is selected by natural conditions in a subtropical climate (simulations for Resistencia, AR), within temperate climates such as in Buenos Aires city (AR), there is pressure favoring the selection of the trait. As we move southward (the cities of Dolores, Azul, Tandil, and Mar del Plata), the pressure increases, while the probability of Aedes aegypti to become established in them decreases, being in accordance with the field observations. The model shows in addition that the field-observable effects of diapause depend on weather variables, especially precipitation, and the dynamics of the nutritional resources in the breeding sites. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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36 pages, 1529 KiB  
Article
Modeling and Stability Analysis of Within-Host IAV/SARS-CoV-2 Coinfection with Antibody Immunity
by Ahmed M. Elaiw, Raghad S. Alsulami and Aatef D. Hobiny
Mathematics 2022, 10(22), 4382; https://doi.org/10.3390/math10224382 - 21 Nov 2022
Cited by 13 | Viewed by 2091
Abstract
Studies have reported several cases with respiratory viruses coinfection in hospitalized patients. Influenza A virus (IAV) mimics the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) with respect to seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to [...] Read more.
Studies have reported several cases with respiratory viruses coinfection in hospitalized patients. Influenza A virus (IAV) mimics the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) with respect to seasonal occurrence, transmission routes, clinical manifestations and related immune responses. The present paper aimed to develop and investigate a mathematical model to study the dynamics of IAV/SARS-CoV-2 coinfection within the host. The influence of SARS-CoV-2-specific and IAV-specific antibody immunities is incorporated. The model simulates the interaction between seven compartments, uninfected epithelial cells, SARS-CoV-2-infected cells, IAV-infected cells, free SARS-CoV-2 particles, free IAV particles, SARS-CoV-2-specific antibodies and IAV-specific antibodies. The regrowth and death of the uninfected epithelial cells are considered. We study the basic qualitative properties of the model, calculate all equilibria and investigate the global stability of all equilibria. The global stability of equilibria is established using the Lyapunov method. We perform numerical simulations and demonstrate that they are in good agreement with the theoretical results. The importance of including the antibody immunity into the coinfection dynamics model is discussed. We have found that without modeling the antibody immunity, the case of IAV and SARS-CoV-2 coexistence is not observed. Finally, we discuss the influence of IAV infection on the dynamics of SARS-CoV-2 single-infection and vice versa. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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25 pages, 2487 KiB  
Article
A Predator–Prey Model with Beddington–DeAngelis Functional Response and Multiple Delays in Deterministic and Stochastic Environments
by Yuanfu Shao and Weili Kong
Mathematics 2022, 10(18), 3378; https://doi.org/10.3390/math10183378 - 17 Sep 2022
Cited by 7 | Viewed by 3307
Abstract
In view of prey’s delayed fear due to predators, delayed predator gestation, and the significance of intra-specific competition between predators when their populations are sufficiently large, a prey–predator population model with a density-dependent functional response is established in a deterministic environment. We research [...] Read more.
In view of prey’s delayed fear due to predators, delayed predator gestation, and the significance of intra-specific competition between predators when their populations are sufficiently large, a prey–predator population model with a density-dependent functional response is established in a deterministic environment. We research the existence and asymptotic stability of the equilibrium statuses. Then, taking into consideration environmental disturbances, we extend the deterministic model to a stochastic model and research the existence and stationary distributions of stochastic solutions. Finally, we perform some numerical simulations to verify the theoretical results. Numerical examples indicate that fear, delays and environmental disturbance play crucial roles in the system stability of the equilibrium status. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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15 pages, 946 KiB  
Article
Leveraging Geographically Distributed Data for Influenza and SARS-CoV-2 Non-Parametric Forecasting
by Pablo Boullosa, Adrián Garea, Iván Area, Juan J. Nieto and Jorge Mira
Mathematics 2022, 10(14), 2494; https://doi.org/10.3390/math10142494 - 18 Jul 2022
Cited by 1 | Viewed by 1759
Abstract
The evolution of some epidemics, such as influenza, demonstrates common patterns both in different regions and from year to year. On the contrary, epidemics such as the novel COVID-19 show quite heterogeneous dynamics and are extremely susceptible to the measures taken to mitigate [...] Read more.
The evolution of some epidemics, such as influenza, demonstrates common patterns both in different regions and from year to year. On the contrary, epidemics such as the novel COVID-19 show quite heterogeneous dynamics and are extremely susceptible to the measures taken to mitigate their spread. In this paper, we propose empirical dynamic modeling to predict the evolution of influenza in Spain’s regions. It is a non-parametric method that looks into the past for coincidences with the present to make the forecasts. Here, we extend the method to predict the evolution of other epidemics at any other starting territory and we also test this procedure with Spanish COVID-19 data. We finally build influenza and COVID-19 networks to check possible coincidences in the geographical distribution of both diseases. With this, we grasp the uniqueness of the geographical dynamics of COVID-19. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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17 pages, 17206 KiB  
Article
A Feasible Method to Control Left Ventricular Assist Devices for Heart Failure Patients: A Numerical Study
by Mohsen Bakouri, Ahmad Alassaf, Khaled Alshareef, Amor Smida, Ibrahim AlMohimeed, Abdulrahman Alqahtani, Mohamed Abdelkader Aboamer and Yousef Alharbi
Mathematics 2022, 10(13), 2251; https://doi.org/10.3390/math10132251 - 27 Jun 2022
Cited by 2 | Viewed by 2112
Abstract
Installing and developing a sophisticated control system to optimize left ventricular assist device (LVAD) pump speed to meet changes in metabolic demand is essential for advancing LVAD technology. This paper aims to design and implement a physiological control method for LVAD pumps to [...] Read more.
Installing and developing a sophisticated control system to optimize left ventricular assist device (LVAD) pump speed to meet changes in metabolic demand is essential for advancing LVAD technology. This paper aims to design and implement a physiological control method for LVAD pumps to provide optimal cardiac output. The method is designed to adjust the pump speed by regulating the pump flow based on a predefined set point (operating point). The Frank–Starling mechanism technique was adopted to control the set point within a safe operating zone (green square), and it mimics the physiological demand of the patient. This zone is predefined by preload control lines, which are known as preload lines. A proportional–integral (PI) controller was utilized to control the operating point within safe limits to prevent suction or overperfusion. In addition, a PI type 1 fuzzy logic controller was designed and implemented to drive the LVAD pump. To evaluate the design method, rest, moderate, and exercise scenarios of heart failure (HF) were simulated by varying the hemodynamic parameters in one cardiac cycle. This evaluation was conducted using a lumped parameter model of the cardiovascular system (CVS). The results demonstrated that the proposed control method efficiently drives an LVAD pump under accepted clinical conditions. In both scenarios, the left ventricle pressure recorded 112 mmHg for rest and 55 mmHg for exercise, and the systematic flow recorded 5.5 L/min for rest and 1.75 L/min for exercise. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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19 pages, 399 KiB  
Article
Global Stability and Thermal Optimal Control Strategies for Hyperthermia Treatment of Malignant Tumors
by Abdulkareem Afolabi Ibrahim, Normah Maan, Khairunadwa Jemon and Afeez Abidemi
Mathematics 2022, 10(13), 2188; https://doi.org/10.3390/math10132188 - 23 Jun 2022
Cited by 3 | Viewed by 1822
Abstract
Malignant tumor (cancer) is the leading cause of death globally and the annual cost of managing cancer is trillions of dollars. Although, there are established therapies including radiotherapy, chemotherapy and phototherapy for malignant tumors, the hypoxic environment of tumors and poor perfusion act [...] Read more.
Malignant tumor (cancer) is the leading cause of death globally and the annual cost of managing cancer is trillions of dollars. Although, there are established therapies including radiotherapy, chemotherapy and phototherapy for malignant tumors, the hypoxic environment of tumors and poor perfusion act as barriers to these therapies. Hyperthermia takes advantage of oxygen deficiency and irregular perfusion in the tumor environment to destroy malignant cells. Despite successes recorded with hyperthermia, there are concerns with the post-treatment condition of patients as well as the required thermal dose to prevent harm. The investigation of the dynamics of tumor-induced immune suppression with hyperthermia treatment using mathematical analysis and optimal control theory is potentially valuable in the development of hyperthermia treatment. The role of novel tumor-derived cytokines in counterattacking immune cells is considered in this study as a mechanism accounting for the aggressiveness of malignant tumors. Since biological processes are not instantaneous, a discrete time delay is used to model biological processes involved in tumor inhibitory mechanisms by secretion, the elaboration of suppressive cells, and effector cell differentiation to produce suppressive cells. Analytical results obtained using Lyapunov’s function indicate the conditions required for global stability of the tumor-present steady-state. A thermal optimal control strategy is pursued based on optimal control theory, and the best strategy to avoid adverse outcomes is obtained. We validate the analytical results numerically and demonstrate the impact of both inadequate and excessive heat on the dynamics of interactive cell functioning. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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15 pages, 3065 KiB  
Article
Turing Instability and Spatiotemporal Pattern Formation Induced by Nonlinear Reaction Cross-Diffusion in a Predator–Prey System with Allee Effect
by Yangyang Shao, Yan Meng and Xinyue Xu
Mathematics 2022, 10(9), 1500; https://doi.org/10.3390/math10091500 - 1 May 2022
Cited by 1 | Viewed by 1812
Abstract
The Allee effect is widespread among endangered plants and animals in ecosystems, suggesting that a minimum population density or size is necessary for population survival. This paper investigates the stability and pattern formation of a predator–prey model with nonlinear reactive cross-diffusion under Neumann [...] Read more.
The Allee effect is widespread among endangered plants and animals in ecosystems, suggesting that a minimum population density or size is necessary for population survival. This paper investigates the stability and pattern formation of a predator–prey model with nonlinear reactive cross-diffusion under Neumann boundary conditions, which introduces the Allee effect. Firstly, the ODE system is asymptotically stable for its positive equilibrium solution. In a reaction system with self-diffusion, the Allee effect can destabilize the system. Then, in a reaction system with cross-diffusion, through a linear stability analysis, the cross-diffusion coefficient is used as a bifurcation parameter, and instability conditions driven by the cross-diffusion are obtained. Furthermore, we show that the system (5) has at least one inhomogeneous stationary solution. Finally, our theoretical results are illustrated with numerical simulations. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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17 pages, 14108 KiB  
Article
An Optimal H-Infinity Controller for Left Ventricular Assist Devices Based on a Starling-like Controller: A Simulation Study
by Mohsen Bakouri, Ahmed Alassaf, Khaled Alshareef, Saleh Abdelsalam, Husham Farouk Ismail, Ali Ganoun and Abdul-Hakeem Alomari
Mathematics 2022, 10(5), 731; https://doi.org/10.3390/math10050731 - 25 Feb 2022
Cited by 10 | Viewed by 2122
Abstract
Left ventricular assist devices (LVADs) are emerging innovations that provide a feasible alternative treatment for heart failure (HF) patients to enhance their quality of life. In this work, a novel physiological control system to optimize LVAD pump speed using an H-infinity controller was [...] Read more.
Left ventricular assist devices (LVADs) are emerging innovations that provide a feasible alternative treatment for heart failure (HF) patients to enhance their quality of life. In this work, a novel physiological control system to optimize LVAD pump speed using an H-infinity controller was developed. The controller regulates the calculated target pump flow vs. measured pump flow to meet the changes in metabolic demand. The method proposes the implementation of the Frank–Starling mechanism (FSM) approach to control the speed of an LVAD using the left ventricle end-diastolic volume (Vlved) parameter (preload). An operating point was proposed to move between different control lines within the safe area to achieve the FSM. A proportional–integral (PI) controller was used to control the gradient angle between control lines to obtain the flow target. A lumped parameter model of the cardiovascular system was used to evaluate the proposed method. Exercise and rest scenarios were assessed under multi-physiological conditions of HF patients. Simulation results demonstrated that the control system was stable and feasible under different physiological states of the cardiovascular system (CVS). In addition, the proposed controller was able to keep hemodynamic variables within an acceptable range of the mean pump flow (Qp) (max = 5.2 L/min and min = 3.2 L/min) during test conditions. Full article
(This article belongs to the Special Issue Mathematical Biology: Modeling, Analysis, and Simulations, 2nd Edition)
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