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.

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 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.

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.

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.

Physical and Mathematical Modeling of the Argon-Oxygen Decarburization Refining Process of Stainless Steel

The available studies in the literature on physical and mathematical modeling of the argon oxygen decarburization (AOD) process of stainless steel have briefly been reviewed. The latest advances made by the author with his research group have been summarized. Water modeling was used to investigate the fluid flow and mixing characteristics in the bath of an 18 t AOD vessel, as well as the 'back attack' action of gas jets and its effects on the erosion and wear of the refractory lining, with sufficiently full kinematic similarity. The non rotating and rotating gas jets blown through two annular tuyeres, respectively of straight tube and spiral flat tube type, were employed in the experiments. The geometric similarity ratio between the model and its prototype (including the straight tube type tuyeres) was 1:3. The influences of the gas flow rate, the angle included between the two tuyeres and other operating parameters, and the suitability of the spiral tuyere as a practical application, were examined. These latest studies have clearly and successfully brought to light the fluid flow and mixing characteristics in the bath and the overall features of the back attack phenomena of gas jets during the blowing, and have offered a better understanding of the refining process. Besides, mathematical modeling for the refining process of stainless steel was carried out and a new mathematical model of the process was proposed and developed. The model performs the rate calculations of the refining and the mass and heat balances of the system. Also, the effects of the operating factors, including adding the slag materials, crop ends, and scrap, and alloy agents; the non isothermal conditions; the changes in the amounts of metal and slag during the refining; and other factors were all considered. The model was used to deal with and analyze the austenitic stainless steel making (including ultra low carbon steel) and was tested on data of 32 heats obtained in producing 304 grade steel in an 18 t AOD vessel. The changes in the bath composition and temperature during the refining process with time can be accurately predicted using this model. The model can provide some very useful information and a reliable basis for optimizing the process practice of the refining of stainless steel and control of the process in real time and online.

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.

Germanium transport across supported liquid membrane with Cyanex 923: Mathematical modeling

A mathematical model was developed to monitor the facilitated transport of germanium(IV) from oxalic acid solutions through a flat sheet supported liquid membrane(FSSLM) containing four trialkylphosphine oxides(Cyanex 923). The FSSLM modeling was based on the extraction constant(Kext) calculated from the liquid-liquid extraction(LLX) modeling. The LLX model presented a reliable calculation of the extraction constant(Kex= 2.057×103 L/mol4). The FSSLM model was solved using Matlab■ software according to extraction constant, Fick’s law, and diffusional principles. The model predicts the overall mass transfer coefficient(Korg) to be 3.84 cm/s. Using this value, diffusion coefficients(Dm) for various Cyanex 923 concentrations of 0.126, 0.252, 0.378, 0.505, 0.631 and 0.757 mol/L are found to be 8.50×10^-4, 4.30×10^-4, 1.87×10^-4, 5.87×10^-5, 2.57×10^-5, 2.09×10^-5 cm2/s, respectively. The results show that the diffusion rate of the current study is approximately more than that of similar FSSLM systems containing Cyanex 923 used to transport various metals. The modeling values are in good agreement with the experimental data, showing the good reliability of the mathematical model.

Impact of pertinent parameters on foam behavior in the entrance region of porous media:mathematical modeling

Foam injection is a promising solution for control of mobility in oil and gas field exploration and development,including enhanced oil recovery,matrix-acidization treatments,contaminated-aquifer remediation and gas leakage prevention.This study presents a numerical investigation of foam behavior in a porous medium.Fractional flow method is applied to describe steady-state foam displacement in the entrance region.In this model,foam flow for the cases of excluding and including capillary pressure and for two types of gas,nitrogen(N2)and carbon dioxide(CO2)are investigated.Effects of pertinent parameters are also verified.Results indicate that the foam texture strongly governs foam flow in porous media.Required entrance region may be quite different for foam texture to accede local equilibrium,depending on the case and physical properties that are used.According to the fact that the aim of foaming of injected gas is to reduce gas mobility,results show that CO2 is a more proper injecting gas than N2.There are also some ideas presented here on improvement in foam displacement process.This study will provide an insight into future laboratory research and development of full-field foam flow in a porous medium.

Mathematical Modeling,Field Calibration and Numerical Simulation of Low-Speed Mixed Traffic Flow in Cities

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Modeling Tracer Flow Characteristics in Different Types of Pores: Visualization and Mathematical Modeling

Structure of porous media and fluid distribution in rocks can significantly affect the transport characteristics during the process of microscale tracer flow.To clarify the effect of micro heterogeneity on aqueous tracer transport,this paper demonstrates microscopic experiments at pore level and proposes an improved mathematical model for tracer transport.The visualization results show a faster tracer movement into movable water than it into bound water,and quicker occupancy in flowing pores than in storage pores caused by the difference of tracer velocity.Moreover,the proposed mathematical model includes the effects of bound water and flowing porosity by applying interstitial flow velocity expression.The new model also distinguishes flowing and storage pores,accounting for different tracer transport mechanisms(dispersion,diffusion and adsorption)in different types of pores.The resulting analytical solution better matches with tracer production data than the standard model.The residual sum of squares(RSS)from the new model is 0.0005,which is 100 times smaller than the RSS from the standard model.The sensitivity analysis indicates that the dispersion coefficient and flowing porosity shows a negative correlation with the tracer breakthrough time and the increasing slope,whereas the superficial velocity and bound water saturation show a positive correlation.

Mathematical Modeling of the Vacuum Circulation Refining Process of Molten Steel

The available studies in the literature on mathematical modeling of the vacuum circulation (RH) refining process of molten steel have briefly been reviewed. The latest advances obtained by the author with his research group have been summarized. On the basis of the mass and momentum balances in the system, a new mathematical model for decarburization and degassing during the RH and RH KTB refining processes of molten steel was proposed and developed. The refining roles of the three reaction sites, i.e. the up snorkel zone, the droplet group and steel bath in the vacuum vessel, were considered in the model. It was assumed that the mass transfer of reactive components in the molten steel is the rate control step of the refining reactions. And the friction losses and drags of flows in the snorkels and vacuum vessel were all counted. The model was applied to the refining of molten steel in a multifunction RH degasser of 90 t capacity. The decarburization and degassing processes in the degasser under the RH and RH KTB operating conditions were modeled and analyzed using this model. Besides, proceeded from the two resistance mass transfer theory and the mass balance of sulphur in the system, a kinetic model for the desulphurization by powder injection and blowing in the RH refining of molten steel was developed. Modeling and predictions of the process of injecting and blowing the lime based powder flux under assumed operating modes with the different initial contents of sulphur and amounts of powder injected and blown in a RH degasser of 300 t capacity were carried out using the model. It was demonstrated that for the RH and RH KTB refining processes, and the desulphurization by powder injection and blowing in the RH refining, the results predicted by the models were all in good agreement respectively with data from industrial experiments and practice. These models may be expected to offer some useful information and a reliable basis for determining and optimizing the technologies of the RH and RH KTB refining and desulphurization by powder injection and blowing in the RH refining and for controlling the processes.

Mathematical modeling of induction heating of discard substitution block for billet hot extrusion process

A magnetic and temperature field-coupled mathematical model is proposed to calculate the induction heating process of a discard substitution block for billet hot extrusion process. The mathematical model is validated by comparing simulation results with temperature measurements recorded during physical modeling. Based on systematical analysis of calculation results, a quantitative sawtooth induction power curve was proposed to realize the aim of achieving the best distributed temperature field in the block within the shortest induction time.

Near Future Perspective of ESBL-Producing Klebsiella pneumoniae Strains Using Mathematical Modeling

While antibiotic resistance is becoming increasingly serious today,there is almost no doubt that more challenging times await us in the future.Resistant microorganisms have increased in the past decades leading to limited treatment options,along with higher morbidity and mortality.Klebsiella pneumoniae is one of the significant microorganisms causing major public health problems by acquiring resistance to antibiotics and acting as an opportunistic pathogen of healthcare-associated infections.The production of extended spectrumbeta-lactamases(ESBL)is one of the resistance mechanisms of K.pneumoniae against antibiotics.In this study,the future clinical situation of ESBL-producing K.pneumoniae was investigated in order to reflect the future scenarios to understand the severity of the issue and to determine critical points to prevent the spread of the ESBL-producing strain.For evaluation purposes,SIS-type mathematical modeling was used with retrospective medical data from the period from 2016 to 2019.Stability of the disease-free equilibrium and basic reproduction ratios were calculated.Numerical simulation of the SISmodel was conducted to describe the dynamics of non-ESBL and ESBL-producing K.pneumoniae.In order to determine the most impactful parameter on the basic reproduction ratio,sensitivity analysis was performed.A study on mathematical modeling using data on ESBL-producing K.pneumoniae strains has not previously been performed in any health institution in Northern Cyprus,and the efficiency of the parameters determining the spread of the relevant strains has not been investigated.Through this study,the spread of ESBL-producing K.pneumoniae in a hospital environment was evaluated using a different approach.According to the study,in approximately seventy months,ESBL-producing K.pneumoniae strains will exceed non-ESBL K.pneumoniae strains.As a result,the analyses showed that hospital admissions and people infected with non-ESBL or ESBL-producing K.pneumoniae have the highest rate of spreading the infections.In addition,it was observed that the use of antibiotics plays a major role in the spread of ESBL-producing K.pneumoniae compared to other risk factors such as in-hospital transmissions.As amatter of course,recoveries fromKlebsiella infections were seen to be the most effective way of limiting the spread.It can be concluded from the results that although the use of antibiotics is one of themost effective factors in the development of the increasing ESBL-producing K.pneumoniae,regulation of antibiotic use policy could be a remedial step together with effective infection control measures.Such steps may hopefully lead to decreased morbidity and mortality rates as well as improved medical costs.

Advances in Mathematical Modeling of NFκB Signal Transduction in Mammals

NFκB is a basic transcription factor of cell signal transduction in mammals. Mathematical modeling can be used to simulate NFκB signal transduction and investigate the molecular mechanism. The initial IKB-NFκB signal transduction model emphasized the effects of negative feedback on NFκB temporal dynamics and gene expression control, while subsequent studies are concentrated on other feedback loops, input-output behaviors of modules, crosslinking of several NFκB activation paths and NFκB oscillation. Computer technology will continue to contribute to studies of NFKB signaling pathway. Finally, several potential development trends were discussed in this paper.

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.

Mathematical Modeling of the Hydrodynamics of an EGSB Reactor

Generally, in the literature, the hydrodynamic behavior of an EGSB （expanded granular sludge bed） reactor is considered as a complete mix reactor. Few works study in detail the flow of such reactors. The aim of this work was to study, in detail, the hydrodynamics of an EGSB reactor and to propose a mathematical model to describe its flow. A 3.04 L reactor was used with HRT （hydraulic retention time） of 12 h, affluent flowrate of 4 mL·min^-1, and the recirculation flow rate was changed to study three different upflow velocities in the tube （6, 8 and 10 m·h^-1. The pulse input method was used, with the use of blue dextran as tracer. In order to consider the dimensional differences between the tube and the separator, the reactor was divided into two regions （tube and separator）. Initially, a model with two tubular reactors with dispersion in series was proposed and the Peclet number was adjusted for the two regions. It was observed that the region of the tube shows the behavior of a tubular reactor with high dispersion, whereas the region of the separator shows the behavior of a complete mix reactor. In order to simplify the equation, and by knowing that the concentration profile along the reactor was almost constant, a model of two CSTRs （continuous stirred tank reactors） was proposed in series and the number of reactors （N） was set. The best combination was five CSTRs, three in the tube region and two in the separator region. The presented models were equivalent and can be used to describe the hydrodynamic behavior of the EGSB reactor.

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.

Study on Mathematical Modeling Software MATLAB Teaching in Higher Vocational Colleges

The present situation of the mathematics teaching in higher vocational colleges is not optimistic. In the new education system, it is an urgent problem for the mathematics teachers in higher vocational colleges to bring forth new ideas for the teaching methods, improve the students＇ interest in learning, and train the application-oriented talented personnel needed by the society. MATLAB software package can help set up a bridge and link for the mathematics teaching and the practical application. Its powerful numerical calculation ability can quickly solve all kinds of calculation problems, so that the basic thinking methods are more closely focused in mathematics teaching and also more conditions are created for mathematics teaching to combine the actual major conditions and life conditions. In this paper, the related problems in the implementation of mathematical modeling software MATLAB and model in higher vocational colleges are discussed.