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.

A Mathematical Modeling of 3D Cubical Geometry Hypothetical Reservoir under the Effect of Nanoparticles Flow Rate,Porosity,and Relative Permeability

This study aims to formulate a steady-state mathematical model for a three-dimensional permeable enclosure(cavity)to determine the oil extraction rate using three distinct nanoparticles,SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3),in unconventional oil reservoirs.The simulation is conducted for different parameters of volume fractions,porosities,and mass flow rates to determine the optimal oil recovery.The impact of nanoparticles on relative permeability(kr)and water is also investigated.The simulation process utilizes the finite volume ANSYS Fluent.The study results showed that when the mass flow rate at the inlet is low,oil recovery goes up.In addition,they indicated that silicon nanoparticles are better at getting oil out of the ground(i.e.,oil reservoir)than Al_(2)O_(3)and Fe_(2)O_(3).Most oil can be extracted from SiO_(2),Al_(2)O_(3),and Fe_(2)O_(3)at a rate of 97.8%,96.5%,and 88%,respectively.

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.

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.

Practical Use of the Subjective Mathematical Model of Bayes and Its External Validation in Dental Medicine & Dentistry

Objective: Our study aims to validate the subjective Bayes mathematical model using the mathematical model of logistic regression. Expert systems are being utilized increasingly in medical fields for the purposes of assisting diagnosis and treatment planning in Dentistry. Existing systems used few symptoms for dental diagnosis. In Dentistry, few symptoms are not enough for diagnosis. In this research, a conditional probability model (Bayes rule) was developed with increased number of symptoms associated with a disease for diagnosis. A test set of recurrent cases was then used to test the diagnostic capacity of the system. The generated diagnosis matched that of the human experts. The system was also tested for its capacity to handle uncommon dental diseases and the system portrayed useful potential. Method: The study used the Subjective Mathematical Bayes Model (SBM) approach and employed Logistic Regression Mathematical Model (LMR) techniques. The external validation of the subjective mathematical Bayes model (MSB) concerns the real cases of 625 patients who developed alveolar osteitis (OA). We propose strategies for reproducibility and reporting standards, outlining an updated WAMBS (when to Worry and how to Avoid the Misuse of Bayesian Statistics) checklist. Finally, we outline the impact of Bayesian analysis Logistic Regression Mathematical Model (LMR) techniques and on artificial intelligence, a major goal in the next decade. Results: The internal validation had identified seven (7) etiological factors of OA, which will be compared to the cases of MRL, for the external validation which retained six (6) etiological factors of OA. The experts in the internal validation of the MSB had generated 40 cases of OA and a COP of (0.5), which will be compared to the MRL that collected 625 real cases of OA to produce a Cop of (0.6) in the external validation, which discriminates between healthy patients (Se) and sick patients (Sp). Compared to real cases and the logistic regression model, the Bayesian model is efficient and its validity is established.

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.

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.

Critical Analysis of Increasingly Mathematical Economics in the Modern Society

This paper critically examines the escalating trend of mathematization in economics,highlighting its implications and controversies in contemporary economic research.While the application of sophisticated mathematical models and statistical techniques has enhanced the precision,rigor,and status of economics within academia and practical application,concerns arise regarding the potential oversimplification and detachment from real-world complexities.The adoption of mathematical tools has arguably led to a focus on theoretically tractable problems at the expense of those more relevant to practical economic and social issues.This paper explores both the benefits and limitations of this trend,discussing how the reliance on quantitative methods affects the innovation,comprehensibility,and application of economic theories.We argue for a balanced approach that fosters innovation by integrating qualitative insights and embracing interdisciplinary methods to ensure economics remains both rigorous and relevant to societal needs.

Refined mathematical model for the breaching of concrete-face sand-gravel dams due to overtopping failure

Overtopping is one of the main reasons for the breaching of concrete-face sand-gravel dams(CFSGDs).In this study,a refined mathematical model was established based on the characteristics of the overtopping breaching of CFSGDs.The model characteristics were as follows:(1)Based on the Renormailzation Group(RNG)k-εturbulence theory and volume of fluid(VOF)method,the turbulent characteristics of the dam-break flow were simulated,and the erosion surface of the water and soil was tracked;(2)In consideration of the influence of the change in the sediment content on the dam-break flow,the dam material transport equation,which could reflect the characteristics of particle settlement and entrainment motion,was used to simulate the erosion process of the sand gravels;(3)Based on the bending moment balance method,a failure equation of the concrete face slab under dead weight and water load was established.The proposed model was verified through a case study on the failure of the Gouhou CFSGD.The results showed that the proposed model could well simulate the erosion mode of the special vortex flow of the CFSGD scouring the support body of the concrete face slab inward and reflect the mutual coupling relationship between the dam-break flow,sand gravels,and concrete face slabs.Compared with the measured values,the relative errors of the peak discharge,final breach average width,dam breaching duration,and maximum failure length of the face slab calculated using the proposed model were all less than 12%,thus verifying the rationality of the model.The proposed model was demonstrated to perform better and provide more detailed results than three selected parametric models and three simplified mathematical models.The study results can aid in establishing the risk level and devising early warning strategies for CFSGDs.

Well-Posedness and a Finite Difference Approximation for a Mathematical Model of HPV-Induced Cervical Cancer

We present a first-order finite difference scheme for approximating solutions of a mathematical model of cervical cancer induced by the human papillomavirus (HPV), which consists of four nonlinear partial differential equations and a nonlinear first-order ordinary differential equation. The scheme is analyzed and used to provide an existence-uniqueness result. Numerical simulations are performed in order to demonstrate the first-order rate of convergence. A sensitivity analysis was done in order to compare the effects of two drug types, those that increase the death rate of HPV-infected cells, and those that increase the death rate of the precancerous cell population. The model predicts that treatments that affect the precancerous cell population by directly increasing the corresponding death rate are far more effective than those that increase the death rate of HPV-infected cells.

Quantification of Ride Comfort Using Musculoskeletal Mathematical Model Considering Vehicle Behavior

This research aims to quantify driver ride comfort due to changes in damper characteristics between comfort mode and sport mode,considering the vehicle’s inertial behavior.The comfort of riding in an automobile has been evaluated in recent years on the basis of a subjective sensory evaluation given by the driver.However,reflecting driving sensations in design work to improve ride comfort is abstract in nature and difficult to express theoretically.Therefore,we evaluated the human body’s effects while driving scientifically by quantifying the driver’s behavior while operating the steering wheel and the behavior of the automobile while in motion using physical quantities.To this end,we collected driver and vehicle data using amotion capture system and vehicle CAN and IMU sensors.We also constructed a three-dimensional musculoskeletal mathematical model to simulate driver movements and calculate the power and amount of energy per unit of time used for driving the joints and muscles of the human body.Here,we used comfort mode and sport mode to compare damper characteristics in terms of hardness.In comfort mode,damper characteristics are soft and steering stability is mild,but vibration from the road is not easily transmitted to the driver making for a lighter load on the driver.In sport mode,on the other hand,damper characteristics are hard and steering stability is comparatively better.Still,vibration from the road is easily transmitted to the driver,whichmakes it easy for a load to be placed on the driver.As a result of this comparison,it was found that a load was most likely to be applied to the driver’s neck.This result in relation to the neck joint can therefore be treated as an objective measure for quantifying ride comfort.

Tight gas charging and accumulation mechanisms and mathematical model

The gas-water distribution and production heterogeneity of tight gas reservoirs have been summarized from experimental and geological observations, but the charging and accumulation mechanisms have not been examined quantitatively by mathematical model. The tight gas charging and accumulation mechanisms were revealed from a combination of physical simulation of nuclear magnetic resonance coupling displacement, numerical simulation considering material and mechanical equilibria, as well as actual geological observation. The results show that gas migrates into tight rocks to preferentially form a gas saturation stabilization zone near the source-reservoir interface. When the gas source is insufficient, gas saturation reduction zone and uncharged zone are formed in sequence from the source-reservoir interface. The better the source rock conditions with more gas expulsion volume and higher overpressure, the thicker the gas saturation stabilization and reduction zones, and the higher the overall gas saturation. When the source rock conditions are limited, the better the tight reservoir conditions with higher porosity and permeability as well as larger pore throat, the thinner the gas saturation stabilization and reduction zones, but the gas saturation is high. The sweet spot of tight gas is developed in the high-quality reservoir near the source rock, which often corresponds to the gas saturation stabilization zone. The numerical simulation results by mathematical model agree well with the physical simulation results by nuclear magnetic resonance coupling displacement, and reasonably explain the gas-water distribution and production pattern of deep reservoirs in the Xujiaweizi fault depression of the Songliao Basin and tight gas reservoirs in the Linxing-Huangfu area of the Ordos Basin.

Simulation Analysis of New Energy Vehicle Engine Cooling System Based on K-E Turbulent Flow Mathematical Model

New energy vehicles have better clean and environmental protection characteristics than traditional fuel vehicles.The new energy engine cooling technology is critical in the design of new energy vehicles.This paper used oneand three-way joint simulation methods to simulate the refrigeration system of new energy vehicles.Firstly,a k-εturbulent flow model for the cooling pump flow field is established based on the principle of computational fluid dynamics.Then,the CFD commercial fluid analysis software FLUENT is used to simulate the flow field of the cooling pump under different inlet flow conditions.This paper proposes an optimization scheme for new energy vehicle engines’“boiling”phenomenon under high temperatures and long-time climbing conditions.The simulation results show that changing the radiator’s structure and adjusting the thermostat’s parameters can solve the problem of a“boiling pot.”The optimized new energy vehicle engine can maintain a better operating temperature range.The algorithm model can reference each cryogenic system component hardware selection and control strategy in the new energy vehicle’s engine.

Modellings of Infectious Diseases and Cancers under Wars and Pollution Impacts in Iraq with Reference to a Novel Mathematical Model and Literature Review

Microbial pathogens include bacteria, viruses, fungi, and parasites and together account for a significant percentage of acute and chronic human diseases. In addition to understanding the mechanisms by which various pathogens cause human disease, research in microbial pathogenesis also addresses mechanisms of antimicrobial resistance and the development of new antimicrobial agents and vaccines. Answering fundamental questions regarding host-microbe interactions requires an interdisciplinary approach, including microbiology, genomics, informatics, molecular and cellular biology, biochemistry, immunology, epidemiology, environment and interaction between host and microbe. Studies investigating the direct effects of pollutants on respiratory tract infections are very vast, but those interested in the role of a pre-existing disease and effects of the exposure on the response to secondary stresses are few. In an experimental study at concentrations of air pollutants found in urban environments, frank toxicological responses are rarely observed, however, exposure to secondary stress like the respiratory challenge with infectious bacteria can exacerbate the response of the experimental host. The models like experimental, mechanical, and mathematical are the most abstract, but they allow analysis and logical proofs in a way that other approaches do not permit. The present review is mostly concerned with these model representations particularly with a novel mathematical model explaining the interaction between pathogen and immunity including the equivalence point.

Mathematical Modeling and Effect of Various Hot-Air Drying on Mushroom(Lentinus edodes)

An experimental study was performed to determine the characteristics and drying process of mushroom （Lentinus edodes） by 6 different hot-air drying methods namely isothermal drying, uniform raise drying, non-uniform raise drying, uniform intermittent drying, non-uniform intermittent drying and combined drying. The chemical composition （dry matter, ash, crude protein, crude fat, total sugars, dietary fiber, and energy）, color parameters （L, a＊, b＊, c＊, and h~） and rehydration capacities were determined. Among all the experiments, non-uniform intermittent drying reached a better comprehensive results due to the higher chemical composition, better color quality associated with high bright （26.381＋5.842）, high color tone （73.670＋2.975）, low chroma （13.349a：3.456） as well as the highest rehydration （453.76% weigh of dried body）. Nine kinds of classical mathematical model were used to obtained moisture data and the Midili-kucuk model can be described by the drying process with the coefficient （R2 ranged from 0.99790 to 0.99967）, chi-square （X2 ranged from 0.00003 to 0.00019） and root mean square error （RMSE ranged from 0.000486 to 0.0012367）.

Nonlinear Mathematical Modeling and Sensitivity Analysis of Hydraulic Drive Unit

The previous sensitivity analysis researches are not accurate enough and also have the limited reference value, because those mathematical models are relatively simple and the change of the load and the initial displacement changes of the piston are ignored, even experiment verification is not conducted. Therefore, in view of deficiencies above, a nonlinear mathematical model is established in this paper, including dynamic characteristics of servo valve, nonlinear characteristics of pressure-flow, initial displacement of servo cylinder piston and friction nonlinearity. The transfer function block diagram is built for the hydraulic drive unit closed loop position control, as well as the state equations. Through deriving the time-varying coefficient items matrix and time-varying free items matrix of sensitivity equations respectively, the expression of sensitivity equations based on the nonlinear mathematical model are obtained. According to structure parameters of hydraulic drive unit, working parameters, fluid transmission characteristics and measured friction-velocity curves, the simulation analysis of hydraulic drive unit is completed on the MATLAB/Simulink simulation platform with the displacement step 2 mm, 5 mm and 10 mm, respectively. The simulation results indicate that the developed nonlinear mathematical model is sufficient by comparing the characteristic curves of experimental step response and simulation step response under different constant load. Then, the sensitivity function time-history curves of seventeen parameters are obtained, basing on each state vector time-history curve of step response characteristic. The maximum value of displacement variation percentage and the sum of displacement variation absolute values in the sampling time are both taken as sensitivity indexes. The sensitivity indexes values above are calculated and shown visually in histograms under different working conditions, and change rules are analyzed. Then the sensitivity indexes values of four measurable parameters, such as supply pressure, proportional gain, initial position of servo cylinder piston and load force, are verified experimentally on test platform of hydraulic drive unit, and the experimental research shows that the sensitivity analysis results obtained through simulation are approximate to the test results. This research indicates each parameter sensitivity characteristics of hydraulic drive unit, the performance-affected main parameters and secondary parameters are got under different working conditions, which will provide the theoretical foundation for the control compensation and structure optimization of hydraulic drive unit.

Mathematical modeling of tornadoes and squall storms

Recent advances in modeling of tornadoes and twisters consist of significant achievements in mathematical calculation of occurrence and evolution of a violent F5-class tornado on the Fujita scale, and four-dimensional mathematical modeling of a tornado with the fourth coordinate time multiplied by its characteristic velocity. Such a tornado can arise in a thunderstorm supercell filled with turbulent whirlwinds. A theory of the squall storms is proposed. The squall storm is modeled by running pertur- bation of the temperature inversion on the lower boundary of cloudiness. This perturbation is induced by the action of strong, hurricane winds in the upper and middle troposphere, and looks like a running solitary wave （soliton）; which is developed also in a field of pressure and velocity of a wind. If a soliton of a squall storm gets into the thunderstorm supercell then this soliton is captured by supercell. It leads to additional pressure fall of air inside a storm supercell and stimulate amplification of wind velocity here. As a result, a cyclostrophic balance inside a storm supercell generates a tornado. Comparison of the radial distribution of wind velocity inside a tornado calculated by using the new formulas and equations with radar observations of the wind velocity inside Texas Tornado Dummit in 1995 and inside the 3 May 1999 Oklahoma City Tornado shows good correspondence.

Experimental optimization and mathematical modeling of supercritical carbon dioxide extraction of essential oil from Pogostemon cablin

The supercritical carbon dioxide extraction was applied to obtain essential oil from Pogostemon cablin in this work.Effect of extraction parameters including temperature,pressure,extraction time and particle size on extraction yield was investigated,and the response surface methodology with a Box–Behnken Design was used to achieve the optimized extraction conditions.The maximum yield of essential oil was 2.4356%under the conditions of extraction temperature 47°C,pressure 24.5 MPa and extraction time 119 min.Moreover,based on the Brunauer–Emmett–Teller theory of adsorption,a mathematical modeling was performed to correlate the measured data.The model shows a function relationship between extraction yield and time by a simple equation with three significantly adjustable parameters.These model parameters have been optimized through simulated annealing algorithm.The predicted data from the mathematical model show a good agreement with the experimental data of the different extraction parameters.