Different Types Of Mathematical Models Research Articles

A brief overview of mathematical modeling of the within-host dynamics of Mycobacterium tuberculosis

Tuberculosis (TB), a disease caused by bacteria Mycobacterium tuberculosis (Mtb), remains one of the major infectious diseases of humans with 10 million TB cases and 1.5 million deaths due to TB worldwide yearly. Upon exposure of a new host to Mtb, bacteria typically infect one local site in the lung, but over time, Mtb disseminates in the lung and in some cases to extrapulmonary sites. The contribution of various host components such as immune cells to Mtb dynamics in the lung, its dissemination in the lung and outside of the lung, remains incompletely understood. Here we overview different types of mathematical models used to gain insights in within-host dynamics of Mtb; these include models based on ordinary or partial differential equations (ODEs and PDEs), stochastic simulation models based on ODEs, agent-based models (ABMs), and hybrid models (ODE-based models linked to ABMs). We illustrate results from several of such models and identify areas for future resesarch.

Implementing measurement error models with mechanistic mathematical models in a likelihood-based framework for estimation, identifiability analysis and prediction in the life sciences.

Throughout the life sciences, we routinely seek to interpret measurements and observations using parametrized mechanistic mathematical models. A fundamental and often overlooked choice in this approach involves relating the solution of a mathematical model with noisy and incomplete measurement data. This is often achieved by assuming that the data are noisy measurements of the solution of a deterministic mathematical model, and that measurement errors are additive and normally distributed. While this assumption of additive Gaussian noise is extremely common and simple to implement and interpret, it is often unjustified and can lead to poor parameter estimates and non-physical predictions. One way to overcome this challenge is to implement a different measurement error model. In this review, we demonstrate how to implement a range of measurement error models in a likelihood-based framework for estimation, identifiability analysis and prediction, called profile-wise analysis. This frequentist approach to uncertainty quantification for mechanistic models leverages the profile likelihood for targeting parameters and understanding their influence on predictions. Case studies, motivated by simple caricature models routinely used in systems biology and mathematical biology literature, illustrate how the same ideas apply to different types of mathematical models. Open-source Julia code to reproduce results is available on GitHub.

A Comparative Study of Mathematical Models for the Tropical Cyclone Intensity–Size Relation

Despite considerable progress in tropical cyclone (TC) research, our current understanding and prediction capabilities regarding the TC intensity–size relation remain limited. This study systematically analyzes the key characteristics and performance of different types of mathematical models for TC intensity–size relations using the 6-hourly Tropical Cyclone Extended Best Track Dataset spanning 1988 to 2020. The models investigated include statistical, idealized (e.g., Rankine vortex), parametric, and theoretical models. In addition to directly comparing the solutions obtained from individual models to the observed TC records, we assess the models that can produce a unique finite-sized radial profile of surface winds for each TC record—a minimal requirement to ensure that the predicted radial profile of the surface winds would align with the observed profile. The results reveal that a sufficient condition to guarantee a unique radial profile of surface winds is that the associated model can be written as a radial invariant quantity, although it does not guarantee a finite-sized profile. Only the effective absolute angular momentum (eAAM) model, among all the models examined in this study, meets the minimum requirement. Furthermore, the solutions obtained from the eAAM model are well correlated with their observational counterparts (85 to 95%) with little systematic bias and small absolute mean errors that are very close to the observational resolution. The eAAM model’s ability to capture the complex intensity–size relation of observed TCs, in combination with these desirable features, suggests its high potential for gaining a better understanding of the underlying physics governing the observed TC intensity–size relation.

Convex modelling for ship speed optimisation

Optimising the ship speed depending on the forecast oceanic and atmospheric conditions is an effective operational measure to reduce both fuel consumption and carbon dioxide emissions. In the literature, this optimal control problem (OCP) has been formulated using different types of mathematical models and solved using various optimisation methods. In this paper, we use convex functions to reformulate the models and cast the OCP as a convex optimisation problem. This type of problem can be solved very efficiently and yields the globally optimal solution. As a first step, we assume that the environmental conditions do not vary with time and only depend on the distance along the route. For this case, we show that the convex reformulation of the OCP is accurate and the computation time to solve it is low. Second, we introduce an iterative method to solve the problem under time-varying conditions, drawing inspiration from the literature on hybrid electric vehicles. Whilst this method converges quickly, it does not converge to the global optimum, which was calculated using dynamic programming. We present an artificial scenario to explain why convergence to the global optimum is not guaranteed. Finally, we discuss the implications of our findings for potential future research on this topic.

Mathematical models for the extraction of volatile oils and active principles from medicinal and aromatic plants. A review

Active principles cand be extracted from medicinal and aromatic plants using different methods depending on the type and condition of the plant, the active compounds to be obtained, the nature of the solvent used in the whole process (water, alcohol). State-of-the-art methods for the separation and quantification of bioactive compounds from plant materials have led to rapid and efficient development in the pharmaceutical, food and agricultural sectors. Compared to the extraction techniques in the past, it is noticed that the ones currently used are techniques with considerable selectivity and as a result, by using non-toxic solvents, they have the characteristics of ecological techniques. Recent research studies describe mathematical models that have recorded the highest extraction rate and capacity of essential oils and volatile compounds from medicinal and aromatic plants. This paper presents a review of different types of mathematical models used for the purpose of obtaining active compounds from plants in the largest possible quantity.

FicoEst – a tool to estimate the body composition of farmed fish

ficoEst – Fish Composition Estimator is a public web tool to estimate the whole-body proximate composition of farmed fish (https://webtools.sparos.pt/ficoest/). The tool was designed for researchers in fish nutrition and fish farmers, and is available for six commercially relevant species: gilthead seabream (Sparus aurata), European seabass (Dicentrarchus labrax), meagre (Argyrosomus regius), rainbow trout (Onchorhynchus mykiss), Atlantic salmon (Salmo salar), and Nile tilapia (Oreochromis niloticus). ficoEst uses three different types of mathematical models (BC1, BC2, and BC3) to estimate the body composition of fish in terms of crude protein, crude lipids, water, ash, phosphorus, and energy. The models differ in the input data used to perform the estimates. BC1 models consider only body weight, BC2 models consider both body weight and water, and BC3 models consider body weight, water, and ash as inputs. The model evaluation results demonstrate that considering water and ash as additional inputs to body weight (BC3 models) significantly improves the accuracy in predicting some body composition components, such as crude lipids (e.g., up to 67.9 % and 28.1 % more accurate, compared to BC1 and BC2 models, respectively, depending on the species considered). ficoEst can be used as a complementary tool to analytical methods to obtain additional information about fish body composition. As a public web tool, ficoEst has the potential to be a valuable resource for researchers and fish farmers interested in estimating the body composition of farmed fish.

МОДЕЛЮВАННЯ ЗМІН АКТИВНОСТІ ВІТЧИЗНЯНОГО БІЗНЕСУ ЗА УМОВ ВІЙНИ

The article examines the effects of changes in the activity of domestic business during the war, as a result of the system of unfavorable factors. The authors analyze the possibilities of using different types of mathematical models to reproduce the dynamics of business activity at the level of a particular country, and selects the most successful one. A phenomenological model describing the dynamics of the process was proposed, which uses the business activity index as the main variable and is based on an ordinary heterogeneous second-order differential equation with a source term. Using a three-component production function, a transition to a system of differential equations describing the dynamics of various components of the business activity index was made, which, in the absence of a source term responsible for the impact of external stimulating factors, is conservative. The modeling results are compared with empirical data, which indicates a good ability of the model to reproduce real processes in the economy under the influence of powerful negative factors, including the restoration of business optimism caused by the return of territories in September-October 2022 and overcoming the consequences of attacks on energy infrastructure in November 2022-January 2023. It is shown that the involvement of other equations describing the dynamics of business activity in the system leads to a loss of conservatism. The frequency and phase-frequency analysis of the dynamics of Ukrainian business activity during the war allows us to conclude that business activity will recover fairly quickly after the cessation of negative depressing factors. Based on the descriptive data, the article clusters the negative factors that suppress domestic business during hostilities and compares them with the parameters that determine the ease of doing business, an internationally recognized indicator that allows assessing obstacles to business activity. Based on the research of recognized foreign experts, a retrospective analysis of obstacles to the development of Ukrainian business was conducted. An empirical study of a number of enterprises from the Dnipropetrovs’k region belonging to various business sectors was implemented, which proves that the main problems that emerged during the war are not much more severe than the problems that domestic business experienced before the aggression. The «classical» factors associated with hostilities are reduced to ensuring uninterrupted supply of electricity and preventing the outflow of human resources through conscription and forced migration. It is concluded that an interesting direction for further research on this problem is the use of the Granger model, which will allow for joint analysis of time series and take into account hidden relationships.

A conceptual multilevel approach to polyolefin reaction engineering

AbstractThis article gives a wide overview of different types of mathematical models that can be used to describe the polymerization of linear olefins with coordination catalysts. We expanded the conventional classification of mathematical models into micro‐, meso‐, and macroscale, to include seven modelling levels: catalysis, polymerization kinetics, thermodynamic equilibrium, particle transport phenomena, particle interactions, reactor fluid dynamics, and reactor residence time distribution. Some of these levels may coexist at the same scale, but they are better treated separately because they make use of distinct modelling approaches. How complex the models in each level need to be, as well as how many modelling levels should beimplicitlyincluded, depends on the type of application intended for the simulations. In this paper, we will argue that the proposed levels of mathematical modelling not only bring to our attention the complexity behind the simulation of laboratory‐ and industrial‐scale olefin polymerization reactors but are also useful conceptual tools to assist us to decide which levels to include and which ones to exclude when we develop simulation packages to describe olefin polymerization processes.

A review on the modelling of hydrothermal liquefaction of biomass and waste feedstocks

Hydrothermal liquefaction is a thermo-chemical conversion process which uses water as a reaction medium at elevated pressure and temperature. It converts biomass and waste feedstock to biofuel and recovers water and fertilizers present in the feedstock. Hydrothermal liquefaction overcomes many technical limitations of the existing technologies such as anaerobic digestion, incineration, gasification, and pyrolysis and it offers a solution to water-energy-climate nexus. Hydrothermal liquefaction has been widely investigated to understand the mechanism and kinetics of hydrothermal liquefaction at different batch scales of operation. Significant efforts have been made recently to develop the kinetic models for various type of feedstocks to predict product yields despite having complex reaction mechanism and pathways. This article critically reviews past work and discuss the different types of mathematical models used to predict products yields and composition for different biomass and waste feedstocks. It encompasses summary of important characteristics of representative biomass and waste feedstocks and quality of biocrude product, experimental studies conducted for various predictive and kinetic model development. A few limitations on existing models were identified to focus for further study. Finally, suggestions have been incorporated with focus on improving hydrothermal liquefaction kinetic model for optimal product yields and composition under varying operating conditions for various feedstocks.

Comparison of mathematical models to estimate the thermal conductivity of TiO2-water based nanofluid: A review

Heat transfer is a desirable phenomenon in many industries such as in refrigeration, transportation, power generation, cell preservation, incubator, metallurgy and material processing, health services, etc. Different types of fluids like water, oil, ethylene glycol etc. are being used as a heat transfer medium. Water is a commonly used as working fluid for transfer of heat. Nanofluids are developed by adding nanosized particle(s) in existing fluid to improve the heat transfer rate. Thermal conductivity of the nanofluid is an important parameter in estimation of heat transfer rate. Different types of mathematical models were developed by various investigators to predict the thermal conductivity of the nanofluids. In this review paper, the theoretical and mathematical model(s) have been compared to predict the thermal conductivity of nanofluids. The experimental data have been collected from literature and compared with Maxwell model, Hamilton and Crosser model, Maxwell-Garnetts model, Pak Cho model, Timofeeva et al. model, Li and Peterson model, Bhattacharya et al. model, respectively in detail. It has been observed that the prediction with the help of the mathematical models is good when the value of volume fraction was less than 0.01.

On the significance of membrane unfolding in mechanosensitive cell spreading: Its individual and synergistic effects.

Mechanosensitivity of cell spread area to substrate stiffness has been established both through experiments and different types of mathematical models of varying complexity including both the mechanics and biochemical reactions in the cell. What has not been addressed in previous mathematical models is the role of cell membrane dynamics on cell spreading, and an investigation of this issue is the goal of this work. We start with a simple mechanical model of cell spreading on a deformable substrate and progressively layer mechanisms to account for the traction dependent growth of focal adhesions, focal adhesion induced actin polymerization, membrane unfolding/exocytosis and contractility. This layering approach is intended to progressively help in understanding the role each mechanism plays in reproducing experimentally observed cell spread areas. To model membrane unfolding we introduce a novel approach based on defining an active rate of membrane deformation that is dependent on membrane tension. Our modeling approach allows us to show that tension-dependent membrane unfolding plays a critical role in achieving the large cell spread areas experimentally observed on stiff substrates. We also demonstrate that coupling between membrane unfolding and focal adhesion induced polymerization works synergistically to further enhance cell spread area sensitivity to substrate stiffness. This enhancement has to do with the fact that the peripheral velocity of spreading cells is associated with contributions from the different mechanisms by either enhancing the polymerization velocity at the leading edge or slowing down of the retrograde flow of actin within the cell. The temporal evolution of this balance in the model corresponds to the three-phase behavior observed experimentally during spreading. In the initial phase membrane unfolding is found to be particularly important.

Mathematical Modelling in Engineering with Integral Transforms via Modified Adomian Decomposition Method

In this work three integral transforms through modified Adomian decomposition method (ADM) are proposed to obtain the approximate analytical solution of different types of mathematical models arising in physical problems. These transformations are applied for both homogeneous and non-homogeneous linear differential equations. The efficiency and accuracy of the proposed methods are implemented through higher order non-homogeneous ordinary differential equations. Numerical tests are reported for applicability of the current scheme based on different transformations and compared with exact solutions.

A STUDY ON MATHEMATICAL AND STATISTICAL ASPECTS OF LINEAR MODELS

The primary objective of this research article is to present the mathematical and statistical aspects of linear models and their characteristic properties. Linear model is the most common modeling used in science. Actually linear models have many different meanings depend on the context. Linear model is often preferred than other model such as quadratic model because of its ability to interpret easily. In the other hand most of the real life cases have linear relationship .Modeling the cases using linear model will able us to determine the relative influence of one or more independent variables to the dependent variable. In the present talk an attempt has been made to propose the specific forms of simple and multiple linear regression models. In this conversation mathematical aspects of linear models have been extensively depicted. Different types of mathematical models are discussed here and the methods of fitting transformed models are proposed.Furthermore specific form of linear statistical model is presented and the crucial assumptions of general linear model are extensively discussed.At the last stage of this article the method of ordinary least squares estimation of parameters of a linear model has been proposed

Formulation and Solution of an Inverse Reliability Problem to Simulate the Dynamic Behavior of COVID-19 Pandemic

Different types of mathematical models have been used to predict the dynamic behavior of the novel coronavirus (COVID-19). Many of them involve the formulation and solution of inverse problems. This kind of problem is generally carried out by considering the model, the vector of design variables, and system parameters as deterministic values. In this contribution, a methodology based on a double loop iteration process and devoted to evaluate the influence of uncertainties on inverse problem is evaluated. The inner optimization loop is used to find the solution associated with the highest probability value, and the outer loop is the regular optimization loop used to determine the vector of design variables. For this task, we use an inverse reliability approach and Differential Evolution algorithm. For illustration purposes, the proposed methodology is applied to estimate the parameters of SIRD (Susceptible-Infectious-Recovery-Dead) model associated with dynamic behavior of COVID-19 pandemic considering real data from China's epidemic and uncertainties in the basic reproduction number (R0). The obtained results demonstrate, as expected, that the increase of reliability implies the increase of the objective function value.

Active and Passive Suspension System Performance under Random Road Profile Excitations

Passive suspensions are designed to satisfy the conflicting criteria of riding comfort and vehicle handling. An active suspension system attempts to overcome these compromises to provide the best performance for vehicle control. Different types of mathematical models have been used to study the suspension system of a vehicle. The quarter vehicle model is used for initial investigation. Later, the half vehicle and full vehicle models are used for the study, which is closer to the actual model of a vehicle suspension. In this paper, the behavior of a suspension system is analyzed using the full vehicle model. In the current work, the dynamic equation and their state-space formulation are presented for the full vehicle model to understand the system prior to the controller design. The open-loop response of the full vehicle suspension system, when subjected to various road excitations, is also studied. The procedure of modeling a SIMULINK model for passive suspensions system is discussed in detail. Design of the simple Proportional Integral Derivative (PID) feedback and feed-forward controller is presented for the active suspension system using transfer functions. Closed-loop transfer functions are also derived and their responses are plotted. To analyze the rollover behavior simulation for cornering is also performed in the current study.

Host–parasite interactions in vector-borne protozoan infections

Protists embrace many species, some of which may be either occasional or permanent parasites of vertebrate animals. Between the parasite species, several of medical and veterinary importance are vector-transmitted. The ecology and epidemiology of vector-borne parasitoses, including babesiosis, leishmaniasis and malaria, are particularly complex, as they are influenced by many factors, such as vector reproductive efficiency and geographical spread, vectorial capacity, host immunity, travel and human behaviour and climatic factors. Transmission dynamics are determined by the interactions between pathogen, vector, host and environmental factors and, given their complexity, many different types of mathematical models have been developed to understand them. A good basic knowledge of vector-pathogen relationships and transmission dynamics is thus essential for disease surveillance and control interventions and may help in understanding the spread of epidemics and be useful for public health planning.

Connecting mathematical models to genomes: joint estimation of model parameters and genome-wide marker effects on these parameters.

Parameters of mathematical models used in biology may be genotype-specific and regarded as new traits. Therefore, an accurate estimation of these parameters and the association mapping on the estimated parameters can lead to important findings regarding the genetic architecture of biological processes. In this study, a statistical framework for a joint analysis (JA) of model parameters and genome-wide marker effects on these parameters was proposed and evaluated. In the simulation analyses based on different types of mathematical models, the JA inferred the model parameters and identified the responsible genomic regions more accurately than the independent analysis (IA). The JA of real plant data provided interesting insights into photosensitivity, which were uncovered by the IA. The statistical framework is provided by the R package GenomeBasedModel available at https://github.com/Onogi/GenomeBasedModel. All R and C++ scripts used in this study are also available at the site. Supplementary data are available at Bioinformatics online.

A New Idea of Fractal-fractional Derivative with Power Law Kernel for Free Convection Heat Transfer in a Channel Flow between Two Static Upright Parallel Plates

Nowadays some new ideas of fractional derivatives have been used successfully in the present research community to study different types of mathematical models. Amongst them, the significant models of fluids and heat or mass transfer are on priority. Most recently a new idea of fractal-fractional derivative is introduced; however, it is not used for heat transfer in channel flow. In this article, we have studied this new idea of fractal fractional operators with power-law kernel for heat transfer in a fluid flow problem. More exactly, we have considered the free convection heat transfer for a Newtonian fluid. The flow is bounded between two parallel static plates. One of the plates is heated constantly. The proposed problem is modeled with a fractal fractional derivative operator with a power-law kernel and solved via the Laplace transform method to find out the exact solution. The results are graphically analyzed via MathCad-15 software to study the behavior of fractal parameters and fractional parameter. For the influence of temperature and velocity profile, it is observed that the fractional parameter raised the velocity and temperature as compared to the fractal operator. Therefore, a combined approach of fractal fractional explains the memory of the function better than fractional only.

Systems Biology of Metabolism.

Metabolism is highly complex and involves thousands of different connected reactions; it is therefore necessary to use mathematical models for holistic studies. The use of mathematical models in biology is referred to as systems biology. In this review, the principles of systems biology are described, and two different types of mathematical models used for studying metabolism are discussed: kinetic models and genome-scale metabolic models. The use of different omics technologies, including transcriptomics, proteomics, metabolomics, and fluxomics, for studying metabolism is presented. Finally, the application of systems biology for analyzing global regulatory structures, engineering the metabolism of cell factories, and analyzing human diseases is discussed.

A Systems Biology Road Map for the Discovery of Drugs Targeting Cancer Cell Metabolism

Despite their different histological and molecular properties, different types of cancers share few essential functional alterations. Some of these cancer hallmarks may easily be studied in in vitro cultures, while others are related to the way in which tumors grow in vivo. According to the systems biology paradigm, complex cellular functions arise as system-level properties from the dynamic interaction of a large number of biomolecules. We previously newly defined four basic cancer cell properties derived from known cancer hallmarks amenable to system-level investigation in cell cultures: enhanced growth, altered response to apoptotic cues, genomic instability and inability to enter senescence following oncogenic signaling. Here we summarize the major properties of enhanced growth that is dependent on metabolism rewiring - in which glucose is mostly used by fermentation while glutamine provides nitrogen and carbon atoms for biosyntheses - and controlled by oncogene signaling. We then briefly review the major drugs used to target signaling pathways in preclinical and clinical studies, whose clinical efficacy is unfortunately severely limited by tumor resistance, substantially due to signaling cross-talk. We present a systems biology roadmap that integrates different types of mathematical models with conventional and post-genomic biomolecular analyses that will provide a deeper mechanistic understanding of the links between metabolism and uncontrolled cancer cell growth. This approach is taken to be instrumental both in unraveling cancer's first principles and in designing novel drugs able to target one or more control or execution steps of the cancer rewired metabolism, in order to achieve permanent arrest of tumor development.