scholarly journals A mathematical Model for the Dynamics of COVID-19 Pandemy Involving the Infective Immigrants

2021 ◽  
pp. 295-307
Author(s):  
Ahmed A. Mohsen ◽  
Hassan F. AL-Husseiny ◽  
Khalid Hattaf ◽  
Bilal Boulfoul
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Foreign Students ◽  
Dynamical Behavior ◽  
Foreign Workers ◽  
Proposed Model ◽  
Rapid Spread ◽  
The Stability ◽  
Control And Management ◽  
Stability Results

Since the first outbreak in Wuhan, China, in December 31, 2019, COVID-19    pandemy  ‎has been spreading to many countries in the world. The ongoing COVID-19 pandemy has caused a ‎major global crisis, with 554,767 total confirmed cases, 484,570 total recovered cases, and ‎‎12,306 deaths in Iraq as of February 2, 2020. In the absence of any effective therapeutics or drugs ‎and with an unknown epidemiological life cycle, predictive mathematical models can aid in ‎the understanding of both control and management of coronavirus disease. Among the important ‎factors that helped the rapid spread of the epidemy are immigration, travelers, foreign workers, and foreign students. In this work, we develop a mathematical model to study the dynamical ‎behavior of COVID-19 pandemy, involving immigrants' effects with the possibility of re-infection. ‎Firstly, we studied the positivity and roundedness of the solution of the proposed model. The stability ‎results of the model at the disease-free equilibrium point were presented when . Further, it was proven that the pandemic equilibrium point will persist uniformly when . Moreover, we ‎confirmed the occurrence of the local bifurcation (saddle-node, pitchfork, and transcritical). Finally, ‎theoretical analysis and numerical results were shown to be consistent.

On the Dynamical Behavior of Three Species System with Time Delays

2011 ◽  
Vol 130-134 ◽  
pp. 1544-1546
Author(s):  
Dan Na Sun ◽  
Zi Ku Wu
Keyword(s):  
Numerical Simulation ◽  
Equilibrium Point ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Zero Point ◽  
The Stability ◽  
Population Equilibrium

A three species system with time delays was considered. Firstly, we got the system’s three population equilibrium point and shifted it to zero point through transformation. Secondly, we analyzed the stability of the system at the equilibrium point. We support our analytical findings with numerical simulation.

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.

Dynamics of a Rolling Wheelset

1993 ◽  
Vol 46 (7) ◽  
pp. 438-444 ◽  
Author(s):  
Hans True
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Chaotic Motion ◽  
Dynamical Behavior ◽  
Railway Track ◽  
Kinematics And Dynamics ◽  
Bifurcation Diagrams ◽  
Speed Range ◽  
Set Up ◽  
The Mathematical Model

We discuss the kinematics and dynamics of a wheelset rolling on a railway track. The mathematical model of a suspended wheelset rolling with constant speed on a straight track is set up and its dynamics is investigated numerically. The results are presented mainly on bifurcation diagrams. Several kinds of dynamical behavior is identified within the investigated speed range. We find a stationary equilibrium point at low speeds and at higher speeds symmetric and asymmetric oscillations are found and ranges with chaotic motion are identified. The bifurcations are described.

scholarly journals Sensitivity and mathematical model analysis on secondhand smoking tobacco

2020 ◽  
Vol 28 (1) ◽  
Author(s):  
Birliew Fekede ◽  
Benyam Mebrate
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Reproductive Number ◽  
Primary Case ◽  
Susceptible Population ◽  
Proposed Model ◽  
Relative Change ◽  
Well Posed ◽  
Mathematical Model Analysis

AbstractIn this paper, we are concerned with a mathematical model of secondhand smoker. The model is biologically meaningful and mathematically well posed. The reproductive number $$R_{0}$$ R 0 is determined from the model, and it measures the average number of secondary cases generated by a single primary case in a fully susceptible population. If $$R_{0}<1,$$ R 0 < 1 , the smoking-free equilibrium point is stable, and if $$R_{0}>1,$$ R 0 > 1 , endemic equilibrium point is unstable. We also provide numerical simulation to show stability of equilibrium points. In addition, sensitivity analysis of parameters involving in the dynamic system of the proposed model has been included. The parameters involving in reproductive number measure the relative change in $$R_{0}$$ R 0 when the value of the parameter changes.

scholarly journals The Dynamics of a Single Species in a Polluted Environment

2020 ◽  
pp. 1-12
Author(s):  
Raid Kamel Naji ◽  
Mona Ghassan Younis ◽  
Mohammad Naeemullah
Keyword(s):  
Mathematical Model ◽  
Equilibrium Point ◽  
Local Stability ◽  
Single Species ◽  
Global Dynamics ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Proposed Model

This article proposed and analysed a nonlinear mathematical model that consist of a single species in a polluted environment (PE). The proposed model was also discussed in terms of its uniqueness, existence, and boundedness of the solution. Also, each possible equilibrium point was analysed for local stability, followed by investigation of the global dynamics of the system using the Lypanov functions. The effects of the presence of toxicants on the dynamics of a single species in the PE was numerically investigated

scholarly journals Mathematical Modeling and Analysis of Khat-Chewing Dynamics

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Kahsay Godifey Wubneh ◽  
Fitsum Mulaw Desta ◽  
Hafte Amsalu Kahsay
Keyword(s):  
Equilibrium Point ◽  
Equilibrium Points ◽  
High Rate ◽  
Religious Leaders ◽  
Modeling And Analysis ◽  
Khat Chewing ◽  
Parameter Estimations ◽  
Proposed Model ◽  
The Stability ◽  
Khat Chewer

Khat is a green leaf and greenish plant where its branches and leaves are chewed to discharge liquid having active chemicals that change the user’s mood. The purpose of this article is to develop and analyze a mathematical model that can be used to understand the dynamics of chewing Khat. The proposed model monitors the dynamics of five compartments, namely, a group of people who do not chew Khat, designated as N t ; a group of people who are surrounded by Khat chewers but do not chew at present and may chew Khat in the future, denoted this as Σ t ; a group of people who chew Khat, which is represented in C t ; a group of people contains individuals who consumed Khat quite temporarily for social, spiritual, and recreational purposes, and we describe this group in T t ; and a group of people those who constantly chew Khat, and they are denoted by H t . We determined the Khat chewing generation number R c 0 using the next-generation matrix method, and we have examined the biological meaningfulness, mathematical wellposedness, and stability of both Khat chewing-free and Khat chewing-present equilibrium points of the model analytically. Numerical simulations were presented by solving our dynamical system using Matlabode45 to check the analytical results by considering parameter estimations. The results of this study show that, for R c 0 = .00039 , the Khat chewing-free equilibrium point is stable, and it is unstable for R c 0 = 1.194 , and the Khat chewing-present equilibrium point is stable if R c 0 = 1.194 , and it is unstable if R c 0 = .00039 . The stability of both equilibrium points implies that, for a high rate of conversion from non-Khat chewer to exposed groups ρ , the inflow of an insignificant number of Khat chewers to the community produces a significant number of Khat chewers , and if the return back from Khat chewing to the exposed group because of socio-economic, environmental, and religious influences α 2 grows exponentially, the inflow of an insignificant number of Khat chewers to the community produces an insignificant number of Khat chewers. It is found that increasing the rate of conversion from non-Khat chewer to exposed groups ρ makes the disease eradication more challenging. We, therefore, strongly urge religious leaders, social committee leaders, elders, and health experts to teach their followers to reduce their Khat-chewing habits.

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.

Role of technology in combating social crimes: A modeling study

2013 ◽  
Vol 24 (4) ◽  
pp. 501-514 ◽  
Author(s):  
J. B. SHUKLA ◽  
ASHISH GOYAL ◽  
KAPIL AGRAWAL ◽  
HARSH KUSHWAH ◽  
AJAY SHUKLA
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Susceptible Population ◽  
Use Of Technology ◽  
Proposed Model ◽  
Intensive Use ◽  
Immigration And Emigration ◽  
The Stability ◽  
Dynamic Population

In this paper, a non-linear mathematical model is proposed and analysed to study the role of technology in combating social crimes in a dynamic population by considering immigration and emigration rates of susceptible population and criminals. The problem is modelled by considering five interacting variables, namely the density of susceptible population, the density of criminals, the density of removed (isolated) criminals, the density of crime burden and the level of technology used to control crime. The proposed model is analysed by using the stability theory of differential equation and simulation. The model analysis shows that the crime burden decreases considerably as the level of technology increases. It is noted that the crime in a society can be controlled almost completely if criminals from the general population are removed by intensive use of technology.

scholarly journals Analisis Dan Simulasi Persamaan Differensial Pada Pemodelan Penyakit Campak di Kota Parepare

2019 ◽  
Vol 1 (2) ◽  
pp. 94
Author(s):  
Syafruddin Side ◽  
Rahmat Syam ◽  
Meisy Tri Elsa
Keyword(s):  
Mathematical Model ◽  
Simulation Model ◽  
Equilibrium Point ◽  
Health Department ◽  
Literature Study ◽  
Measles Vaccination ◽  
The Stability

Abstrak. Penelitian ini membahas mengenai model matematika SEIRV pada penyakit campak di kota Parepare. Data yang digunakan adalah data jumlah penderita penyakit campak di kota Parepare tahun 2015 dari Dinas Kesehatan Kota Parepare. Pembahasan dimulai dari membangun model matematika SEIRV penyakit campak, penentuan titik ekulibrium, selanjutnya mencari analisis kestabilan titik ekuilibrium dan membuat simulasi model. Penulisan tugas akhir ini dilakukan dengan menggunakan metode kajian literatur. Penulisan ini diharapkan dapat memberikan gambaran umum tentang model matematika SEIRV. Langkah-langkah yang dilakukan yaitu mengidentifikasi masalah, menyusun asumsi-asumsi untuk menyederhanakan model, membuat diagram transfer, mengidentifikasikan parameter-parameter, menentukan titik ekuilibrium kemudian melakukan analisis kestabilan dan mansimulasikan model. Berdasarkan hasil yang diperoleh, vaksinasi adalah cara terbaik dalam penyembuhan penyakit campak.Kata Kunci: campak, vaksinasi, SEIRV.Abstract. This research discusses the SEIRV model of measles. The data used is the number of people with measles in Parepare City in 2015. This data is obtained from Parepare City Health Department. The discussion begins with constructing the SEIRV model of measles,determining the equilibrium point and analyzing the stability. Then, creating a simulation model. This research is conducted by using method of literature study. It is expected to proside an overview of the SEIRV mathematical model. The steps taken are identifying the problem, formulating assumptions to obtained, vaccination is the best way to cure measlesKeyword: Measles, Vaccination, SEIRV.

scholarly journals A Stability Mathematical Model of Nasopharyngeal Carcinoma on Cellular Level

2016 ◽  
Vol 5 (2) ◽  
pp. 61
Author(s):  
Sugiyanto Sugiyanto ◽  
Fajar Adi Kusumo ◽  
Lina Aryati ◽  
Mardiah Suci Hardianti
Keyword(s):  
Mathematical Model ◽  
Nasopharyngeal Carcinoma ◽  
Equilibrium Point ◽  
Normal Cell ◽  
Invasive Carcinoma ◽  
Cellular Level ◽  
Previous Theorem ◽  
The Stability

<p>This paper discussed the stability of “Tumorigenesis Models” to link between EBV and carcinoma of the nasopharyngeal from normal cell to invasive carcinoma. The review on this case accomplished the previous theorem of equilibrium point on “Tumorigenesis Models”.</p>

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