Analytical and Numerical Boundedness of a Model with Memory Effects for the Spreading of Infectious Diseases: A Theoretical Study of Rabies | Chapter 6 | Mathematics and Computer Science: Research Updates Vol. 3

In this study, an integer order rabies model is converted into the fractional order epidemic model is converted into the fractional order epidemic model. To this end, the Caputo fractional order derivatives are plugged in place of classical derivatives. Rabies is a primary health problem in many populations dense with dogs, specifically in regions where there less or no preventive measures are adopted (vaccination and remedy) for puppies and human beings. Remedy after exposure to the rabies virus is referred to as post-exposure prophylaxis (PEP) and vaccination earlier than exposure to the infection is known as pre-exposure prophylaxis. The positivity and boundedness of the fractional order mathematical model is investigated by applying Laplace transformation and its inversion. To study the qualitative behavior of the non-integer rabies model, two steady states and the basic reproductive number of the underlying model are worked out. The local and global stability is investigated at both the steady states of the fractional order epidemic model. After analytic treatment, a structure preserving numerical template is constructed to solve numerically the fractional order epidemic model. Moreover, the positivity and boundedness of the numerical scheme is examined. Lastly, numerical experiment and simulations are accomplished to substantiate the significant traits of the projected numerical design. Consequences of the study are highlighted in the closing section. The significant features of numerical design are the positivity, boundedness and convergence towards accurate steady states. These traits of the numerical design are identified by establishing some standard results. Moreover, simulations are presented to validate all the key features of the novel numerical design.

 

Author (s) Details

Zafar Iqbal
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.

 

Siegfried Macias
Departamento de Matematicas y Fisica, Universidad Autonoma de Aguascalientes, Aguascalientes, Mexico.

 

Jorge E. Macias-Diaz
Departamento de Matematicas y Fisica, Universidad Autonoma de Aguascalientes, Aguascalientes, Mexico and Department of Mathematics and Didactics of Mathematics, Tallinn University, 10120 Tallinn, Estonia.

 

Nauman Ahmed
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.

 

Aqsa Javaid
Department of Mathematics and Statistics, The University of Lahore, Lahore, Pakistan.

 

Muhammad Rafiq
Department of Mathematics, Faculty of Science and Technology, University of Central Punjab, Lahore, Pakistan. India and Department of Mathematics, Near East University, Mathematics Research Center, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, Turkey.

 

Ali Raza
Department of Mathematics, Govt. Mulana Zafar Ali Khan Graduate College Wazirabad, Gujranwala, Pakistan.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v3/4482

Investigation of RBF Hyperparameter Variation on Evolutionary Search | Chapter 4 | Novel Perspectives of Engineering Research Vol. 4

 A metamodel-assisted evolutionary method is frequently used to address computationally difficult issues in engineering and science. The radial basis functions (RBF), which is based on a hyperparameter, is a widely used metamodel. The latter requires a numerical technique, which can be time-consuming in and of itself, and this raises the question of whether it is justified, namely when do changes in the hyperparameter result in significant performance increases. This work addresses this issue by presenting a large number of numerical experiments and analysing them to determine when hyperparameter change is justified.

Author(S) Details

Yoel Tenne
Ariel University, Israel.

View Book:- https://stm.bookpi.org/NPER-V4/article/view/5104

Optimal Methods of Input for Pedagogic Engineering Software | Chapter 13 | New Ideas Concerning Science and Technology Vol. 7

 While computer simulations are frequently used to teach intuitive causal engineering relationships, little research has been done on what factors make such simulations the most pedagogically efficient. This study looks at how the discrete vs. continuous essence of user feedback, such as moving a dial vs. typing a parameter, influences both real and perceived learning. The N = 91 cohort size was insufficient to determine statistical differences at the = 0.05 stage, but at = 0.1, it was discovered that continuous input simulations allowed students to learn more effectively, and that students who used continuous input methods assumed that continuous input learning methods were more efficient than discrete input learning methods after using them. Surprisingly, objectively assessed student comprehension and subjectively rated student confidence in their own subject mastery were found to have an inverse relationship. In other words, even though they thought their particular learning was insufficient, students who used continuous feedback simulations thought they were better teaching tools in general.

Author (s) Details

Dr. James C. Squire
Virginia Military Institute, Lexington, VA, USA.

Dr. Gerald A. Sullivan
Virginia Military Institute, Lexington, VA, USA.

Dr. Thomas J. McCormick
Virginia Military Institute, Lexington, VA, USA.

View Book :- https://stm.bookpi.org/NICST-V7/issue/view/41