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Ordinary Differential Equations and Applied Dynamics Commons

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All Articles in Ordinary Differential Equations and Applied Dynamics

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A Dynamical System Model Of Dengue Transmission For Rio De Janeiro, Brazil, Gregory Schmidt, Benjamin Whipple, Vinodh Chellamuthu, Xiaoxia Xie 2023 Utah Tech University

A Dynamical System Model Of Dengue Transmission For Rio De Janeiro, Brazil, Gregory Schmidt, Benjamin Whipple, Vinodh Chellamuthu, Xiaoxia Xie

Spora: A Journal of Biomathematics

The dengue virus is a serious concern in many parts of the world, including Brazil. As data indicates, a prominent vector for dengue is the mosquito Aedes aegypti. By using the dengue incidence records from the Brazilian SINAN database, we estimate the population of A. aegypti within the city of Rio de Janeiro. Using historical climate data for Rio de Janeiro and the computed population estimates, we extend an existing model for the population dynamics of mosquitoes to incorporate precipitation in aquatic stages of development for A. aegypti.


Numerical Solutions Of Singular Nonlinear Ordinary Differential Equations Using Said-Ball Polynomials, Mobarek A. Assabaai, Ahmed Kherd 2022 Hadhrmout University

Numerical Solutions Of Singular Nonlinear Ordinary Differential Equations Using Said-Ball Polynomials, Mobarek A. Assabaai, Ahmed Kherd

Emirates Journal for Engineering Research

In this article, the collocation method based on Said-Ball polynomials have been used to solve the singular nonlinear ordinary differential equations of various orders numerically. An operational matrix forms of these ordinary differential equations are obtained from Said-Ball polynomial with variated relations of solution and different derivatives. The presented method reduces the given problem to a system of nonlinear algebraic equations, which removed the singularity of ordinary differential equations. Resulting system is solved using Newton's iteration method to get the coefficients of Said-Ball polynomials. We obtained approximate solutions of the problem under study. Numerical results have been obtained and compared …


On The Spatial Modelling Of Biological Invasions, Tedi Ramaj 2022 The University of Western Ontario

On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

Electronic Thesis and Dissertation Repository

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …


(R1969) On The Approximation Of Eventual Periodicity Of Linearized Kdv Type Equations Using Rbf-Ps Method, Hameed Ullah Jan, Marjan Uddin, Asma Norin, Tamheeda . 2022 University of Engineering and Technology Peshawar

(R1969) On The Approximation Of Eventual Periodicity Of Linearized Kdv Type Equations Using Rbf-Ps Method, Hameed Ullah Jan, Marjan Uddin, Asma Norin, Tamheeda .

Applications and Applied Mathematics: An International Journal (AAM)

Water wave propagation phenomena still attract the interest of researchers from many areas and with various objectives. The dispersive equations, including a large body of classes, are widely used models for a great number of problems in the fields of physics, chemistry and biology. For instance, the Korteweg-de Vries (KdV) equation is one of the famous dispersive wave equation appeared in the theories of shallow water waves with the assumption of small wave-amplitude and large wave length, also its various modifications serve as the modeling equations in several physical problems. Another interesting qualitative characteristic of solutions of some dispersive wave …


(R1522) Modelling The Influence Of Desertic Aerosols On The Transmission Dynamics Of Neisseria Meningitidis Serogroup A, Francis Signing, Berge Tsanou, Samuel Bowong 2022 University of Dschang; Sorbonne University

(R1522) Modelling The Influence Of Desertic Aerosols On The Transmission Dynamics Of Neisseria Meningitidis Serogroup A, Francis Signing, Berge Tsanou, Samuel Bowong

Applications and Applied Mathematics: An International Journal (AAM)

This paper assesses the role of desert aerosols and vaccine on the transmission dynamics of Neisseria Meningitis serogroup A (NmA). It is biologically well-documented that the inhalation of aerosol dust and its presence in the nasal cavity weakens the nasopharyngeal mucosa by damaging the mucosal barrier and inhibiting the mucosal immune defenses of susceptible and vaccinated individuals. We address the latter by proposing and analyzing a mathematical model for the dynamics of NmA that specifically accounts for the fast progression of susceptible and vaccinated individuals to the invasive stage of the disease. We compute the basic reproduction number and use …


(R1980) Effect Of Climate Change On Brain Tumor, Pardeep Kumar, Sarita Jha, Rajiv Aggarwal, Govind Kumar Jha 2022 University of Delhi

(R1980) Effect Of Climate Change On Brain Tumor, Pardeep Kumar, Sarita Jha, Rajiv Aggarwal, Govind Kumar Jha

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we introduce a new dynamical model addressing the variation in climate condition due the presence of microorganisms. We also introduce a new dynamical model of cancer growth which includes three interactive cell populations with drug free environment, namely tumor cells, healthy host cells, and immune effector cells. In this, we considered the super growth of tumor cells. For the choice of certain parameters, both of the systems exhibit chaotic behavior. The aim of this work is to design the controller to control the chaos and to provide sufficient conditions which achieve synchronization of two non-identical systems, which …


(R1888) On The Mackey-Glass Model With A Piecewise Constant Argument, Mehtap Lafci Büyükkahraman 2022 Uşak University

(R1888) On The Mackey-Glass Model With A Piecewise Constant Argument, Mehtap Lafci Büyükkahraman

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we deal with the Mackey-Glass model with piecewise constant argument. Because the corresponding difference equation is the difference solution of the equation, the difference equation can clearly predict the dynamic behavior of the equation. So, we look at how the difference equation behaves.We study the asymptotic stability of the equilibrium point of the difference equation and it is obtained that this point is a repeller under some conditions. Also, it is shown that every oscillatory solution of the difference equation has semi-cycles of length at least two, and every oscillatory solution of the difference equation is attracted …


Solving Clostridioides Difficile: Mathematical Models Of Transmission And Control In Healthcare Settings, Cara Sulyok, Max Lewis, Laila Mahrat, Brittany Stephenson, Malen De la Fuente Arruabarrena, David Kovalev, Justyna Sliwinska 2022 Lewis University

Solving Clostridioides Difficile: Mathematical Models Of Transmission And Control In Healthcare Settings, Cara Sulyok, Max Lewis, Laila Mahrat, Brittany Stephenson, Malen De La Fuente Arruabarrena, David Kovalev, Justyna Sliwinska

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, Emmanuel Adara 2022 Illinois State University

An Implementation Of The Method Of Moments On Chemical Systems With Constant And Time-Dependent Rates, Emmanuel Adara

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer 2022 George Mason University

Physics-Informed Neural Networks For Informed Vaccine Distribution In Heterogeneously Mixed Populations, Alvan Arulandu, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


A Mathematical Model For Understanding And Predicting Dynamics Of Depression As An Epidemic, Bianca Linares 2022 Illinois State University

A Mathematical Model For Understanding And Predicting Dynamics Of Depression As An Epidemic, Bianca Linares

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Humanizing Mathematical Biology Research And Education, Carrie Diaz Eaton, Ognyan Simeonov 2022 Bates College

Humanizing Mathematical Biology Research And Education, Carrie Diaz Eaton, Ognyan Simeonov

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


The Effect Of Vaccine Misinformation On Disease Spread, Anthony DeLegge, Yina Wang 2022 Benedictine University

The Effect Of Vaccine Misinformation On Disease Spread, Anthony Delegge, Yina Wang

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Immuno-Epidemiological Model Of Hiv And Opioid Epidemics, Churni Gupta, Necibe Tuncer, Maia Martcheva 2022 University of Florida

Immuno-Epidemiological Model Of Hiv And Opioid Epidemics, Churni Gupta, Necibe Tuncer, Maia Martcheva

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Sentiment Analysis In Application To Behavior Prediction, Anna Singley 2022 University of Portland

Sentiment Analysis In Application To Behavior Prediction, Anna Singley

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Stochastic Models Of Zoonotic Avian Influenza With Multiple Hosts, Environmental Transmission, And Migration In The Natural Reservoir, Kaia Smith 2022 Illinois State University

Stochastic Models Of Zoonotic Avian Influenza With Multiple Hosts, Environmental Transmission, And Migration In The Natural Reservoir, Kaia Smith

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini 2022 Illinois State University

On Analysis Of Effectiveness Controlling Covid-19 With Quarantine And Vaccination Compartments In Indonesia, Prihantini Prihantini

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


Modularity In Gene Regulatory Networks, Mehak Kapoor, Claus Kadelka 2022 Iowa State University

Modularity In Gene Regulatory Networks, Mehak Kapoor, Claus Kadelka

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.


(Si10-056) Fear Effect In A Three Species Prey-Predator Food-Web System With Harvesting, R. P. Gupta, Dinesh K. Yadav 2022 Banaras Hindu University

(Si10-056) Fear Effect In A Three Species Prey-Predator Food-Web System With Harvesting, R. P. Gupta, Dinesh K. Yadav

Applications and Applied Mathematics: An International Journal (AAM)

Some recent studies and field experiments show that predators affect their prey not only by direct capture; they also induce fear in prey species, which reduces their reproduction rate. Considering this fact, we propose a mathematical model to study the fear effect of a middle predator on its prey in a three-species food web system with harvesting. The ecological feasibility of solutions to the proposed system is guaranteed in terms of positivity and boundedness. The local stability of stationary points in the proposed system is derived. Multiple co-existing stationary points for the proposed system are observed, which makes the problem …


(Si10-083) Approximate Controllability Of Infinite-Delayed Second-Order Stochastic Differential Inclusions Involving Non-Instantaneous Impulses, Shobha Yadav, Surendra Kumar 2022 University of Delhi

(Si10-083) Approximate Controllability Of Infinite-Delayed Second-Order Stochastic Differential Inclusions Involving Non-Instantaneous Impulses, Shobha Yadav, Surendra Kumar

Applications and Applied Mathematics: An International Journal (AAM)

This manuscript investigates a broad class of second-order stochastic differential inclusions consisting of infinite delay and non-instantaneous impulses in a Hilbert space setting. We first formulate a new collection of sufficient conditions that ensure the approximate controllability of the considered system. Next, to investigate our main findings, we utilize stochastic analysis, the fundamental solution, resolvent condition, and Dhage’s fixed point theorem for multi-valued maps. Finally, an application is presented to demonstrate the effectiveness of the obtained results.


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