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.

Research on the Applications of Advanced Mathematics on Mathematical Modeling and the Inner Connections with Linear Algebra and Probability Statistics

In this paper, we conduct research on the applications of advanced mathematics on the mathematical modeling and the inner connections with linear algebra and the probability statistics. Aiming at model in mathematical modeling and solving and model of evaluation and promotion of the two links, put forward the ＂bystander＂ and ＂the authorities＂ this two characters, and points out that excellent mathematical modeling participants should have ＂from a bystander to the authorities＂ and ＂from the authorities to return to bystanders＂ two-way role transformation ability. Great situation in mathematics teaching, by means of the mathematical modeling formed in the development of the teachers, as well as the teaching thought, teaching experience and achievements, the onward march of mathematical experiment should be faster than mathematical modeling. Our research provides the new paradigm for the math development which will be meaningful.

Analysis of Mathematical Modeling Thought in College Mathematics Teaching

The mathematical analysis enters the higher mathematics as the mathematics specialized student from the general elementary mathematics the initiation curriculum, its content and middle school mathematics still exist relate very much, while it during the expansion knowledge as also has many transformations. Under this basis, this paper proposes the analysis of the mathematical modeling thought in college mathematics teaching. Mathematics modelling teaching uses the open style teaching method also to wait for consummates regards the concrete course content the main point, the function as carries on each kind of variant to the open style mathematics educational model enable this kind of pattern to have pointed. We propose the novel paradigm for the education that will then be essential for the further development of the systems, in the future, we will then apply more of the methodologies to enhance the current proposed model.

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.

Principle, Modeling and Control of DC-DC Convertors for EV

DC DC convertors can convert the EV's high voltage DC power supply into the low voltage DC power supply. In order to design an excellent convertor one must be guided by theory of automatic control. The principle and the method of design, modeling and control for DC DC convertors of EV are introduced. The method of the system response to a unit step function input and the frequency response method are applied to researching the convertor's mathematics model and control characteristic. Experiments show that the designed DC DC convertor's output voltage precision is high, the antijamming ability is strong and the adjustable performance is fast and smooth.

A dynamic soil freezing characteristic curve model for frozen soil

The soil freezing characteristic curve(SFCC)plays a fundamental role in comprehending thermohydraulic behavior and numerical simulation of frozen soil.This study proposes a dynamic model to uniformly express SFCCs amidst varying total water contents throughout the freezing-thawing process.Firstly,a general model is proposed,wherein the unfrozen water content at arbitrary temperature is determined as the lesser of the current total water content and the reference value derived from saturated SFCC.The dynamic performance of this model is verified through test data.Subsequently,in accordance with electric double layer(EDL)theory,the theoretical residual and minimum temperatures in SFCC are calculated to be-14.5℃to-20℃for clay particles and-260℃,respectively.To ensure that the SFCC curve ends at minimum temperature,a correction function is introduced into the general model.Furthermore,a simplified dynamic model is proposed and investigated,necessitating only three parameters inherited from the general model.Additionally,both general and simplified models are evaluated based on a test database and proven to fit the test data exactly across the entire temperature range.Typical recommended parameter values for various types of soils are summarized.Overall,this study provides not only a theoretical basis for most empirical equations but also proposes a new and more general equation to describe the SFCC.

System-Level Modeling and Simulation of Force-Balance MEMS Accelerometers

This paper presents two approaches for system-level simulation of force-balance accelerometers. The derivation of the system-level model is elaborated and simulation results are obtained from the implementation of those strategies on the fabricated silicon force-balance MEMS accelerometer. The mathematical model presented is implemented in VHDL- AMS and SIMULINK TM,respectively. The simulation results from the two approaches are compared and show a slight difference. Using VHDL-AMS is flexible,reusable,and more accurate. But there is not a mature solver developed for the language and this approach takes more time, while the simulation model can be easily built and quickly evaluated using SIMULINK.

Research advances in enhanced coal seam gas extraction by controllable shock wave fracturing

With the continuous increase of mining in depth,the gas extraction faces the challenges of low permeability,great ground stress,high temperature and large gas pressure in coal seam.The controllable shock wave(CSW),as a new method for enhancing permeability of coal seam to improve gas extraction,features in the advantages of high efficiency,eco-friendly,and low cost.In order to better utilize the CSW into gas extraction in coal mine,the mechanism and feasibility of CSW enhanced extraction need to be studied.In this paper,the basic principles,the experimental tests,the mathematical models,and the on-site tests of CSW fracturing coal seams are reviewed,thereby its future research directions are provided.Based on the different media between electrodes,the CSW can be divided into three categories:hydraulic effect,wire explosion and excitation of energetic materials by detonating wire.During the process of propagation and attenuation of the high-energy shock wave in coal,the shock wave and bubble pulsation work together to produce an enhanced permeability effect on the coal seam.The stronger the strength of the CSW is,the more cracks created in the coal is,and the greater the length,width and area of the cracks being.The repeated shock on the coal seam is conducive to the formation of complex network fracture system as well as the reduction of coal seam strength,but excessive shock frequency will also damage the coal structure,resulting in the limited effect of the enhanced gas extraction.Under the influence of ground stress,the crack propagation in coal seam will be restrained.The difference of horizontal principal stress has a significant impact on the shape,propagation direction and connectivity of the CSW induced cracks.The permeability enhancement effect of CSW is affected by the breakage degree of coal seam.The shock wave is absorbed by the broken coal,which may hinder the propagation of CSW,resulting in a poor effect of permeability enhancement.When arranging two adjacent boreholes for CSW permeability enhancement test,the spacing of boreholes should not be too close,which may lead to negative pressure mutual pulling in the early stage of drainage.At present,the accurate method for effectively predicting the CSW permeability enhanced range should be further investigated.

Model informed precision medicine of Chinese herbal medicines formulas-A multi-scale mechanistic intelligent model

Recent trends suggest that Chinese herbal medicine formulas(CHM formulas)are promising treatments for complex diseases.To characterize the precise syndromes,precise diseases and precise targets of the precise targets between complex diseases and CHM formulas,we developed an artificial intelligence-based quantitative predictive algorithm(DeepTCM).DeepTCM has gone through multilevel model calibration and validation against a comprehensive set of herb and disease data so that it accurately captures the complex cellular signaling,molecular and theoretical levels of traditional Chinese medicine(TCM).As an example,our model simulated the optimal CHM formulas for the treatment of coronary heart disease(CHD)with depression,and through model sensitivity analysis,we calculated the balanced scoring of the formulas.Furthermore,we constructed a biological knowledge graph representing interactions by associating herb-target and gene-disease interactions.Finally,we experimentally confirmed the therapeutic effect and pharmacological mechanism of a novel model-predicted intervention in humans and mice.This novel multiscale model opened up a new avenue to combine“disease syndrome”and“macro micro”system modeling to facilitate translational research in CHM formulas.