MATHEMATICAL MODELING AND BIFURCATION ANALYSIS FOR A BIOLOGICAL MECHANISM OF CANCER DRUG RESISTANCE

Drug resistance is one of the most intractable issues in targeted therapy for cancer diseases.It has also been demonstrated to be related to cancer heterogeneity,which promotes the emergence of treatment-refractory cancer cell populations.Focusing on how cancer cells develop resistance during the encounter with targeted drugs and the immune system,we propose a mathematical model for studying the dynamics of drug resistance in a conjoint heterogeneous tumor-immune setting.We analyze the local geometric properties of the equilibria of the model.Numerical simulations show that the selectively targeted removal of sensitive cancer cells may cause the initially heterogeneous population to become a more resistant population.Moreover,the decline of immune recruitment is a stronger determinant of cancer escape from immune surveillance or targeted therapy than the decay in immune predation strength.Sensitivity analysis of model parameters provides insight into the roles of the immune system combined with targeted therapy in determining treatment outcomes.

Aggravation of Cancer,Heart Diseases and Diabetes Subsequent to COVID-19 Lockdown via Mathematical Modeling

The global populationhas beenandwill continue to be severely impacted by theCOVID-19 epidemic.The primary objective of this research is to demonstrate the future impact of COVID-19 on those who suffer from other fatal conditions such as cancer,heart disease,and diabetes.Here,using ordinary differential equations(ODEs),two mathematical models are developed to explain the association between COVID-19 and cancer and between COVID-19 and diabetes and heart disease.After that,we highlight the stability assessments that can be applied to these models.Sensitivity analysis is used to examine how changes in certain factors impact different aspects of disease.The sensitivity analysis showed that many people are still nervous about seeing a doctor due to COVID-19,which could result in a dramatic increase in the diagnosis of various ailments in the years to come.The correlation between diabetes and cardiovascular illness is also illustrated graphically.The effects of smoking and obesity are also found to be significant in disease compartments.Model fitting is also provided for interpreting the relationship between real data and the results of thiswork.Diabetic people,in particular,need tomonitor their health conditions closely and practice heart health maintenance.People with heart diseases should undergo regular checks so that they can protect themselves from diabetes and take some precautions including suitable diets.The main purpose of this study is to emphasize the importance of regular checks,to warn people about the effects of COVID-19(including avoiding healthcare centers and doctors because of the spread of infectious diseases)and to indicate the importance of family history of cancer,heart diseases and diabetes.The provision of the recommendations requires an increase in public consciousness.

Mathematical Modeling of Cell Polarity Establishment of Budding Yeast

The budding yeast Saccharomyces cerevisiae is a powerful model system for studying the cell polarity establishment.The cell polarization process is regulated by signaling molecules,which are initially distributed in the cytoplasm and then recruited to a proper location on the cell membrane in response to spatial cues or spontaneously.Polarization of these signaling molecules involves complex regulation,so the mathematical models become a useful tool to investigate the mechanism behind the process.In this review,we discuss how mathematical modeling has shed light on different regulations in the cell polarization.We also propose future applications for the mathematical modeling of cell polarization and morphogenesis.

Mathematical Modeling of the Co-Infection Dynamics of HIV and Tuberculosis Incorporating Inconsistency in HIV Treatment

A non-linear HIV-TB co-infection has been formulated and analyzed. The positivity and invariant region has been established. The disease free equilibrium and its stability has been determined. The local stability was determined and found to be stable under given conditions. The basic reproduction number was obtained and according to findings, co-infection diminishes when this number is less than unity, and persists when the number is greater than unity. The global stability of the endemic equilibrium was calculated. The impact of HIV on TB was established as well as the impact of TB on HIV. Numerical solution was also done and the findings indicate that when the rate of HIV treatment increases the latent TB increases while the co-infected population decreases. When the rate of HIV treatment decreases the latent TB population decreases and the co-infected population increases. Encouraging communities to prioritize the consistent treatment of HIV infected individuals must be emphasized in order to reduce the scourge of HIV-TB co-infection.

Mathematical Modeling of HIV Investigating the Effect of Inconsistent Treatment

HIV is a retrovirus that infects and impairs the cells and functions of the immune system. It has caused a great challenge to global public health systems and leads to Acquired Immunodeficiency Syndrome (AIDS), if not attended to in good time. Antiretroviral therapy is used for managing the virus in a patient’s lifetime. Some of the symptoms of the disease include lean body mass and many opportunistic infections. This study has developed a SIAT mathematical model to investigate the impact of inconsistency in treatment of the disease. The arising non-linear differential equations have been obtained and analyzed. The DFE and its stability have been obtained and the study found that it is locally asymptotically stable when the basic reproduction number is less than unity. The endemic equilibrium has been obtained and found to be globally asymptotically stable when the basic reproduction number is greater than unity. Numerical solutions have been obtained and analyzed to give the trends in the spread dynamics. The inconsistency in treatment uptake has been analyzed through the numerical solutions. The study found that when the treatment rate of those infected increases, it leads to an increase in treatment population, which slows down the spread of HIV and vice versa. An increase in the rate of treatment of those with AIDS leads to a decrease in the AIDS population, the reverse happens when this rate decreases. The study recommends that the community involvement in advocating for consistent treatment of HIV to curb the spread of the disease.

Data-driven intelligent modeling framework for the steam cracking process

Steam cracking is the dominant technology for producing light olefins,which are believed to be the foundation of the chemical industry.Predictive models of the cracking process can boost production efficiency and profit margin.Rapid advancements in machine learning research have recently enabled data-driven solutions to usher in a new era of process modeling.Meanwhile,its practical application to steam cracking is still hindered by the trade-off between prediction accuracy and computational speed.This research presents a framework for data-driven intelligent modeling of the steam cracking process.Industrial data preparation and feature engineering techniques provide computational-ready datasets for the framework,and feedstock similarities are exploited using k-means clustering.We propose LArge-Residuals-Deletion Multivariate Adaptive Regression Spline(LARD-MARS),a modeling approach that explicitly generates output formulas and eliminates potentially outlying instances.The framework is validated further by the presentation of clustering results,the explanation of variable importance,and the testing and comparison of model performance.

Problem-based Learning Combining Seminar Teaching Method for the Practice of Mathematical Modeling Course's Teaching Reform for Computer Discipline

Mathematical modeling course has been one of the fast development courses in China since 1992,which mainly trains students’innovation ability.However,the teaching of mathematical modeling course is quite difficult since it requires students to have a strong mathematical foundation,good ability to design algorithms,and programming skills.Besides,limited class hours and lack of interest in learning are the other reasons.To address these problems,according to the outcome-based education,we adopt the problem-based learning combined with a seminar mode in teaching.We customize cases related to computer and software engineering,start from simple problems in daily life,step by step deepen the difficulty,and finally refer to the professional application in computer and software engineering.Also,we focus on ability training rather than mathematical theory or programming language learning.Initially,we prepare the problem,related mathematic theory,and core code for students.Furtherly,we train them how to find the problem,and how to search the related mathematic theory and software tools by references for modeling and analysis.Moreover,we solve the problem of limited class hours by constructing an online resource learning library.After a semester of practical teaching,it has been shown that the interest and learning effectiveness of students have been increased and our reform plan has achieved good results.

Simulation-based Graphic Method for Dynamic System Modeling

The first step for engineering students to understand the practical system is to describe the system,which means to establish the mathematic model for the considered system.However,traditional mathematical modeling techniques are not readily assimilated by students,because the traditional modeling needs to obey the complicated physical laws for different engineering areas and requires a highly iterative process.In this paper,the simulation-based graphic modeling method is introduced to help students model the system and improve their performance in engineering education.The results from the questionnaire indicate that the simulation-based graphic method can help students to do the modeling of the system and improve their performance compared to the traditional ways.

Kinetic Modeling of Light Naphtha Hydroisomerization in an Industrial Universal Oil Products Penex^(TM)Unit

Recently,the isomerization of light naphtha has been increasingly significant in assisting refiners in meeting sternness specifications for gasoline.Isomerization process provides refiners with the advantage of reducing sulfur,olefin,and benzene in the gasoline basin without significantly victimizing the octane.The mathematical modeling of a chemical reaction is a critical tool due to it can used to optimize the experimental data to estimate the optimum operating conditions for industrial reactors.This paper describes light naphtha isomerization reactions over a Pt/Al_(2)O_(3)-Cl catalyst at the Al-Dura Oil Refinery(Baghdad,Iraq)using a newly developed universal mathematical model.The proposed kinetic model involves 117 isomerization reactions and 90 cracking reactions to describe 52 real components graded from methane to n-octane.A Genetic Algorithm stochastic optimization technique applied in MATLAB R2020a software was employed to estimate the optimal set of kinetic parameters.The calculated activation energies for hydrocracking reactions was found to be higher than the other reactions because of hydrocracking reactions occur at higher range of temperatures.By benchmarking between the experimental and theoretical results for all 117 data sets,the mean absolute error was obtained to be 0.00360 for all 52 components.Also,a positive effect of increasing reaction temperatures was recognized on enhancing the research octane number(RON).

Towards a Modeling of the Impacts of Road Verge Management on the Pollination Service Using System Dynamics: A Case Study in France

Several research studies have proven that eliciting and predicting the impact of human activity on ecosystem services will be crucial to support stakeholders’ awareness and to decide how to interact with the environment in a more sustainable manner. In this sense, the ecosystems known as road verges are particularly important because of their length and surface at an international scale, and their role in mitigating the damage done by roads. Plant pollination by insects is one of the most important ecosystem services. Because of its nature and the fact that they extend across a variety of landscapes, roadside can contribute to the maintenance of healthy ecosystems, under the condition of adapted management practices. This research is the first attempt to develop a System Dynamics-based aiming to estimate the ecological and economic impact of maintenance on the road verge pollination service in France. Maintenance strategies of road verges are simulated to compare their performance. The results show that there are ways to improve current maintenance strategies in terms of pollination value, but also that the model needs to consider other ecosystem services and synergistic effects that could further affect pollination to obtain more accurate estimations.

Co-digestion of Waste Coffee and Cocoa Hulls: Modeling of Biogas Production by the Particle Swarm Method

Energy is a crucial material for the development of our economy.Access to sufficient energy remains a major concern for developing countries,particularly those in sub-Saharan Africa.The major challenge lies in access to clean,environmentally friendly,quality and low-cost energy in different households in our municipalities.To cope with this vast energy gap,many households are dependent on fossil fuels.In Cameroon,the consumption of wood for the supply of energy is increasing by 4%per year.Overall,approximately 80%of households in Cameroon depend on woody biomass as the sole main source of energy supply in Cameroon and demand is growing over time.In view of the climatic variations that our countries,particularly Cameroon,undergo through deforestation,the use of wood as a source of energy is expensive and harmful to the environment,hence the urgency of replacing wood with renewable energy.Biogas is one of the most versatile sources of renewable energy.On an industrial scale,it is important to automate the process control.The main objective of the present work is to model the anaerobic digestion of coffee and cocoa hulls using the particle swarm optimisation method.Pretreatment using the organosolv process was done.This resulted in 48%lignin removal and 22%cellulose increase.For the pretreated biomass,the maximum production rate was 21 NmLCH4 per day with a biomethane yield of 90 NmLCH4/gVS.This represents an enhancement of 117%in biomethane yield.A positive flammability test was recorded after the 10th day of retention time.Moreover,the data collected during anaerobic digestion allowed implementation of a two-phase mathematical model.The thirteen parameters of the model were estimated with particle swarm optimisation method in Matlab.The model was able to simulate the biomethane production kinetics and variation of volatile fatty acid concentration.

Modeling, Simulation and Experimental Studies of Refractometric Fiber Optic Sensor

Refractometric fiber optic sensors have a number of applications in industry due to advantages like remote sensing ability, compact size, easy to fit, etc. A refractometric sensor contains a pair of parallel fibers and a gap between the sensor probe and reflector, wherein the liquid whose refractive index is to be measured is filled. This paper describes the importance of mathematical modeling of this sensor. Ray tracing approach is used to model the sensor mathematically. This mathematical model is generalized for any scenario which is useful to avoid tedious trial and error techniques to design the sensor prototype. Mathematical modelling is a useful tool to optimize the gap distance for a detection of refractive index of liquid. The model is developed and analyzed rigorously considering adulteration of diesel by kerosene where refractive index varies from 1.44 to 1.46. Simulation experiments are carried out to optimize the gap distance which is found to be 6.8 mm using both models. Experiments are carried out where sensor probe is fabricated and results are analyzed. It is observed that for suggested gap distance sensor output varies almost linear over the entire range.

A Method for Constructing Mathematical Modeling of the Spread of a New Crown Pneumonia Epidemic Based on the Effect of Temperature

To better predict the spread of the COVID-19 outbreak, mathematical modeling and analysis of the spread of the COVID-19 outbreak is proposed based on data analysis and infectious disease theory. Firstly, the mathematical model indicators of the spread of the new coronavirus pneumonia epidemic are determined by combining the theory of infectious diseases, the basic assumptions of the spread model of the new coronavirus pneumonia epidemic are given based on the theory of data analysis model, the spread rate of the new coronavirus pneumonia epidemic is calculated by combining the results of the assumptions, and the spread rate of the epidemic is inverted to push back into the assumptions to complete the construction of the mathematical modeling of the diffusion. Relevant data at different times were collected and imported into the model to obtain the spread data of the new coronavirus pneumonia epidemic, and the results were analyzed and reflected. The model considers the disease spread rate as the dependent variable of temperature, and analyzes and verifies the spread of outbreaks over time under real temperature changes. Comparison with real results shows that the model developed in this paper is more in line with the real disease spreading situation under specific circumstances. It is hoped that the accurate prediction of the epidemic spread can provide relevant help for the effective containment of the epidemic spread.

Effect of solvent on the initiation mechanism of living anionic polymerization of styrene:A computational study

For living anionic polymerization(LAP),solvent has a great influence on both reaction mechanism and kinetics.In this work,by using the classical butyl lithium-styrene polymerization as a model system,the effect of solvent on the mechanism and kinetics of LAP was revealed through a strategy combining density functional theory(DFT)calculations and kinetic modeling.In terms of mechanism,it is found that the stronger the solvent polarity,the more electrons transfer from initiator to solvent through detailed energy decomposition analysis of electrostatic interactions between initiator and solvent molecules.Furthermore,we also found that the stronger the solvent polarity,the higher the monomer initiation energy barrier and the smaller the initiation rate coefficient.Counterintuitively,initiation is more favorable at lower temperatures based on the calculated results ofΔG_(TS).Finally,the kinetic characteristics in different solvents were further examined by kinetic modeling.It is found that in benzene and n-pentane,the polymerization rate exhibits first-order kinetics.While,slow initiation and fast propagation were observed in tetrahydrofuran(THF)due to the slow free ion formation rate,leading to a deviation from first-order kinetics.

Cascade equilibrium stage relaxation method by introducing equilibrium efficiency parameter

Optimizing multistage processes,such as distillation or absorption,is a complex mixed-integer nonlinear programming(MINLP)problem.Relaxing integer into continuous variables and solving the easier nonlinear programming(NLP)problem is an optimization idea for the multistage process.In this article,we propose a relaxation method based on the efficiency parameter.When the efficiency parameter is 1or 0,the proposed model is equivalent to the complete existence or inexistence of the equilibrium stage.And non-integer efficiency represents partial existence.A multi-component absorption case shows a natural penalty for non-integer efficiency,which can assist the efficiency parameter converging to 0 or 1.However,its penalty is weaker than the existing relaxation models,such as the bypass efficiency model.In a simple distillation case,we show that this property can weaken the nonconvexity of the optimization problem and increase the probability of obtaining better optimization results.

采用解析和数值方法分析浮动式矩形浮箱的波浪诱导载荷研究

A three-dimensional mathematical hydrodynamic model associated with surface wave radiation by a floating rectangular box-type structure due to heave,sway,and roll motions in finite water depth is investigated based on small amplitude water wave theory and linear structural response.The analytical expressions for the radiation potentials,wave forces,and hydrodynamic coefficients are presented based on matched eigenfunction expansion method(MEFEM).The correctness of the analytical results of wave forces is compared with the construction of a numerical model using the open-source boundary element method code NEMOH.In addition,the present result is compared with the existing published experimental results available in the literature.The effects of the different design parameters on the floating box-type rectangular structure are studied by analyzing the vertical wave force,horizontal wave force,torque,added mass,and damping coefficients due to the heave,sway,and roll motions,and the comparison analysis between the forces is also analyzed in detail.Further,the effect of reflection and transmission coefficients by varying the structural width and drafts are analyzed.

Using Improved Particle Swarm Optimization Algorithm for Location Problem of Drone Logistics Hub

Drone logistics is a novel method of distribution that will become prevalent.The advantageous location of the logistics hub enables quicker customer deliveries and lower fuel consumption,resulting in cost savings for the company’s transportation operations.Logistics firms must discern the ideal location for establishing a logistics hub,which is challenging due to the simplicity of existing models and the intricate delivery factors.To simulate the drone logistics environment,this study presents a new mathematical model.The model not only retains the aspects of the current models,but also considers the degree of transportation difficulty from the logistics hub to the village,the capacity of drones for transportation,and the distribution of logistics hub locations.Moreover,this paper proposes an improved particle swarm optimization(PSO)algorithm which is a diversity-based hybrid PSO(DHPSO)algorithm to solve this model.In DHPSO,the Gaussian random walk can enhance global search in the model space,while the bubble-net attacking strategy can speed convergence.Besides,Archimedes spiral strategy is employed to overcome the local optima trap in the model and improve the exploitation of the algorithm.DHPSO maintains a balance between exploration and exploitation while better defining the distribution of logistics hub locations Numerical experiments show that the newly proposed model always achieves better locations than the current model.Comparing DHPSO with other state-of-the-art intelligent algorithms,the efficiency of the scheme can be improved by 42.58%.This means that logistics companies can reduce distribution costs and consumers can enjoy a more enjoyable shopping experience by using DHPSO’s location selection.All the results show the location of the drone logistics hub is solved by DHPSO effectively.

A Vertex Network Model of Arabidopsis Leaf Growth

Biology provides many examples of complex systems whose properties allow organisms to develop in a highly reproducible,or robust,manner.One such system is the growth and development of flat leaves in Arabidopsis thaliana.This mechanistically challenging process results from multiple inputs including gene interactions,cellular geometry,growth rates,and coordinated cell divisions.To better understand how this complex genetic and cellular information controls leaf growth,we developed a mathematical model of flat leaf production.This two-dimensional model describes the gene interactions in a vertex network of cells which grow and divide according to physical forces and genetic information.Interestingly,the model predicts the presence of an unknown additional factor required for the formation of biologically realistic gene expression domains and iterative cell division.This two-dimensional model will form the basis for future studies into robustness of adaxial-abaxial patterning.

A framework for dynamic modelling of railway track switches considering the switch blades,actuators and control systems

The main contribution of this paper is the development and demonstration of a novel methodology that can be followed to develop a simulation twin of a railway track switch system to test the functionality in a digital environment.This is important because,globally,railway track switches are used to allow trains to change routes;they are a key part of all railway networks.However,because track switches are single points of failure and safety-critical,their inability to operate correctly can cause significant delays and concomitant costs.In order to better understand the dynamic behaviour of switches during operation,this paper has developed a full simulation twin of a complete track switch system.The approach fuses finite element for the rail bending and motion,with physics-based models of the electromechanical actuator system and the control system.Hence,it provides researchers and engineers the opportunity to explore and understand the design space around the dynamic operation of new switches and switch machines before they are built.This is useful for looking at the modification or monitoring of existing switches,and it becomes even more important when new switch concepts are being considered and evaluated.The simulation is capable of running in real time or faster meaning designs can be iterated and checked interactively.The paper describes the modelling approach,demonstrates the methodology by developing the system model for a novel“REPOINT”switch system,and evaluates the system level performance against the dynamic performance requirements for the switch.In the context of that case study,it is found that the proposed new actuation system as designed can meet(and exceed)the system performance requirements,and that the fault tolerance built into the actuation ensures continued operation after a single actuator failure.

Rapid Prototype Development Approach for Genetic Programming

Genetic Programming (GP) is an important approach to deal with complex problem analysis and modeling, and has been applied in a wide range of areas. The development of GP involves various aspects, including design of genetic operators, evolutionary controls and implementations of heuristic strategy, evaluations and other mechanisms. When designing genetic operators, it is necessary to consider the possible limitations of encoding methods of individuals. And when selecting evolutionary control strategies, it is also necessary to balance search efficiency and diversity based on representation characteristics as well as the problem itself. More importantly, all of these matters, among others, have to be implemented through tedious coding work. Therefore, GP development is both complex and time-consuming. To overcome some of these difficulties that hinder the enhancement of GP development efficiency, we explore the feasibility of mutual assistance among GP variants, and then propose a rapid GP prototyping development method based on πGrammatical Evolution (πGE). It is demonstrated through regression analysis experiments that not only is this method beneficial for the GP developers to get rid of some tedious implementations, but also enables them to concentrate on the essence of the referred problem, such as individual representation, decoding means and evaluation. Additionally, it provides new insights into the roles of individual delineations in phenotypes and semantic research of individuals.