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The complexity of mathematical models in biology has rendered model reduction an essential tool in the quantitative biologist's toolkit. For stochastic reaction networks described using the Chemical Master Equation, commonly used methods include time-scale separation, Linear Mapping Approximation, and state-space lumping. Despite the success of these techniques, they appear to be rather disparate, and at present, no general-purpose approach to model reduction for stochastic reaction networks is known. In this paper, we show that most common model reduction approaches for the Chemical Master Equation can be seen as minimizing a well-known information-theoretic quantity between the full model and its reduction, the Kullback–Leibler divergence defined on the space of trajectories. This allows us to recast the task of model reduction as a variational problem that can be tackled using standard numerical optimization approaches. In addition, we derive general expressions for propensities of a reduced system that generalize those found using classical methods. We show that the Kullback–Leibler divergence is a useful metric to assess model discrepancy and to compare different model reduction techniques using three examples from the literature: an autoregulatory feedback loop, the Michaelis–Menten enzyme system, and a genetic oscillator. [ABSTRACT FROM AUTHOR]

The Gilpin-Ayala (GA) ecosystem is one of the most important biological mathematical models. The exploration of various kinetics behaviours of GA-ecological model has attracted the attention of many mathematicians. This paper focuses on a nonlinear periodic GA-predation ecosystem with infinite distributed lags on time scales. In the sense of time scale, our model unifies the difference model and differential model of GA-predation ecosystem. We first discuss a class of auxiliary functions with only two real roots. By using these auxiliary functions, coincidence degree and some inequality techniques, we next obtain some existence conditions of periodic solution. Furthermore, we explore the global asymptotic stability of periodic solution on account of Lyapunov stability theory. An example and its simulation are provided to inspect the correctness and availability of our main results at last. [ABSTRACT FROM AUTHOR]

Controller motifs are simple biomolecular reaction networks with negative feedback. They can explain how regulatory function is achieved and are often used as building blocks in mathematical models of biological systems. In this paper we perform an extensive investigation into structural identifiability of controller motifs, specifically the so–called basic and antithetic controller motifs. Structural identifiability analysis is a useful tool in the creation and evaluation of mathematical models: it can be used to ensure that model parameters can be determined uniquely and to examine which measurements are necessary for this purpose. This is especially useful for biological models where parameter estimation can be difficult due to limited availability of measureable outputs. Our aim with this work is to investigate how structural identifiability is affected by controller motif complexity and choice of measurements. To increase the number of potential outputs we propose two methods for including flow measurements and show how this affects structural identifiability in combination with, or in the absence of, concentration measurements. In our investigation, we analyze 128 different controller motif structures using a combination of flow and/or concentration measurements, giving a total of 3648 instances. Among all instances, 34% of the measurement combinations provided structural identifiability. Our main findings for the controller motifs include: i) a single measurement is insufficient for structural identifiability, ii) measurements related to different chemical species are necessary for structural identifiability. Applying these findings result in a reduced subset of 1568 instances, where 80% are structurally identifiable, and more complex/interconnected motifs appear easier to structurally identify. The model structures we have investigated are commonly used in models of biological systems, and our results demonstrate how different model structures and measurement combinations affect structural identifiability of controller motifs. Author summary: Creating a mathematical model of a biological system can be a powerful way to gain insight into the behavior of the system. However, the accuracy and quality of model predictions depend heavily on model parameters. Compared to traditional human–engineered systems, such as mechanical or electrical systems, the availability of measurable outputs is severely limited for many biological systems. Furthermore, parameter estimation for biological models is often both challenging and associated with high cost. In this context, structural identifiability analysis is a helpful tool for finding the smallest or easiest to perform set of measurements that is sufficient to uniquely determine the model parameters. In this paper, we investigate a group of biological models called controller motifs, and we examine how varying model complexity and choice of measurements affect structural identifiability. We propose two alternative ways to include flow measurements as model output and show that structural identifiability can be achieved using a combination of concentration and/or flow measurements. Controller motifs can be used in a wide range of biological models, and our results can contribute to create structurally identifiable models. [ABSTRACT FROM AUTHOR]

Simple Summary: Coffee is an essential agricultural product in the worldwide economy. Unfortunately, the coffee berry borer (CBB), the crop's primary pest, significantly impacts the bean's quantity and quality. One strategy for controlling this insect is to use biological control agents, such as ants, some known for naturally living on coffee plantations and consuming CBB throughout all stages of development. Our paper examines a predator–prey interaction between these two insects using a novel mathematical model based on differential equations, where state variables correspond to adult CBBs, immature CBBs, and ants. Coffee is a relevant agricultural product in the global economy, with the amount and quality of the bean being seriously affected by the coffee berry borer Hypothenemus hampei (Ferrari), CBB, its principal pest. One of the ways to deal with this beetle is through biological control agents, like ants (Hymenoptera: Formicidae), some of which are characterized by naturally inhabiting coffee plantations and feeding on CBB in all their life stages. Our paper considers a predator–prey interaction between these two insects through a novel mathematical model based on ordinary differential equations, where the state variables correspond to adult CBBs, immature CBBs, and ants from one species, without specifying whether preying on the CBB is among their feeding habits, in both adult and immature stages. Through this new mathematical model, we could qualitatively predict the different dynamics present in the system as some meaningful parameters were varied, filling the existing gap in the literature and envisioning ways to manage pests. Mathematically, the system's equilibrium points were determined, and its stability was studied through qualitative theory. Bifurcation theory and numerical simulations were applied to illustrate the stability of the results, which were interpreted as conditions of the coexistence of the species, as well as conditions for eradicating the pest, at least theoretically, through biocontrol action in combination with other actions focused on eliminating only adult CBBs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a mathematical model given by ... where ... to enhance established mathematical methodologies for better understanding glioblastoma dynamics at the macroscopic scale. The tumor growth model exhibits an innovative structure even within the conventional framework, including a proliferation term, f (u), presented in a different form compared to existing macroscopic glioblastoma models. Moreover, it represents a further refined model by incorporating a calibration criterion based on the integration of a fractional derivative, a, which differs from the existing models for glioblastoma. Throughout this study, we initially discuss the modeling dynamics of the tumor growth model. Given the frequent recurrence observed in glioblastoma cases, we then track tumor mass formation and provide predictions for tumor visibility timing on medical imaging to elucidate the recurrence periods. Furthermore, we investigate the correlation between tumor growth speed and survival duration to uncover the relationship between these two variables through an experimental approach. To conduct these patient-specific analyses, we employ glioblastoma patient data and present the results via numerical simulations. In conclusion, the findings on tumor visibility timing align with empirical observations, and the investigations into patient survival further corroborate the well-established inter-patient variability for glioblastoma cases. [ABSTRACT FROM AUTHOR]

In this paper, we concern with the spatial dynamics of the lattice Lotka-Volterra competition system in a shifting habitat. We study the impact of the environmental deterioration rate on the population density under the strong competition condition. Our results show that if the environment deteriorates rapidly, both species will become extinct. However, when the environmental degradation rate is not so fast, the species with slow diffusion will go extinct, while those with fast diffusion will survive. The extinction of species with slow diffusion can be divided into two situations: one is the extinction caused by environmental deterioration faster than its own diffusion speed, the other is the extinction caused by slow diffusion speed under the influence of strong competition. [ABSTRACT FROM AUTHOR]

This paper proposes a mathematical modeling approach to examine the two-dimensional flow stagnates at x = 0 over a heated stretchable sheet in a porous medium influenced by nonlinear thermal radiation, variable viscosity, and MHD. This study’s main purpose is to examine how thermal radiation and varying viscosity affect fluid flow motion. Additionally, we consider the convective boundary conditions and incorporate the gyrotactic microorganisms equation, which describes microorganism behavior in response to fluid flow. The partial differential equations (PDEs) that represent the conservation equations for mass, momentum, energy, and microorganisms are then converted into a system of coupled ordinary differential equations (ODEs) through the inclusion of nonsimilarity variables. Using MATLAB’s built-in solver bvp4c, the resulting ODEs are numerically solved. The model’s complexity is assessed by plotting two-dimensional graphics of the solution profiles at various physical parameter values. The physical parameters considered in this study include skin friction coefficient, local Nusselt number, local Sherwood number, and density of motile microorganisms. These parameters measure, respectively, the roughness of the sheet, the transformation rate of heat, the rate at which mass is transferred to it, and the rate at which microorganisms are transferred to it. Our study shows that, depending on the magnetic parameter M, the presence of a porous medium causes a significant increase in fluid velocity, ranging from about 25% to 45%. Furthermore, with an increase in the Prandtl number Pr, we have seen a notable improvement of about 6% in fluid thermal conductivity. Additionally, our latest findings are in good agreement with published research for particular values. This study provides valuable insights into the behavior of fluid flow under various physical conditions and can be useful in designing and optimizing industrial processes. [ABSTRACT FROM AUTHOR]

In this paper, the generalized Kudryashov (GK) approach and the sine-Gordon expansion approach are used for constructing new specific analytical solutions of the deoxyribonucleic acid model, which include the well-known bell-shaped soliton, kink, singular kink, periodic soliton, contracted bell-shaped soliton and anti-bell-shaped soliton. The efficacy of these strategies demonstrates their utility and efficiency in addressing a wide range of integer and fractional-order nonlinear evolution problems. The physical relevance of the demonstrated results has been proven using three-dimensional forms. It is interesting to mention that the solutions achieved here using the provided methods are extra-extensive and may be used to explain the internal interaction of the deoxyribonucleic acid model originating in mathematical biology. The suggested approach was utilized to get exact traveling wave solutions for fractional nonlinear partial differential equations appearing in nonlinear science. [ABSTRACT FROM AUTHOR]

In this paper, we present an updated review on the mathematical modeling of different biological methods of hydrogen production. The presented mathematical modeling and methods range from inception to the current state-of-the-art developments in hydrogen production using biological methods. A comparative study was performed along with indications for future research and shortcomings of earlier research. This review will be helpful for all researchers working on different methods of hydrogen production. However, we only covered biological methods such as biophotolysis, fermentation and microbial electrolysis cells, and this list is not exhaustive of all other methods of hydrogen production. [ABSTRACT FROM AUTHOR]

Many challenges are still faced in bridging the gap between mathematical modeling and biological sciences. Measuring population immunity to assess the epidemiology of health and disease is a challenging task and is currently an active area of research. However, to meet these challenges, mathematical modeling is an effective technique in shaping the population dynamics that can help disease control. In this paper, we introduce a susceptible–infected–recovered (SIR) model and a susceptible–exposed–infected–recovered–deceased (SEIRD) model based on conformable space‐time partial differential equations (PDEs) for the coronavirus disease 2019 (COVID‐19) pandemic. As efficient analytical tools, we present new modifications based on the fractional exponential rational function method (ERFM) and an analytical technique based on the Adomian decomposition method for obtaining the solutions for the proposed models. These analytical approaches are more efficacious for obtaining analytical solutions for nonlinear systems of PDEs with conformable derivatives. The interesting result of this paper is that it yields new exact and approximate solutions to the proposed COVID‐19 pandemic models with conformable space‐time partial derivatives. [ABSTRACT FROM AUTHOR]

Inverse Data Envelopment Analysis (IDEA) has gained significant attention among researchers as an analytical tool for assessing efficiency. Estimating input values while ensuring cost efficiency through changes in output quantities is complex and sensitive. In contrast to conventional data envelopment analysis methods, IDEA enables the quantification of input/output variations resulting from output/input reductions or expansions while preserving the measurement efficiency level. This paper aims to introduce a novel approach for estimating input values by incrementally increasing the value of each output of decision-making units (DMUs) during the evaluation process, thereby maintaining or improving cost efficiency. By utilizing IDEA and manipulating the output values of the DMU under evaluation, the input values are estimated while ensuring constant or enhanced cost efficiency. A simple numerical example and a case study from a Turkish automotive company are presented to validate the proposed method. The obtained results demonstrate significant improvements and hold promising prospects, indicating the potential applicability of this approach to other similar problems and research areas. [ABSTRACT FROM AUTHOR]

Stochastic ultimate boundedness has always been a very important property, which plays an important role in the study of stochastic models. Thus, in this paper, we will study a stochastic periodic chemostat system, in which we assume that the nutrient input concentration and noise intensities are periodic. In order to make the stochastic periodic model have mathematical and biological significance, we will study a very important issue: the existence, uniqueness and ultimate boundedness of a global positive solution for a stochastic periodic chemostat system. [ABSTRACT FROM AUTHOR]

Mathematical modeling in biology is quite interesting in the field of real-world problems. This research paper focused on the interaction between two prey and one predator species. Here, our interaction is based upon the competition between two prey and one predator including an additive Allee effect in the predator population along with a Holling type II functional response. Further, this intuition allowed us to prove the positive invariance and boundedness of the model. This analysis shows that there are six equilibrium points including the coexistence of all three populations. Stability analyses are also derived and proved both locally and globally. Also in this paper, we discussed the optimal control approach to reduce the population affected by an Allee effect by the predator population. Numerical simulations are carried out to support our theoretical results. [ABSTRACT FROM AUTHOR]

Understanding spermatozoa transportation in the human female cervical canal, particularly in relation to the fertilization process, holds significant physiological importance. Present paper accords with the assessment of the self-propelling sheet of spermatozoa (SPSS) between porous cervical walls continuously secreting viscoelastic mucus in the human cervical canal (HCC). Mathematical modelling of the biological model yielded two inhomogeneous partial differential equations. These partial differential equations along with Saffman slip conditions are solved for exact solutions. It is delineated that an increase in the Reynolds number, Jeffrey parameter, and slip parameter results in an increase in the propulsive velocity and mucus velocity. Conversely, an increase in Darcy number results in a decrease in both propulsive and mucus velocity. When the secreting velocity is constant, the propulsive velocity is maximal, and when the secreting velocity is exponential, it is minimal. Spermatozoa move through the Jeffrey fluid more quickly than they do in the Newtonian fluid. The propulsive velocity through the channel is higher than in unbounded domain. The propulsive velocity of the spermatozoa in cervical canal is approximately 80 μ m/s in particular environment. [ABSTRACT FROM AUTHOR]

In this paper, we show the possibility of creating and identifying the features of an artificial neural network (ANN), which consists of mathematical models of biological neurons. The FitzHugh–Nagumo (FHN) system is used as a paradigmatic model demonstrating basic neuron activities. First, in order to reveal how biological neurons can be embedded within an ANN, we train the ANN with nonlinear neurons to solve a basic image recognition problem with an MNIST database; next, we describe how FHN systems can be introduced into this trained ANN. After all, we show that an ANN with FHN systems inside can be successfully trained with improved accuracy comparing with first trained ANN and then with inserted FHN systems. This approach opens up great opportunities in terms of the direction of analog neural networks, in which artificial neurons can be replaced by more appropriate biological ones. [ABSTRACT FROM AUTHOR]

Despite recent advances in the mathematical modeling of biological processes and real-world situations raised in the day-to-day life phase, some phenomena such as immune cell populations remain poorly understood. The mathematical modeling of complex phenomena such as immune cell populations using nonlinear differential equations seems to be a quite promising and appropriate tool to model such complex and nonlinear phenomena. Fractional differential equations have recently gained a significant deal of attention and demonstrated their relevance in modeling real phenomena rather than their counterpart, classical (integer) derivative differential equations. We report in this paper a mathematical approach susceptible to answering some relevant questions regarding the side effects of ionizing radiation (IR) on DNA with a particular focus on double-strand breaks (DSBs), leading to the destruction of the cell population. A theoretical elucidation of the population memory was carried out within the framework of fractional differential equations (FODEs). Using FODEs, the mathematical approach presented herein ensures connections between fractional calculus and the nonlocal feature of the fractional order of immune cell populations by taking into account the memory trace and genetic qualities that are capable of integrating all previous actions and considering the system's long-term history. An illustration of both fractional modeling, which provides an excellent framework for the description of memory and hereditary properties of immune cell populations, is elucidated. The mathematics presented in this research hold promise for modeling real-life phenomena and paves the way for obtaining accurate model parameters resulting from the mathematical modeling. Finally, the numerical simulations are conducted for the analytical approach presented herein to elucidate the effect of various parameters that govern the influence of ionizing irradiation on DNA in immune cell populations as well as the evolution of cell population dynamics, and the results are presented using plots and contrasted with previous theoretical findings. [ABSTRACT FROM AUTHOR]

Patients with metastatic castration-resistant prostate cancer (mCRPC) are divided into three groups based on their response to Abiraterone treatment: best responder, responder, and non-responder. In the latter two groups, successful outcomes may not be achieved due to the development of drug-resistant cells in the tumor environment during treatment. To overcome this challenge, a secondary drug can be used to control the population of drug-resistant cells, potentially leading to a longer period of disease inhibition. This paper proposes using a combination of Docetaxel and Abiraterone in some polytherapy methods to control both the overall cancer cell population and the drug-resistant subpopulation. To investigate the competition and evolution of mCRPC cancer phenotypes, as in previous studies, the Evolutionary Game Theory (EGT) has been used as a mathematical modeling of evolutionary biology concepts. [ABSTRACT FROM AUTHOR]

Such models could be used to develop feedback control strategies in fed-batch or perfused bioreactors. To completely circumvent the abovementioned problem of system underdetermination, Bastin et al. [[3]] use relatively simple macroscopic models that allow obtaining a unique flux distribution to describe VERO cell behavior in different bioreactor culture conditions, e.g., exponential growth phase or substrate-limited growth phase. This Special Issue (SI) of Processes on Mathematical Modeling and Control of Bioprocesses (MMCB) contains papers focusing, on the one hand, on mathematical modeling of biological processes at different scales ranging from microscopic to macroscopic levels and, on the other hand, on model-based estimation, optimization and control of these processes. [Extracted from the article]

Mathematical modeling is a powerful method to understand how biological systems work. By creating a mathematical model of a given phenomenon one can investigate which model assumptions are needed to explain the phenomenon and which assumptions can be omitted. Creating an appropriate mathematical model (or a set of models) for a given biological system is an art, and classical textbooks on mathematical modeling in biology go into great detail in discussing how mathematical models can be understood via analytical and numerical analyses. In the last few decades mathematical modeling in biology has grown in size and complexity, and along with this growth new tools for the analysis of mathematical models and/or comparing models to data have been proposed. Examples of tools include methods of sensitivity analyses, methods for comparing alternative models to data based on AIC/BIC/etc.), and mixed-effect-based fitting of models to data. I argue that the use of many of these "toolbox" approaches for the analysis of mathematical models has negatively impacted the basic philosophical principle of the modeling--to understand what the model does and why it does what it does. I provide several examples of limitations of these toolbox-based approaches and how they hamper generation of insights about the system in question. I also argue that while we should learn new ways to automate mathematical modeling-based analyses of biological phenomena, we should aim beyond a mechanical use of such methods and bring back intuitive insights into model functioning, by remembering that after all, modeling is an art and not simply engineering. [ABSTRACT FROM AUTHOR]

The paper is concerned with optimal control problems for a parabolic system, coupled with zero Neumann boundary conditions and with nonlinear source terms. Inspired by applications in biology and medicine, the system aims to describe two species in competition in the same spatial region and is supplemented with measure valued distributed controls, acting as source terms. Introducing general cost functionals, one can study optimal control problems. We prove the existence of solutions for the parabolic equations with measure valued controls, together with suitable stability estimates. Moreover, the existence of optimal solutions in a distributional sense is also established. [ABSTRACT FROM AUTHOR]

In this paper, the double-chain model for deoxyribonucleic acid (DNA) is studied analytically by taking advantage of two reliable methodologies: the new auxiliary equation method (NAEM) and the expa function method. The deoxyribonucleic acid (DNA) contains the genetic information that creatures require for their survival and reproduction. The used approaches produce exact explicit solutions to the double chain model of DNA in mathematical biology, which are presented in this paper. Many novel solutions such as trigonometric, exponential, singular, and hyperbolic solutions, are obtained by using the aforementioned techniques. Numerical simulations are employed to supplement the obtained solutions, making this research biologically relevant. Eventually, kink wave, nonlinear wave, plane wave-front and doubly soliton profiles of solutions are presented in analysis and discussion section. It is indeed important to note that the solutions produced using these techniques are more generalized and can be more useful to demonstrate the internal interactions of the double chain DNA model. [ABSTRACT FROM AUTHOR]

Symmetries are ubiquitous in nature. Almost all organisms have some kind of "symmetry", meaning that their shape does not change under some geometric transformation. This geometrical concept of symmetry is intuitive and easy to recognize. On the other hand, the behavior of many biological systems over time can be described with ordinary differential equations. These dynamic models may also possess "symmetries", meaning that the time courses of some variables remain invariant under certain transformations. Unlike the previously mentioned symmetries, the ones present in dynamic models are not geometric, but infinitesimal transformations. These mathematical symmetries can be related to certain features of the system's dynamic behavior, such as robustness or adaptation capabilities. However, they can also arise from questionable modeling choices, which may lead to non-identifiability and non-observability. This paper provides an overview of the types of symmetries that appear in dynamic models, the mathematical tools available for their analyses, the ways in which they are related to system properties, and the implications for biological modeling. [ABSTRACT FROM AUTHOR]

This paper is devoted to the construction and analysis of coupled mathematical models of hydrophysics and biological kinetics used for predicting hazardous natural phenomena occurring in shallow basins. The propagation and transformation of aquatic organisms is affected by such physical factors as three-dimensional spatial motion of water taking into account the advective transfer and microturbulent diffusion, spatially inhomogeneous distribution of temperature, salinity, and oxygen. Biogenic pollutants cause algae growth, including toxic and harmful ones; this growth can cause hazardous phenomena in the basin, including eutrophication and suffocation phenomena. A three-dimensional mathematical model of hydrodynamics is constructed and used for calculating the water flow velocity field. To investigate hazardous phenomena in a shallow basin related to suffocation phenomena in it, a three-dimensional spatially inhomogeneous ichthyological model of commercial fish dynamics is developed. Models of observations parameterized on the basis of stoichiometric relations, Monod, Michaelis–Menten, and Mitscherlich–Baule laws that describe the consumption and accumulation of nutrients by phytoplankton and commercial detritophagous fish and the growth of aquatic organisms depending on the spatial distribution of salinity, temperature, and oxygen regimen are considered. To calibrate and verify the models, constantly updated ecological databases obtained, in particular, in field research of the Sea of Azov and Taganrog Bay are used. To improve the accuracy of predictive simulation, the field data is filtered using the Kalman algorithm. As a result of processing the hydrological data, salinity and temperature isolines in the surface layer are obtained; for this purpose, a recognition algorithm is used. Using interpolation and superposition of domain boundaries, more detailed depth, salinity, and temperature maps for the Sea of Azov are obtained. Numerical methods for solving the formulated problems that are based on finite difference schemes taking into account the degree of filling of the computation domain control cells are developed. These methods are implemented on high-performance computers, and they decrease the numerical solution error and reduce the computation time by several fold. Based on the numerical implementation of the developed models, hazardous natural phenomena in shallow basins (related to the propagation of harmful pollutants), eutrophication, and algae bloom, which causes suffocation phenomena, are reconstructed. [ABSTRACT FROM AUTHOR]

Mathematical modeling of biological systems is an important issue having significant effect on human beings. In this direction, the description of immune systems is an attractive topic as a result of its ability to detect and eradicate abnormal cells. Therefore, this manuscript aims to investigate the asymptotic behavior of immunogenic tumor dynamics based on a new fractional model constructed by the concept of general fractional operators. We discuss the stability and equilibrium points corresponding to the new model; then we modify the predictor–corrector method in general sense to implement the model and compare the associated numerical results with some real experimental data. As an achievement, the new model provides a degree of flexibility enabling us to adjust the complex dynamics of biological system under study. Consequently, the new general model and its solution method presented in this paper for the immunogenic tumor dynamics are new and comprise quite different information than the other kinds of classical and fractional equations. In addition to these, we implement a tracking control method in order to decrease the development of tumor‐cell population. The satisfaction of control purpose is confirmed by some simulation results since the controlled variables track the tumor‐free steady state in the whole realistic cases. [ABSTRACT FROM AUTHOR]

In this paper we provide a description of the project DrIVE-MATH, highlighting the main goals, intellectual outputs, outcomes, the involved partners, and activities and reports from the three-years' project. At the end we discuss the impact of the new proposed Education models at various levels, from students, to HEIs, to stakeholders. [ABSTRACT FROM AUTHOR]

The School of Engineering of the Polytechnic of Porto (ISEP) has embraced the DrIVE-MATH project, since September 2017. Active-learning (AL) techniques were implemented in several Math courses, namely Linear Algebra and Analytic Geometry, Probability and Statistics, Statistical Models, Computational Mathematics, and Differential and Integral Calculus I. In this paper, we will share the strengths, weaknesses, opportunities and threats of the implementation of the active-learning (AL) environment in these courses. We will detail the courses' plans, emphasizing the syllabus, pedagogical methodologies, assessment methods, students' perceptions, and other related issues. Several questionnaires were posed to the students enrolled in these Math courses during the last three academic years. The statistical analysis of the gathered data provided valuable indications of students' perceptions on the effectiveness of several AL methods, on the development of their own essential (soft+hard) skills. These skills will be a valuable resource to their future professional and personal lives. The 5th Industrial Revolution is just around the corner. [ABSTRACT FROM AUTHOR]

Both mathematical models and biological model systems stand as tractable representations of complex biological systems or behaviors. They facilitate research and provide insights, and they can describe general rules. Models that represent biological processes or formalize general hypotheses are essential to any broad understanding. Mathematical or biological models necessarily omit details of the natural systems and thus may ultimately be "incorrect" representations. A key challenge is that tractability requires relatively simple models but simplification can result in models that are incorrect in their qualitative, broad implications if the abstracted details matter. Our paper discusses this tension, and how we can improve our inferences from models. We advocate for further efforts dedicated to model development, improvement, and acceptance by the scientific community, all of which may necessitate a more explicit discussion of the purpose and power of models. We argue that models should play a central role in reintegrating biology as a way to test our integrated understanding of how molecules, cells, organs, organisms, populations, and ecosystems function. [ABSTRACT FROM AUTHOR]

Coupled hybrid models, gathering the advantages of multiscale approaches, are nowadays spreading in the field of mathematical models for biological phenomena. The structure of the investigated system arises in modelling collective cell migrations and growth, and particularly fits to those scenarios in which the dynamics of discrete particles is influenced by a continuum chemical concentration. In this paper we focus on existence of solutions in the case of a local concentration. Our construction will rely on approximation techniques, involving a suitable family approximating problems with a nonlocal term in the corresponding Ode, and passage to the limit. [ABSTRACT FROM AUTHOR]

In this paper, we explore the effects of biological (pathological) and mechanical damage on bone tissue within a benchmark model. Using the Finite Element Methodology, we analyze and numerically test the model's components, capabilities, and performance under physiologically and pathologically relevant conditions. Our findings demonstrate the model's effectiveness in simulating bone remodeling processes and self-repair mechanisms for micro-damage induced by biological internal conditions and mechanical external ones within bone tissue. This article is the second part of a series, where the first part presented the mathematical model and the biological and physical significance of the terms used in a simplified benchmark model. It explored the bone remodeling model's application, implementation, and results under physiological conditions. [ABSTRACT FROM AUTHOR]

We have come a long way since the start of the COVID-19 pandemicÑfrom hoarding toilet paper and wiping down groceries to sending our children back to school and vaccinating billions. Over this period, the global community of epidemiologists and evolutionary biologists has also come a long way in understanding the complex and changing dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus that causes COVID-19. In this Review, we retrace our steps through the questions that this community faced as the pandemic unfolded. We focus on the key roles that mathematical modeling and quantitative analyses of empirical data have played in allowing us to address these questions and ultimately to better understand and control the pandemic. [ABSTRACT FROM AUTHOR]

The article emphasizes the significance of including life scientists in quantitative systems pharmacology (QSP) modeling teams. QSP models integrate data on physiology, pathophysiology, and pharmacology to enhance drug development. However, many QSP modelers lack a background in biological sciences, which can result in limitations in model quality and impact. Life scientists contribute essential expertise in model design, data curation, and result interpretation, ensuring the model's relevance and biological accuracy. Without life scientists, modelers may overlook crucial connections and construct models with unrealistic parameters. Including life scientists in modeling teams enhances model development and outcomes. The article suggests providing educational programs and workshops to train life scientists in modeling concepts and biology. Including life scientists in the core modeling team leads to more efficient model building and improved result interpretation. [Extracted from the article]

This work investigates the dynamics of discrete reaction-diffusion Gierer-Meinhardt system as mathematical models of biological pattern formation. We study the system's local asymptotic behaviour with and without the diffusion once developing the discrete integer variant of the well-known Gierer-Meinhardt model and proving that the model has a unique equilibrium. The requirements for the steady-state solution's local and global stability are found with the help of relevant approaches and the Lyapunov technique. Two large biological models and simulations are used throughout the work to validate the utility of the suggested technique. [ABSTRACT FROM AUTHOR]

In this study, we investigate the application of fractional calculus to the mathematical modeling of biological systems, focusing on fractional-order-in-time partial differential equations (FTPDEs). Fractional derivatives, especially those defined in the Caputo sense, provide a useful tool for modeling memory and hereditary characteristics, which are problems that are frequently faced with integer-order models. We use the Chebyshev spectral approach for spatial derivatives, which is known for its faster convergence rate, in conjunction with the L 1 scheme for time-fractional derivatives because of its high accuracy and robustness in handling nonlocal effects. A detailed theoretical analysis, followed by a number of numerical experiments, is performed to confirmed the theoretical justification. Our simulation results show that our numerical technique significantly improves the convergence rates, effectively tackles computing difficulties, and provides a realistic simulation of biological population dynamics. [ABSTRACT FROM AUTHOR]

Background: Antimicrobial resistance (AMR) is considered one of the key health challenges facing the globe. It has various implications for shaping the future of the health and healthcare industries. Aim: This study aims to explore potential socioeconomic and health system factors shaping the AMR burden globally. Methods: This secondary dataanalysis study was conducted during the period from 2022 to 2023 between Cairo and Copenhagen. Data from the "global sewage surveillance project" in addition to several published datasets were composed, validated, and cleaned. Several exploratory data analyses were applied to examine the relationship between AMR and different factors, especially health system-related and socio-economic conditions and environmental and behavioral-related factors. Mathematical modeling using generalized multiple mixed models (GLMM) modeling techniques was applied to shape and describe these relations. The dependent variable was AMR burden measured by the number of resistant genes in the sewage sample that were expressed by FPKM; the independent variables were more than forty, covering various proposed factors. Results: The stepwise multiple fixed effects modeling showed that the proportion of the population with basic drinking water, care for newborns index, and the number of all health workers in the 10,000 population are the main determinants with negative coefficients. When a random effect model was fitted, it showed a significant association between AMR burden and region (p < 0.001). Conclusion: This study highlights the importance of basic hygienic measures and the empowered healthcare system in reducing the burden of antimicrobial resistance globally. Regional variations in AMR prevalence emphasize the need for tailored interventions that address specific regional contexts to combat this global health challenge effectively. [ABSTRACT FROM AUTHOR]

We present a novel set of quantitative measures for "likeness" (error function) designed to alleviate the time-consuming and subjective nature of manually comparing biological recordings from electrophysiological experiments with the outcomes of their mathematical models. Our innovative "blended" system approach offers an objective, high-throughput, and computationally efficient method for comparing biological and mathematical models. This approach involves using voltage recordings of biological neurons to drive and train mathematical models, facilitating the derivation of the error function for further parameter optimization. Our calibration process incorporates measurements such as action potential (AP) frequency, voltage moving average, voltage envelopes, and the probability of post-synaptic channels. To assess the effectiveness of our method, we utilized the sea slug Melibe leonina swim central pattern generator (CPG) as our model circuit and conducted electrophysiological experiments with TTX to isolate CPG interneurons. During the comparison of biological recordings and mathematically simulated neurons, we performed a grid search of inhibitory and excitatory synapse conductance. Our findings indicate that a weighted sum of simple functions is essential for comprehensively capturing a neuron's rhythmic activity. Overall, our study suggests that our blended system approach holds promise for enabling objective and high-throughput comparisons between biological and mathematical models, offering significant potential for advancing research in neural circuitry and related fields. [ABSTRACT FROM AUTHOR]

Syphilis is one of the deadly sexually-transmitted diseases. This paper studied the impacts of sexual behavior, mass media report and treatment of infected individuals on the dynamics of syphilis transmission. The analytical and numerical analyses of the model are presented. The disease free equilibrium of the model is both locally and globally asymptotic stable when the associated reproduction number is less than unity. Analysis of the Reproduction number shows that it is not possible to control syphilis disease transmission if the rate of individuals practicing risky sexual behavior is high. Furthermore, the treatment of late (latent and tertiary) syphilis infection is beneficial to the infected individuals, but has no impact in the lowering of the reproduction number. This study suggests that the effective control strategy of syphilis must focus on lowering the number of individuals practicing risky sexual behavior and applying higher treatment rates for early syphilis infections. Furthermore, the media function should address the issues regarding safe sexual behavior. [ABSTRACT FROM AUTHOR]

The present paper theoretically accords a biomechanical model with a brief biological and mathematical description of the growing embryo transport in the human fallopian tube. This model incorporates transport mechanisms that involve the pressure gradient at the ampullar region entrance, peristaltic contractions of smooth muscle cells and swaying motions of ciliary cells. Shear rate dependent viscoelastic fluid characterizes the nature of growing embryo and secreted fluid. The pressure gradient at the ampullar region entrance ξ , metachronal wave parameter ∊ , amplitude ratio ϕ , the ratio of shear viscosity at infinity shear rate to shear viscosity at zero shear rate μ ∞ / 0 and Weissenberg number We emerged as flow control parameters. The assessment showed that the fluid model parameters ( μ ∞ / 0 and We) have opposite effects on appropriate residue time, boluses size and local flow behaviour. Progesterone ( P 4) and estradiol ( E 2 ), prostaglandin E 2 ( PGE 2 ) and prostaglandin F 2 α ( PGF 2 α ) constraint the fluid motion by controlling the ξ , secretion of the fluid through the goblet cells and amplitudes of both the sinusoidal and the metachronal waves. Furthermore, a comparison between the current results and available literature is made. The relevance of the obtained results with the growing embryo transport in the human fallopian tube is also explored. [ABSTRACT FROM AUTHOR]

As mathematical models of biological pattern generation, this study investigates the dynamics of the fractional discrete Gierer-Meinhardt reaction-diffusion system. After deriving the discrete non-integer fractional variant of the Gierer-Meinhardt system and establishing that the system has a unique equilibrium, we analyze the system's local asymptotic behavior in both the presence and absence of diffusion. The conditions for the global stability of the steady-state solution are determined using relevant approaches and the Lyapunov method. Throughout the study, two comprehensive biological models and simulations are employed to validate the utility of the considered approach. [ABSTRACT FROM AUTHOR]

The research & development (R&D) of novel therapeutic agents for the treatment of autoimmune diseases is challenged by highly complex pathogenesis and multiple etiologies of these conditions. The number of targeted therapies available on the market is limited, whereas the prevalence of autoimmune conditions in the global population continues to rise. Mathematical modeling of biological systems is an essential tool which may be applied in support of decision-making across R&D drug programs to improve the probability of success in the development of novel medicines. Over the past decades, multiple models of autoimmune diseases have been developed. Models differ in the spectra of quantitative data used in their development and mathematical methods, as well as in the level of "mechanistic granularity" chosen to describe the underlying biology. Yet, allmodels strive towards the same goal: to quantitatively describe various aspects of the immune response. The aim of this review was to conduct a systematic review and analysis of mathematical models of autoimmune diseases focused on the mechanistic description of the immune system, to consolidate existing quantitative knowledge on autoimmune processes, and to outline potential directions of interest for future model-based analyses. Following a systematic literature review, 38 models describing the onset, progression, and/or the effect of treatment in 13 systemic and organ-specific autoimmune conditions were identified, mostmodels developed for inflammatory bowel disease, multiple sclerosis, and lupus (5 models each). =70% of the models were developed as nonlinear systems of ordinary differential equations, others - as partial differential equations, integro-differential equations, Boolean networks, or probabilistic models. Despite covering a relatively wide range of diseases, most models described the same components of the immune system, such as T-cell response, cytokine influence, or the involvement of macrophages in autoimmune processes. All models were thoroughly analyzed with an emphasis on assumptions, limitations, and their potential applications in the development of novel medicines. [ABSTRACT FROM AUTHOR]

This article examines the question of whether Alzheimer's disease (AD) is a disease that affects individuals differently. It discusses the biological markers that characterize AD and lead to brain degeneration. The article suggests that different variants of AD may arise from a complex interaction of various factors. It also discusses the presence of other diseases and risk factors in AD, as well as the variability in abnormal proteins and the effectiveness of certain treatments. Overall, the article emphasizes the need for further research to fully understand AD and proposes personalized treatment strategies. [Extracted from the article]

The main purpose of the article is to develop a multifactorial model for rapid assessment of the efficiency of biological wastewater treatment reactors. A mathematical model of the process of biological wastewater treatment has been developed based on: changes in the concentration of organic contaminants in the bioreactor over time, taking into account the uneven flow of wastewater to the treatment plant, the process of substrate entering the bioreactor (different amounts may enter at different times). The software implementation of the proposed algorithm for solving the corresponding model problem in Python is carried out. The results of computer experiments on the study of the efficiency of wastewater treatment in biological treatment reactors for different operating conditions of facilities are presented. In particular, such processes were considered with taking into account the unevenness of the load, because the maximum cleaning loads are in the morning and in the evening. The task was solved to simulate a real situation and show how cleaning takes place at the maximum load at a certain time of the day. The results obtained will be useful for calculations in the design of biological treatment facilities or in the reconstruction of existing bioreactors for their prospective operation under new operating conditions. [ABSTRACT FROM AUTHOR]

Mathematical modelling of biological population dynamics often involves proposing high-fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an approximate coarse-grained differential equation that captures population-level features only. These coarse-grained models are only accurate in certain asymptotic parameter regimes, such as enforcing that the time scale of individual motility far exceeds the time scale of birth/death processes. When these coarse-grained models are accurate, the discrete model still abides by conservation laws at the microscopic level, which implies that there is some macroscopic conservation law that can describe the macroscopic dynamics. In this work, we introduce an equation learning framework to find accurate coarse-grained models when standard continuum limit approaches are inaccurate. We demonstrate our approach using a discrete mechanical model of epithelial tissues, considering a series of four case studies that consider problems with and without free boundaries, and with and without proliferation, illustrating how we can learn macroscopic equations describing mechanical relaxation, cell proliferation, and the equation governing the dynamics of the free boundary of the tissue. While our presentation focuses on this biological application, our approach is more broadly applicable across a range of scenarios where discrete models are approximated by approximate continuum-limit descriptions. [ABSTRACT FROM AUTHOR]

Influenza A virus (IAV) infections represent a substantial global health challenge and are often accompanied by coinfections involving secondary viruses or bacteria, resulting in increased morbidity and mortality. The clinical impact of coinfections remains poorly understood, with conflicting findings regarding fatality. Isolating the impact of each pathogen and mechanisms of pathogen synergy during coinfections is challenging and further complicated by host and pathogen variability and experimental conditions. Factors such as cytokine dysregulation, immune cell function alterations, mucociliary dysfunction, and changes to the respiratory tract epithelium have been identified as contributors to increased lethality. The relative significance of these factors depends on variables such as pathogen types, infection timing, sequence, and inoculum size. Mathematical biological modeling can play a pivotal role in shedding light on the mechanisms of coinfections. Mathematical modeling enables the quantification of aspects of the intra-host immune response that are difficult to assess experimentally. In this narrative review, we highlight important mechanisms of IAV coinfection with bacterial and viral pathogens and survey mathematical models of coinfection and the insights gained from them. We discuss current challenges and limitations facing coinfection modeling, as well as current trends and future directions toward a complete understanding of coinfection using mathematical modeling and computer simulation. [ABSTRACT FROM AUTHOR]

A function with finite asymptotic limits gives rise to a transition equation between a "past system" and a "future system." This question is analyzed in the case of nonautonomous coercive nonlinear scalar ordinary differential equations with concave derivative with respect to the state variable. The fundamental hypothesis is the existence of three hyperbolic solutions for the limit systems, in which case the upper and lower ones are attractive. All the global dynamical possibilities are described in terms of the internal dynamics of the pullback attractor: cases of tracking of the two hyperbolic attractive solutions or lack of it (tipping) may arise. This analysis, made in the language of processes and also in terms of the skewproduct formulation of the problem, includes cases of rate-induced critical transitions, as well as cases of phase-induced and size-induced tipping. The conclusions are applied in models of mathematical biology and population dynamics. Rate-induced tracking phenomena causing extinction of a native species or invasion of a nonnative one are described, as well as population models affected by a Holling type III functional response to predation where tipping due to the changes in the size of the transition may occur. In all these cases, the appearance of a critical transition can be understood as a consequence of the strength of the Allee effect. [ABSTRACT FROM AUTHOR]

Likelihood ratios are frequently utilized as basis for statistical tests, for model selection criteria and for assessing parameter and prediction uncertainties, e.g. using the profile likelihood. However, translating these likelihood ratios into p-values or confidence intervals requires the exact form of the test statistic's distribution. The lack of knowledge about this distribution for nonlinear ordinary differential equation (ODE) models requires an approximation which assumes the so-called asymptotic setting, i.e. a sufficiently large amount of data. Since the amount of data from quantitative molecular biology is typically limited in applications, this finite-sample case regularly occurs for mechanistic models of dynamical systems, e.g. biochemical reaction networks or infectious disease models. Thus, it is unclear whether the standard approach of using statistical thresholds derived for the asymptotic large-sample setting in realistic applications results in valid conclusions. In this study, empirical likelihood ratios for parameters from 19 published nonlinear ODE benchmark models are investigated using a resampling approach for the original data designs. Their distributions are compared to the asymptotic approximation and statistical thresholds are checked for conservativeness. It turns out, that corrections of the likelihood ratios in such finite-sample applications are required in order to avoid anti-conservative results. Author summary: Statistical methods based on the likelihood ratio are ubiquitous in mathematical modelling in systems biology. For example confidence intervals of estimated parameters rely on the statistical properties of the likelihood-ratio test. However, it is often overlooked that these intervals sizes rely on assumptions on the amounts of data, which are regularly violated in typical applications in systems biology. By checking the appropriateness of these assumptions in models from the literature, this study shows that in a surprisingly large fraction of confidence intervals might be too small. Using a geometric interpretation of parameter estimation in the so-called data space, it is motivated why these issues appear and how they depend on the identifiability of the model parameters. In order to avoid such problematic situations, this work makes suggestions on how to adapt the statistical threshold values for likelihood-ratio test. By this, it can be assured that valid statistical conclusions are drawn from the analysis, also in situations where only smaller data sets are available. Such corrections yield for example more conservative confidence interval sizes and thus decrease a potential underestimation of the parameter uncertainty. [ABSTRACT FROM AUTHOR]

Ordinary differential equations are frequently employed for mathematical modeling of biological systems. The identification of mechanisms that are specific to certain cell types is crucial for building useful models and to gain insights into the underlying biological processes. Regularization techniques have been proposed and applied to identify mechanisms specific to two cell types, e.g., healthy and cancer cells, including the LASSO (least absolute shrinkage and selection operator). However, when analyzing more than two cell types, these approaches are not consistent, and require the selection of a reference cell type, which can affect the results. To make the regularization approach applicable to identifying cell-type specific mechanisms in any number of cell types, we propose to incorporate the clustered LASSO into the framework of ordinary differential equation modeling by penalizing the pairwise differences of the logarithmized fold-change parameters encoding a specific mechanism in different cell types. The symmetry introduced by this approach renders the results independent of the reference cell type. We discuss the necessary adaptations of state-of-the-art numerical optimization techniques and the process of model selection for this method. We assess the performance with realistic biological models and synthetic data, and demonstrate that it outperforms existing approaches. Finally, we also exemplify its application to published biological models including experimental data, and link the results to independent biological measurements. Author summary: Mathematical models enable insights into biological systems beyond what is possible in the wet lab alone. However, constructing useful models can be challenging, since they both need a certain amount of complexity to adequately describe real-world observations, and simultaneously enough simplicity to enable understanding of these observations and precise predictions. Regularization techniques were suggested to tackle this challenge, especially when building models that describe two different types of cells, such as healthy and cancer cells. Typically, both cell types have a large portion of biological mechanisms in common, and the task is to identify the relevant differences that need to be included into the model. For more than two types of cells, the existing approaches are not readily applicable, because they require defining one of the cell types as reference, which potentially influences the results. In this work, we present a regularization method that is independent from the choice of a reference. We demonstrate its working principle and compare its performance to existing approaches. Since we implemented this method in a freely available software package, it is accessible to a broad range of researchers and will facilitate the construction of useful mathematical models for multiple types of cells. [ABSTRACT FROM AUTHOR]

Modern computational biology makes widespread use of mathematical models of biological systems, in particular systems of ordinary differential equations, as well as models of dynamic systems described in other formalisms, such as agent-based models. Parameters are numerical values of quantities reflecting certain properties of a modeled system and affecting model solutions. At the same time, depending on parameter values, different dynamic regimes—stationary or oscillatory, established as a result of transient modes of various types—can be observed in the modeled system. Predicting changes in the solution dynamics type depending on changes in model parameters is an important scientific task. Nevertheless, this problem does not have an analytical solution for all formalisms in a general case. The routinely used method of performing a series of computational experiments, i.e., solving a series of direct problems with various sets of parameters followed by expert analysis of solution plots is labor-intensive with a large number of parameters and a decreasing step of the parametric grid. In this regard, the development of methods allowing the obtainment and analysis of information on a set of computational experiments in an aggregate form is relevant. This work is devoted to developing a method for the visualization and classification of various dynamic regimes of a model using a composition of the dynamic time warping (DTW-algorithm) and principal coordinates analysis (PCoA) methods. This method enables qualitative visualization of the results of the set of solutions of a mathematical model and the performance of the correspondence between the values of the model parameters and the type of dynamic regimes of its solutions. This method has been tested on the Lotka–Volterra model and artificial sets of various dynamics. [ABSTRACT FROM AUTHOR]

In this study, we proposed a biological model explaining the progress of autoimmune activation along different stages of systemic lupus erythematosus (SLE). For any upcoming stage of SLE, any new component is introduced, when it is added to the model. Particularly, the interaction of mesenchymal stem cells, with the components of the model, is specified in a way that both the inflammatory and anti-inflammatory functions of these cells would be covered. The biological model is then recapitulated to a model with less complexity that explains the main features of the problem. Later, a 7th-order mathematical model for SLE is proposed, based on this simplified model. Finally, the range of validity of the proposed mathematical model was assessed. For this purpose, we simulated the model and analyzed the simulation results in case of some known behaviors of the disease, such as tolerance breach, the appearance of systemic inflammation, development of clinical signs, and occurrence of flares and improvements. The model was able to reproduce these events, qualitatively. [ABSTRACT FROM AUTHOR]