Mathematical Evaluation of the Impact of Awareness on Epidemic Model using Weighted Network

2019 ◽  
Vol 1 ◽  
pp. 214-223
Author(s):  
G O Agaba
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Human Population ◽  
System Analysis ◽  
Biological Systems ◽  
System Of Equations ◽  
Weighted Network ◽  
The Stability ◽  
Mathematical Evaluation ◽  
The Impact

The applications of graph theory in the area of networking are of great significance in system analysis of different varieties, including biological systems. In biological systems, the use of networks finds importance in the study of epidemic and its control. A practical example include the evaluation of the spread of disease within human population and the impact of awareness circulating admist the same population as a result of the infection. Agaba et al. in 2017 proposed a mathematical model that analysed the impact of awareness on the spread of infectious diseases. This was done using the stability analyses of the various steady states of the system of equations and also through the evaluation of some numerical simulations. This paper, with the aid of the system of equations developed by Agaba et al., 2017b, studies the impact of awareness spreading simultaneously with an infectious disease within human population using weighted network.

Dynamics of the impact of Twitter with time delay on the spread of infectious diseases

2018 ◽  
Vol 11 (05) ◽  
pp. 1850067 ◽  
Author(s):  
Maoxing Liu ◽  
Yuting Chang ◽  
Haiyan Wang ◽  
Benxing Li
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Reproduction Number ◽  
Behavioral Changes ◽  
The Public ◽  
The Stability ◽  
The Impact ◽  
The Basic Reproduction Number

In this paper, a mathematical model to study the impact of Twitter in controlling infectious disease is proposed. The model includes the dynamics of “tweets” which may enhance awareness of the disease and cause behavioral changes among the public, thus reducing the transmission of the disease. Furthermore, the model is improved by introducing a time delay between the outbreak of disease and the release of Twitter messages. The basic reproduction number and the conditions for the stability of the equilibria are derived. It is shown that the system undergoes Hopf bifurcation when time delay is increased. Finally, numerical simulations are given to verify the analytical results.

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 A mathematical model of infectious disease transmission

2020 ◽  
Vol 34 ◽  
pp. 02002
Author(s):  
Aurelia Florea ◽  
Cristian Lăzureanu
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Nonlinear System ◽  
Numerical Simulations ◽  
Disease Transmission ◽  
Three Dimensional ◽  
Type System ◽  
Epidemic Disease ◽  
Infectious Disease Transmission ◽  
The Stability

In this paper we consider a three-dimensional nonlinear system which models the dynamics of a population during an epidemic disease. The considered model is a SIS-type system in which a recovered individual automatically becomes a susceptible one. We take into account the births and deaths, and we also consider that susceptible individuals are divided into two groups: non-vaccinated and vaccinated. In addition, we assume a medical scenario in which vaccinated people take a special measure to quarantine their newborns. We study the stability of the considered system. Numerical simulations point out the behavior of the considered population.

scholarly journals An Approach for the Global Stability of Mathematical Model of an Infectious Disease

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1778
Author(s):  
Mojtaba Masoumnezhad ◽  
Maziar Rajabi ◽  
Amirahmad Chapnevis ◽  
Aleksei Dorofeev ◽  
Stanford Shateyi ◽  
...  
Keyword(s):  
Infectious Disease ◽  
Mathematical Model ◽  
Global Stability ◽  
Incidence Rates ◽  
Endemic Equilibrium ◽  
Symmetry Properties ◽  
Nonlinear Incidence Rates ◽  
Lyapunov Matrix ◽  
The Stability ◽  
The Mathematical Model

The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

Fuzzy Parameter Based Mathematical Model on Forest Biomass

2018 ◽  
Vol 13 (04) ◽  
pp. 179-193 ◽  
Author(s):  
Prabir Panja
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Time Delay ◽  
Human Population ◽  
Equilibrium Points ◽  
Forest Biomass ◽  
Simulation Results ◽  
The Stability ◽  
Fuzzy Parameter

In this paper, a fuzzy mathematical model has been developed by considering forest biomass, human population and technological effort for the conservation of forest biomass as separate compartments. We have assumed that the forest biomass and human population grows logistically. We have considered that forest biomass decreases due to industrialization, food, shelter, etc., for humans. For the conservation of forest biomass, some modern technological efforts have been used in this model. Also, time delay of use of modern technological effort for the conservation of forest biomass has been considered on forest biomass. According to the assumptions, a fuzzy mathematical model on forest biomass is formulated. Next we have determined different possible equilibrium points. Also, the stability of our proposed system around these equilibrium points has been discussed. Finally, some numerical simulation results have been presented for better understanding of our proposed mathematical model.

scholarly journals Modeling the Impact of Rain on Population Exposed to Air Pollution

2020 ◽  
Vol 21 (3-4) ◽  
pp. 363-370
Author(s):  
Sandeep Sharma ◽  
Nitu Kumari
Keyword(s):  
Mathematical Model ◽  
Air Pollution ◽  
Adverse Effects ◽  
Air Pollutants ◽  
Human Population ◽  
Anthropogenic Activities ◽  
Living Species ◽  
The Impact ◽  
Concentration Of Air Pollutants

AbstractAir pollution is caused by contamination of air due to various natural and anthropogenic activities. The growing air pollution has diverse adverse effects on human health and other living species. However, a significant reduction in the concentration of air pollutants has been observed during the rainy season. Recently, a number of studies have been performed to understand the mechanism of removal of air pollutants due to the rain. These studies have found that rain is helpful in removing many air pollutants from the environment. In this paper, we proposed a mathematical model to investigate the role of rain in the removal of air pollutants and its subsequent impacts on the human population.

scholarly journals STABILITY OF THE RUSSIAN BANKING SECTOR: TRENDS AND RISKS

2021 ◽  
pp. 10-19
Author(s):  
E.V. Travkina ◽  
Keyword(s):  
Commercial Bank ◽  
Banking Sector ◽  
System Analysis ◽  
Negative Impact ◽  
Banking System ◽  
Qualitative Assessment ◽  
The Stability ◽  
Procedural Components ◽  
Statistical Survey ◽  
The Impact

In the modern conditions of functioning of the banking system, the issues that arise with the assess¬ment of the stability of a commercial bank individually and the banking sector as a whole in connection with the aggravation of the negative impact of many risk-forming factors associated with the manifestation of the pandemic are updated. In this regard, a comprehensive systematization of the existing Russian and international practice of implementing a qualitative assessment of the stability of banking organizations becomes important. The purpose of the study is to identify trends in the development of the Russian banking sector and the manifestations of banking risks that have a negative impact on its stability, as well as to identify practical opportunities to reduce the impact of these risks. The following general scientific and special methods were chosen as scientific tools for conducting this study: the method of system analysis, the method of retrospective analysis, as well as the methods of statistical survey. The information base of the study was the statistical data of the Bank of Russia. The theoretical and meth¬odological basis of the study was the works of such researchers as Fetisov G. G., Lavrushin O. I., Tarkhanov E. A., Muraviev A. K. Ovchinnikov O. P., Betz A. Yu., Peresetsky A. A. Kromonov V. S., etc. The study is based on the basic definitions of the stability of banking organizations and the regulatory framework for assessing the stability of the Russian commercial bank, as well as methods, mechanisms and procedural components for assessing the stability of the Russian banking sector. The results of the study are aimed at identifying trends and risks that affect the stability of both the Russian banking system as a whole and individual commercial banks. As practical recom¬mendations, the directions for further sustainable development of the Russian banking sector in the context of the negative impact of the pandemic on the national economy are presented.

scholarly journals Spherically symmetric anisotropic charged solution under complete geometric deformation approach

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
S. K. Maurya ◽  
Asma Mohammed Al Aamri ◽  
Athari Khalifa Al Aamri ◽  
Riju Nag
Keyword(s):  
Systematic Approach ◽  
Compact Objects ◽  
System Of Equations ◽  
Field Equations ◽  
Stellar Objects ◽  
Spacetime Geometry ◽  
Geometric Deformation ◽  
Physical Validity ◽  
The Stability ◽  
The Impact

AbstractWe present a new systematic approach to find the exact gravitationally decoupled anisotropic spherical solution in the presence of electric charge by using the complete geometric deformation (CGD) methodology. To do this, we apply the transformations over both gravitational potentials by introducing two unknown deformation functions. This new systematic approach allows us to obtain the exact solution of the field equations without imposing any particular ansatz for the deformation functions. Specifically, a well-known mimic approach and equation of state (EOS) have been applied together for solving the system of equations, which determine the radial and temporal deformation functions, respectively. The matching conditions at the boundary of the stellar objects with the exterior Reissner–Nordström metric are discussed in detail. In order to see the physical validity of the solution, we used well-behaved interior seed spacetime geometry and solved the system of equations using the above approaches. Next, we presented several physical properties of the solution through their graphical representations. The stability and dynamical equilibrium of the solution have been also discussed. Finally, we predicted the radii and mass-radius ratio for several compact objects for different decoupling parameters together with the impact of the decoupling parameters on the thermodynamical observables.

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.

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