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Title: The dynamics of Coronavirus pandemic disease
model in the existence of a curfew strategy
Abstract:
The dynamical behavior of the Coronavirus disease-2019 COVID-19 pandemic model is proposed and analyzed. It is assumed that a curfew strategy is applied to control the outbreak of the disease in addition to a social distancing between the individuals. All the basic properties of the solution including existence, uniqueness, and boundedness are discussed. The basic reproduction number R0, is determined. The local stability analysis is studied. While the global stability analysis of disease-free equilibrium point is investigated using the method of Castillo-Chavez, however for the endemic equilibrium point, the method of Lyapunov function is used. Furthermore, the local bifurcation of the model at the disease-free equilibrium point is discussed. Finally, the numerical simulations are performed in order to show validation of the theoretical results and determine how changes in parameters affect the dynamical behavior of the system.
Title: On the Returned Sequences and their Applications
Abstract:
In this work we study the behavior of the sequence {an} of complex numbers, satisfying the relation an+k=q1an +q2an+1 +…+ qkan+k-1 , where {qm} is a fixed sequence of complex numbers. Such kind of sequences arise in problems of analysis, fixed point theory, dynamical systems, theory of chaos and ets.
For example, investigation of the spectra of triple and more than triple band triangle operator-matrices arise above mentioned sequences which required to study the behavior of the sequence. Till now the received formulas for the spectra of considered operator-matrices from the point of application looks like very complicated.
In this work the eliminating of indicated flaws we apply new approach, where the formulas for the spectra describe circular domains.
We apply the received results to some problems of the natural processes.
Title: Hopf Bifurcation of 3D Sprott Systems
Abstract:
This presentation is focus on an important types of bifurcation which is the Hopf bifurcation of 3D systems. Hopf bifurcation refers to the appearance or disappearance of a periodic solution from an equilibrium point as a parameter crosses a critical value. The Sproot systems of type C and E are modified and parameterized. In addition to study the stability of the equilibrium points, the different techniques are applied to study the bifurcated periodic orbits from the Hopf point, for both systems.
Title: The Art of Graph Visualization: A Hands-On
Introduction to NetworkX and Matplotlib in Python
Abstract:
Graphs are an essential tool for visualizing and analyzing complex relationships between data points. NetworkX and Matplotlib are two popular and powerful libraries in Python that make it easy to work with graphs and create beautiful visualizations. In this workshop, attendees will receive a hands-on introduction to NetworkX and Matplotlib and learn how to use these libraries to visualize and analyze graphs. Starting with an overview of graph theory and its various applications. The workshop will cover topics such as creating graph structures, working with node and edge attributes, and performing graph analysis and measurements. In addition, attendees will learn how to visualize graphs using Matplotlib, including creating basic plots, customizing visual styles, and visualizing complex relationships in the data.
Title: Monogenity of number fields
Abstract:
Let Q ≤ K be a field extension of degree n and let OK be the ring of integers of K. We say that K is monogenic over Q, if OK is mono-generated as a ring over Z, i.e. OK = Z[α] for some α ∈ OK. In this case (1, α, α2, . . . , αn−1) is an integral basis of K and consequently, the index [OK : Z[α]] is one. It is a classical topic of algebraic number theory to decide if a number field is monogenic or not.
The first example of a non-monogenic number field was given by Dedekind. His example is based on the fact that if a prime p ∈ Z does not divide the index of α, then the ramification of the prime ideal pOK is in one-to-one correspondence with the modulo p factorisation of the minimal polynomial of α over Q. It turns out that one can deal with the monogenity of a number field through the prime ramication if and only if the field index is not 1. Unfortunately, this approach is not complete in the sense that there are non-monogenic number fields with field index 1.
In this talk I summarise some classical results and methods concerning the mongenity of number fields and some new directions that has been in the scope of the most recent papers.
Title: The Role of Mathematical Modelling in
Understanding Infectious Disease Transmissions
Abstract:
The spreading of infectious diseases such as influenza, Ebola, HIV/AIDS and COVID-19 has been considered a worldwide issue, and many global efforts have been suggested. Mathematical models including SIR, SEIR and SVEIR play an important role with computational simulations to minimize the impact of such diseases in the community. Accordingly, these are some mathematical approaches to discuss such issues more widely and theoretically. Firstly, these infectious diseases can be modeled as a system of differential equations with transmission parameters. Secondly, identifying model critical transmissions are also key elements to study these epidemics further. In addition, the basic reproduction number, R_0, and its parameter elasticity can be calculated…
Title: The Potential of Hybrid System Dynamics in
Healthcare
Abstract:
Literature as evidence the usage of system dynamics simulation in healthcare since 1999. The recent COVID-19 pandemic has increased the interest in developing system dynamics simulation models to analyze complex healthcare problems. System Dynamics models are used to understand and anticipate changes over time in puzzlingly complex healthcare systems. The initial exploitation of system dynamics was broadly used in the healthcare industry to gain understanding about policy planning and public health decisions. Post pandemics there is a significant interest in system dynamics simulation in physiological modelling for Digital Health monitoring. Even though lately there is reducing interest in continuous simulation in healthcare, the strength of hybrid simulation is expected to exploit the native power of the holistic view of system dynamics in Digital Health.
Prof.Dr. Mohammad Sajid
Prof.Dr. Mohammad Sajid
Qassim University, Saudi Arabia
Title: Chaos and Fractals in Dynamical Systems by
Differential Equations
Abstract:
In many disciplines of science and engineering, chaos and fractals are found to show chaotic behaviour and visualize graphically. Several physical process can be modelled in terms of mathematical expressions which generally lead to differential equations. Generally, these equations are extremely difficult to solve analytically or much harder to analyze. We can find chaotic behaviour of solutions as well as visualize effectively through fractals. Chaos exists everywhere in the world since most of problems are nonlinear in nature. In many cases of nonlinear systems, a small change in a parameter can lead to sudden and dramatic changes in both the qualitative and quantitative behaviour of the system. Recently, chaos and fractals are most popular topics of exploration from mathematicians, physicians, engineers and scientists. The purpose of this talk is to demonstrate chaos and fractals in dynamical systems by differential equations.
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