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Ordinary Differential Equations and Applied Dynamics Commons™

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2021

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Full-Text Articles in Ordinary Differential Equations and Applied Dynamics

Numerical Study Of The Seiqr Model For Covid-19, Caitlin Holt Dec 2021

Numerical Study Of The Seiqr Model For Covid-19, Caitlin Holt

Departmental Honors & Graduate Capstone Projects

In this research project, we used numerical methods to investigate trends in the susceptible, exposed, infectious, quarantined, recovered, closed cases and insusceptible populations for the COVID-19 pandemic in 2021. We used the SEIQR model containing seven ordinary differential equations, based on the SIR model for epidemics. An analytical solution was derived from a simplified version of the model, created by making various assumptions about the original model. Numerical solutions were generated for the first 100 days of 2021 using algorithms based on Euler's Method, Runge-Kutta Method, and Multistep Methods. Our goal is to show that numerical methods can help us …

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(R1497) On The Invariant Subspaces Of The Fractional Integral Operator, Mehmet Gürdal, Anar Adiloglu Nabiev, Meral Ayyıldız Dec 2021

(R1497) On The Invariant Subspaces Of The Fractional Integral Operator, Mehmet Gürdal, Anar Adiloglu Nabiev, Meral Ayyıldız

Applications and Applied Mathematics: An International Journal (AAM)

In operator theory, there is an important problem called the invariant subspace problem. This important problem of mathematics has been clear for more than half a century. However the solution seems to be nowhere in sight. With this motivation, we investigate the invariant subspaces of the fractional integral operator in the Banach space with certain conditions in this paper. Also by using the Duhamel product method, unicellularity of the fractional integral operator on some space is obtained and the description of the invariant subspaces is given.

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(R1468) Global Analysis Of An Seirs Model For Covid-19 Capturing Saturated Incidence With Treatment Response, David A. Oluyori, Helen O. Adebayo, Ángel G.C. Pérez Dec 2021

(R1468) Global Analysis Of An Seirs Model For Covid-19 Capturing Saturated Incidence With Treatment Response, David A. Oluyori, Helen O. Adebayo, Ángel G.C. Pérez

Applications and Applied Mathematics: An International Journal (AAM)

In this work, a new SEIRS model with saturated incidence rate and piecewise linear treatment response is proposed to describe the dynamics of COVID-19. It is assumed that the treatment response is proportional to the number of infected people as long as the incidence cases are within the capacity of the healthcare system, after which the value becomes constant, when the number of confirmed cases exceeds the carrying capacity of the available medical facilities. Thus, the basic reproduction number of the model is obtained. It is proved that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number …

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(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat Dec 2021

(R1488) Transformation Of Glucokinase Under Variable Rate Constants And Thermal Conditions: A Mathematical Model, Mukhtar Ahmad Khanday, Roohi Bhat

Applications and Applied Mathematics: An International Journal (AAM)

The glucokinase (GK) in cells plays a pivotal role in the regulation of carbohydrate metabolism and acts as a sensor of glucose. It helps us to control glucose levels during fast and food intake conditions through triggering shifts in metabolism or cell functions. Various forms of hypoglycaemia and hyperglycaemia occur due to the transformations of the gene of the Glucokinase. The mathematical modelling of enzyme dynamics is an emerging research area to serve its role in biological investigations. Thus, it is imperative to establish a mathematical model to understand the kinetics of native and denatured forms of enzyme-GK under thermal …

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(R1523) Abundant Natural Resources, Ethnic Diversity And Inclusive Growth In Sub-Saharan Africa: A Mathematical Approach, Juliet I. Adenuga, Kazeem B. Ajide, Anthonia T. Odeleye, Abayomi A. Ayoade Dec 2021

(R1523) Abundant Natural Resources, Ethnic Diversity And Inclusive Growth In Sub-Saharan Africa: A Mathematical Approach, Juliet I. Adenuga, Kazeem B. Ajide, Anthonia T. Odeleye, Abayomi A. Ayoade

Applications and Applied Mathematics: An International Journal (AAM)

The sub-Saharan African region is blessed with abundant natural resources and diverse ethnic groups, yet the region is dominated by the largest number of poor people worldwide due to inequitable distribution of national income. Existing statistics forecast decay in the quality of lives over the years compared to the continent of Asia that shares similar history with the region. In this paper, a-five dimensional first-order nonlinear ordinary differential equations was formulated to give insight into various factors that shaped dynamics of inclusive growth in sub-Saharan Africa. The validity test was performed based on ample mathematical theorems and the model was …

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(R1524) The Existence And Uniqueness Of Solution For Fractional Newel-Whitehead-Segel Equation Within Caputo-Fabrizio Fractional Operator, Ali Khalouta Dec 2021

(R1524) The Existence And Uniqueness Of Solution For Fractional Newel-Whitehead-Segel Equation Within Caputo-Fabrizio Fractional Operator, Ali Khalouta

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce and study the existence and uniqueness theorem of the solution for the fractional Newell-Whitehead-Segel equation within Caputo-Fabrizio fractional operator. Also, we propose a new numerical method known as natural reduced differential transform method (NRDTM) for solving this equation. We confirm our theoretical discussion with two numerical examples in order to achieve the validity and accuracy of the proposed method. The computations, associated with these examples, are performed by MATLAB software package.

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(R1412) Stability And Bifurcation Of A Cholera Epidemic Model With Saturated Recovery Rate, Huda Abdul-Satar, Raid K. Naji Dec 2021

(R1412) Stability And Bifurcation Of A Cholera Epidemic Model With Saturated Recovery Rate, Huda Abdul-Satar, Raid K. Naji

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound …

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Optimal Control Techniques In Addiction Modeling, Leigh Pearcy, William Christopher Strickland, Suzanne Lenhart Nov 2021

Optimal Control Techniques In Addiction Modeling, Leigh Pearcy, William Christopher Strickland, Suzanne Lenhart

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Ecological Dynamics On Large Metapopulation Graphs, Daniel Cooney Nov 2021

Ecological Dynamics On Large Metapopulation Graphs, Daniel Cooney

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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The Impact Of Fungicide Treatment On The Dynamics Of Cocoa Black Pod Disease, Bismark Oduro Nov 2021

The Impact Of Fungicide Treatment On The Dynamics Of Cocoa Black Pod Disease, Bismark Oduro

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Modeling, Analysis And Simulation Of Covid-19 Interaction Dynamics Between Local Community In Saudi Arabia And Visiting Sub-Population, Manal Badgaish, Padmanabhan Seshaiyer Nov 2021

Modeling, Analysis And Simulation Of Covid-19 Interaction Dynamics Between Local Community In Saudi Arabia And Visiting Sub-Population, Manal Badgaish, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Estimation Of Parameters Of Epidemiological Models Under A Non-Parametric Approach And Its Application For Covid-19 In Bogotá D.C., Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, Soledad Torres Nov 2021

Estimation Of Parameters Of Epidemiological Models Under A Non-Parametric Approach And Its Application For Covid-19 In Bogotá D.C., Andrés Ríos-Gutiérrez, Viswanathan Arunachalam, Soledad Torres

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Building Model Prototypes From Time-Course Data, David Murrugarra, Alan Veliz-Cuba Nov 2021

Building Model Prototypes From Time-Course Data, David Murrugarra, Alan Veliz-Cuba

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Estimation Analysis For The Seir Model With Stochastic Perturbation For The Covid-19 Outbreak In Bogotá, Viswanathan Arunachalam, Andres Rios-Gutierrez Nov 2021

Estimation Analysis For The Seir Model With Stochastic Perturbation For The Covid-19 Outbreak In Bogotá, Viswanathan Arunachalam, Andres Rios-Gutierrez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Chemoimmunotherapy Treatment Strategies On A Mathematical Model Of Cancer Evolution, Sandra M. Lopez, Yolocuauhtli Salazar, Paul A. Valle Nov 2021

Chemoimmunotherapy Treatment Strategies On A Mathematical Model Of Cancer Evolution, Sandra M. Lopez, Yolocuauhtli Salazar, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Neural Network Controller Vs Pulse Control To Achieve Complete Eradication Of Cancer Cells In A Mathematical Model, Joel A. Quevedo, Sergio A. Puga, Paul A. Valle Nov 2021

Neural Network Controller Vs Pulse Control To Achieve Complete Eradication Of Cancer Cells In A Mathematical Model, Joel A. Quevedo, Sergio A. Puga, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Mathematical Model For Understanding The Spread Of Covid-19 In Saudi Arabia With Access To Vaccination, Maha Alshabrawi Nov 2021

Mathematical Model For Understanding The Spread Of Covid-19 In Saudi Arabia With Access To Vaccination, Maha Alshabrawi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Reconstructing Mathematical Models With Chaotic Attractors Via Genetic Algorithms, Luis A. Ramirez Islas, Paul A. Valle Nov 2021

Reconstructing Mathematical Models With Chaotic Attractors Via Genetic Algorithms, Luis A. Ramirez Islas, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Age-Dependent Ventilator-Induced Lung Injury, Quintessa Hay Nov 2021

Age-Dependent Ventilator-Induced Lung Injury, Quintessa Hay

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa Nov 2021

Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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Mathematical Modeling And Analysis Of Covid-19 Epidemic With Vaccination, Caitlin Seibel, Tina Huang, Jackson Reisman, Erika Johanna Martinez Salinas, Viswanathan Arunachalam, Moatlhodi Kgosimore, Anuj Mubayi, Padmanabhan Seshaiyer, Allen Bone Sehunelo Nov 2021

Mathematical Modeling And Analysis Of Covid-19 Epidemic With Vaccination, Caitlin Seibel, Tina Huang, Jackson Reisman, Erika Johanna Martinez Salinas, Viswanathan Arunachalam, Moatlhodi Kgosimore, Anuj Mubayi, Padmanabhan Seshaiyer, Allen Bone Sehunelo

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

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An Upper Bound On The Spectral P-Norms Of Tensors And Matrix Permanent, Killian J. Hitsman, Vehbi E. Paksoy Aug 2021

An Upper Bound On The Spectral P-Norms Of Tensors And Matrix Permanent, Killian J. Hitsman, Vehbi E. Paksoy

Mako: NSU Undergraduate Student Journal

No abstract provided.

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Representation Of Nonlinear Pseudo-Random Generators Using State-Space Equations, Raghad K. Salih Jul 2021

Representation Of Nonlinear Pseudo-Random Generators Using State-Space Equations, Raghad K. Salih

Emirates Journal for Engineering Research

The idea of research is a representation of the nonlinear pseudo-random generators using state-space equations that is not based on the usual description as shift register synthesis but in terms of matrices. Different types of nonlinear pseudo-random generators with their algorithms have been applied in order to investigate the output pseudo-random sequences. Moreover, two examples are given for conciliated the results of this representation.

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Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer Jul 2021

Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

Due to the rise of COVID-19 cases, many mathematical models have been developed to study the disease dynamics of the virus. However, despite its role in the spread of COVID-19, many SEIR models neglect to account for human behavior. In this project, we develop a novel mathematical modeling framework for studying the impact of mixing patterns and social behavior on the spread of COVID-19. Specifically, we consider two groups, one exhibiting normal behavior who do not reduce their contacts and another exhibiting altered behavior who reduce their contacts by practicing non-pharmaceutical interventions such as social distancing and self-isolation. The dynamics …

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Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng Jul 2021

Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng

Theses and Dissertations

Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.

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Gradient Estimates And The Fundamental Solution For Higher-Order Elliptic Systems With Lower-Order Terms, Michael J. Duffy Jr. Jul 2021

Gradient Estimates And The Fundamental Solution For Higher-Order Elliptic Systems With Lower-Order Terms, Michael J. Duffy Jr.

Graduate Theses and Dissertations

Here we generalize the higher-order divergence-form elliptic differential equations studied by Barton in [4] by the inclusion of certain lower-order terms. The methods used here compare to those used in [4], with the addition of further Sobolev-type estimates to handle included lower-order terms. In section 3 we derive a Caccioppoli inequality in which we bound the L2 norm of the mth order gradient, in terms of the L2 norm of the solution. In section 5 we adapt some of the ideas from [9] to derive Lp bounds on gradients of solutions as a substitute for a reverse Holder inequality. Finally …

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Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria Jun 2021

Qualitative Analysis Of A Modified Leslie-Gower Predator-Prey Model With Weak Allee Effect Ii, Manoj K. Singh, B. S. Bhadauria

Applications and Applied Mathematics: An International Journal (AAM)

The article aims to study a modified Leslie-Gower predator-prey model with Allee effect II, affecting the functional response with the assumption that the extent to which the environment provides protection to both predator and prey is the same. The model has been studied analytically as well as numerically, including stability and bifurcation analysis. Compared with the predator-prey model without Allee effect, it is found that the weak Allee effect II can bring rich and complicated dynamics, such as the model undergoes to a series of bifurcations (Homoclinic, Hopf, Saddle-node and Bogdanov-Takens). The existence of Hopf bifurcation has been shown for …

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Anti-Synchronization Scheme For The Stability Analysis Of A Newly Designed Hamiltonian Chaotic System Based On Hénon-Heiles Model Using Adaptive Control Method, Ayub Khan, Anu Jain, Santosh Kaushik, Manoj Kumar, Harindri Chaudhary Jun 2021

Anti-Synchronization Scheme For The Stability Analysis Of A Newly Designed Hamiltonian Chaotic System Based On Hénon-Heiles Model Using Adaptive Control Method, Ayub Khan, Anu Jain, Santosh Kaushik, Manoj Kumar, Harindri Chaudhary

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a systematic approach to investigate the anti-synchronization among identical Hamiltonian chaotic systems has been proposed by using adaptive control method (ACM). Initially an adaptive controller and parameter update law are described to achieve asymptotical stability of state variables of given system with uncertain parameters using Lyapunov stability theory (LST). In addition, numerical simulations using MATLAB software are performed to validate the efficacy and effectiveness of the designed technique. Moreover, the proposed technique has numerous applications in encryption and secure communication.

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Variation Iteration Method For Solving Ethanol And Acetaldehyde Concentrations In A Fixed Bed Laboratory Reactor, K. M. Dharmalingam, M. Veeramuni, Hadi Rezazadeh, Cemil Tunç Jun 2021

Variation Iteration Method For Solving Ethanol And Acetaldehyde Concentrations In A Fixed Bed Laboratory Reactor, K. M. Dharmalingam, M. Veeramuni, Hadi Rezazadeh, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate the effects of nonlinear behaviour of the dimensionless concentrations of the ethanol and acetaldehyde in a fixed bed laboratory reactor. The work is based on solving the nonlinear differential equation of concentration of the ethanol and acetaldehyde by means of the He’s variational iteration method (VIM). Also, the numerical simulation (4th order Runge – Kutta method) is reported using Matlab software. The analytical solutions are compared with numerical results in order to achieve conclusions based on not only for accuracy and efficiency of the solutions, but also the simplicity of the taken procedures which would …

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Covid-19 Modeling With Caution In Relaxing Control Measures And Possibilities Of Several Peaks In Cameroon, S. Y. Tchoumi, Y. T. Kouakep, D. J. Fotsa Mbogne, J. C. Kamgang, V. C. Kamla, D. Bekolle Jun 2021

Covid-19 Modeling With Caution In Relaxing Control Measures And Possibilities Of Several Peaks In Cameroon, S. Y. Tchoumi, Y. T. Kouakep, D. J. Fotsa Mbogne, J. C. Kamgang, V. C. Kamla, D. Bekolle

Applications and Applied Mathematics: An International Journal (AAM)

We construct a new model for the comprehension of the Covid-19 dynamics in Cameroon. We present the basic reproduction number and perform some numerical analysis on the possible outcomes of the epidemic. The major results are the possibilities to have several peaks before the end of the first outbreak for an uniform strategy, and the danger to have a severe peak after the adoption of a careless strategy of barrier anti-Covid-19 measures that follow a good containment period.

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