scholarly journals On Mathematical Modelling of the Indian Human Hair Industry in the Post-COVID-19 Era

2021 ◽  
Vol 8 (3) ◽  
pp. 447-452
Author(s):  
Shibam Manna ◽  
Tanmay Chowdhury ◽  
Asoke Kumar Dhar ◽  
Juan Jose Nieto
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Human Hair ◽  
Control Parameter ◽  
Employment Opportunities ◽  
Alternative Employment ◽  
Job Opportunities ◽  
Proposed Model ◽  
The Stability ◽  
The Impact

An attempt to model the human hair industry in the post-COVID-19 pandemic situation using mathematical modelling has been the goal of this article. Here we introduce a novel mathematical modelling using a system of ordinary differential equations to model the human hair industry as well as the human hair waste management and related job opportunities. The growth of human hair in the months of nationwide total lockdown has been taken into account and graphs have been plotted to analyze the effect of Lockdown in this model. The alternative employment opportunities that can be created for collecting excessive hair in the post-pandemic period has been discussed. A probable useful mathematical model and mechanism to utilize the migrant labours who became jobless due to the pandemic situation and the corresponding inevitable lockdown situation resulting out of that crisis has been discussed in this paper. We discussed the stability analysis of the proposed model and obtained the criteria for an optimal profit of the said model. Graphs have also been plotted to analyze the impact of the control parameter on the optimal profit.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

scholarly journals NECESSITY TO IMPROVE THE MATHEMATICAL MODEL OF FREIGHT CARS TO STUDY CASES OF ITS DERAILMENTS

2020 ◽  
pp. 442-451
Author(s):  
А.V. Batig ◽  
A. Ya. Kuzyshyn
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Computer Experiment ◽  
Rolling Stock ◽  
Software Systems ◽  
Freight Car ◽  
The Stability ◽  
The Many ◽  
The Impact ◽  
The Mathematical Model

One of the most important problems that pose a serious threat to the functioning of railways is the problem of freight cars derailment. However, according to statistics, the number of cases of the derailments of freight cars in trains annually grows. Тo prevent such cases, the necessary preventive measures are developed, and to study the causes of their occurrence, a significant number of mathematical models, programs and software systems created by leading domestic and foreign scientists. Studies of such mathematical models by the authors of this work have led to the conclusion that they are not sufficiently detailed to the extent that it is necessary for analyze the reasons of its derailment. At the same time, an analysis of the causes of the rolling stock derailments on the railways of Ukraine over the past five years showed that in about 20 % of cases they are obvious, and in 7 % of cases they are not obvious and implicitly expressed. The study of such cases of rolling stock derailment during an official investigation by the railway and during forensic railway transport expertises requires the use of an improved mathematical model of a freight car, which would allow a quantitative assessment of the impact of its parameters and rail track on the conditions of railway accidents. Therefore, taking into account the main reasons that caused the occurrence of such railroad accidents over the last five years on the railways of Ukraine, the article selected the main directions for improving the mathematical model of a freight car, allowing to cover all the many factors (explicit and hidden) and identify the most significant ones regarding the circumstances of the derailment rolling stock off the track, established on the basis of a computer experiment. It is proposed in the mathematical model of a freight car to take into account the guiding force, the value of which is one of the main indicators of the stability of the rolling stock. The authors of the article noted that not taking into account the influence of the guiding forces on the dynamics of the freight car can lead to an erroneous determination of the reasons for the rolling stock derailment or even to the impossibility of establishing them.

scholarly journals KGPMH: A hybrid approach for solving a novel facility location problem

2021 ◽  
Author(s):  
Maryam DehghanChenary ◽  
Arman Ferdowsi ◽  
Fariborz Jolai ◽  
Reza Tavakkoli-Moghaddam
Keyword(s):  
Mathematical Model ◽  
Location Problem ◽  
Hybrid Approach ◽  
Facility Location Problem ◽  
Evaluation Function ◽  
Genetic Approach ◽  
Hub Location ◽  
Hub Location Problem ◽  
Proposed Model ◽  
The Impact

<pre>The focus of this paper is to propose a bi-objective mathematical model for a new extension of a multi-period p-mobile hub location problem and then to devise an algorithm for solving it. The developed model considers the impact of the time spent traveling at the hubs' network, the time spent at hubs for processing the flows, and the delay caused by congestion at hubs with specific capacities. Following the unveiled model, a hybrid meta-heuristic algorithm will be devised that simultaneously takes advantage of a novel evaluation function, a clustering technique, and a genetic approach for solving the proposed model.</pre>

scholarly journals Quantification of plasma cell dynamics using mathematical modelling

2018 ◽  
Vol 5 (1) ◽  
pp. 170759 ◽  
Author(s):  
Marcel Mohr ◽  
Dirk Hose ◽  
Anja Seckinger ◽  
Anna Marciniak-Czochra
Keyword(s):  
Mathematical Model ◽  
Bone Marrow ◽  
Mathematical Modelling ◽  
Plasma Cells ◽  
Cell Dynamics ◽  
Growth And Survival ◽  
Specific Antibodies ◽  
Health And Disease ◽  
Potential Basis ◽  
The Impact

Plasma cells (PCs) are the main antibody-producing cells in humans. They are long-lived so that specific antibodies against either pathogens or vaccines are produced for decades. PC longevity is attributed to specific areas within the bone marrow micro-environment, the so-called ‘niche’, providing the cells with required growth and survival factors. With antigen encounters, e.g. infection or vaccination, new PCs are generated and home to the bone marrow where they compete with resident PCs for the niche. We propose a parametrized mathematical model describing healthy PC dynamics in the bone marrow. The model accounts for competition for the niche between newly produced PCs owing to vaccination and resident PCs. Mathematical analysis and numerical simulations of the model allow explanation of the recovery of PC homoeostasis after a vaccine-induced perturbation, and the fraction of vaccine-specific PCs inside the niche. The model enables quantification of the niche-related dynamics of PCs, i.e. the duration of PC transition into the niche and the impact of different rates for PC transitions into and out of the niche on the observed cell dynamics. Ultimately, it provides a potential basis for further investigations in health and disease.

Assessing the impact of agrochemicals on schistosomiasis transmission: A mathematical study

2021 ◽  
pp. 2150049
Author(s):  
Liming Cai ◽  
Peixia Yue ◽  
Mini Ghosh ◽  
Xuezhi Li
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Agricultural Pollution ◽  
Parasitic Disease ◽  
Mathematical Study ◽  
Proposed Model ◽  
Existence And Stability ◽  
The Impact

Schistosomiasis is a snail-borne parasitic disease, which is affecting almost 240 million people worldwide. The number of humans affected by schistosomiasis is continuously increasing with the rise in the use of agrochemicals. In this paper, a mathematical model is formulated and analyzed to assess the effect of agrochemicals on the transmission of schistosomiasis. The proposed model incorporates the effects of fertilizers, herbicides and insecticides on susceptible snails and snail predators along with schistosomiasis disease transmission. The existence and stability of the equilibria in the model are discussed. Sensitivity analysis is performed to identify the key parameters of the proposed model, which contributes most in the transmission of this disease. Numerical simulations are also performed to assess the impact of fertilizers, herbicides and insecticides on schistosomiasis outbreaks. Our study reveals that the agricultural pollution can enhance the transmission intensity of schistosomiasis, and in order to prevent the outbreak of schistosomiasis, the use of pesticides should be controlled.

scholarly journals Pneumatic Adaptive Absorber: Mathematical Modelling with Experimental Verification

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Grzegorz Mikułowski ◽  
Rafał Wiszowaty
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Experimental Verification ◽  
Load Capacity ◽  
Mechanical Energy ◽  
Specific Situation ◽  
Engineering Structures ◽  
Piston Cylinder ◽  
Proposed Model ◽  
Energy Absorbers

Many of mechanical energy absorbers utilized in engineering structures are hydraulic dampers, since they are simple and highly efficient and have favourable volume to load capacity ratio. However, there exist fields of applications where a threat of toxic contamination with the hydraulic fluid contents must be avoided, for example, food or pharmacy industries. A solution here can be a Pneumatic Adaptive Absorber (PAA), which is characterized by a high dissipation efficiency and an inactive medium. In order to properly analyse the characteristics of a PAA, an adequate mathematical model is required. This paper proposes a concept for mathematical modelling of a PAA with experimental verification. The PAA is considered as a piston-cylinder device with a controllable valve incorporated inside the piston. The objective of this paper is to describe a thermodynamic model of a double chamber cylinder with gas migration between the inner volumes of the device. The specific situation considered here is that the process cannot be defined as polytropic, characterized by constant in time thermodynamic coefficients. Instead, the coefficients of the proposed model are updated during the analysis. The results of the experimental research reveal that the proposed mathematical model is able to accurately reflect the physical behaviour of the fabricated demonstrator of the shock absorber.

scholarly journals Stabiizing The Steady State Solution of Lasser Fever: Problems and Prospect

2022 ◽  
Vol 05 (01) ◽  
Author(s):  
Innocent C. Eli ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Control Parameter ◽  
Steady State Solution ◽  
Lassa Fever ◽  
Sexual Contact ◽  
Opposite Sex ◽  
The Stability ◽  
And Control ◽  
Disease Free

The study of mathematical modeling of the stability analysis of Lassa fever was examined. A mathematical model for the spread and control of Lassa fever was formulated and analyzed. The model incorporates a control parameter, the use of condom to control human to human transmission through sexual contact with opposite sex. The disease free and endemic equilibrium states were analyzed.

scholarly journals A Mathematical Modelling of The Dynamics of Voters Model of Two Political Fanaticism Figures with The Interaction Between Voters in Indonesian Presidential Elections

2021 ◽  
Vol 2123 (1) ◽  
pp. 012006
Author(s):  
B. Yong
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Modelling ◽  
Presidential Elections ◽  
Dynamical Analysis ◽  
Equilibrium Solutions ◽  
Presidential Candidates ◽  
The Difference ◽  
The Stability ◽  
Political Figure

Abstract In this study, we present a dynamical analysis of the NS1S2A mathematical model that describe votes movement of voters in presidential elections. The NS1S2A deterministic voters model of two political fanaticism figures is described by ordinary differential equations. We considering the interaction between voters in the supportive voters compartment. We investigate the existence and the stability of four equilibrium solutions; free of supportive voters, supportive voters to first political figure, supportive voters to second political figure, and supportive voters to all political figures. Then we demonstrate this model by estimating the number of votes of two presidential candidates in Indonesian presidential elections. A numerical simulation is given to verify our analytical results. The result shows that the difference in the number of votes between the model with the interaction between voters and survey conducted by Litbang KOMPAS is smaller than the model without the interaction between voters.

scholarly journals Systemic Risk in the Interbank Market with Overlapping Portfolios

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Shanshan Jiang ◽  
Hong Fan
Keyword(s):  
Interest Rate ◽  
Systemic Risk ◽  
Banking System ◽  
Bipartite Network ◽  
Investment Risk ◽  
Interbank Market ◽  
Operating Rules ◽  
Proposed Model ◽  
The Stability ◽  
The Impact

The increasing frequency and scope of the financial crisis have attracted more attention in the research of the systemic risk of banking system. A new model for the interbank market with overlapping portfolios is proposed to simulate a banking system in this work. The proposed model uses a bipartite network of banks and their assets to analyze the impact of bank investment on the stability of the banking system. In addition, this model introduces investment risk and allows banks to make up for liquidity by selling devaluated assets, which reflects the operating rules of the banking system more realistically. The results show that allowing banks to sell devaluated assets to make up for liquidity can improve the stability of the banking system and the interbank market can also improve the stability of the banking system. For the investment of banks, the investment risk is an uncertain factor that affects the stability of the banking system. The proposed model further analyzes the impact of average investment interest rate, savings interest rate, deposit reserve ratio, and investment asset diversity on the stability of the banking system. The model provides a tool for policy-makers and supervision agencies to prevent the systemic risk of banking system.

scholarly journals Estimating Parameters in Mathematical Model for Societal Booms through Bayesian Inference Approach

2020 ◽  
Vol 25 (3) ◽  
pp. 42
Author(s):  
Yasushi Ota ◽  
Naoki Mizutani
Keyword(s):  
Mathematical Model ◽  
Bayesian Inference ◽  
Diffusion Of Innovation ◽  
Model Fitting ◽  
Sir Model ◽  
Actual Data ◽  
Diffusion Of Innovation Theory ◽  
Mathematical Properties ◽  
Proposed Model ◽  
The Stability

In this study, based on our previous study in which the proposed model is derived based on the SIR model and E. M. Rogers’s Diffusion of Innovation Theory, including the aspects of contact and time delay, we examined the mathematical properties, especially the stability of the equilibrium for our proposed mathematical model. By means of the results of the stability in this study, we also used actual data representing transient and resurgent booms, and conducted parameter estimation for our proposed model using Bayesian inference. In addition, we conducted a model fitting to five actual data. By this study, we reconfirmed that we can express the resurgences or minute oscillations of actual data by means of our proposed model.

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