Advanced SIWR Model: Optimal Control of Multiple Transmission Pathways in Water-borne Diseases | Chapter 6 | Science and Technology: Recent Updates and Future Prospects Vol. 10

 

In this paper, a controlled SIWR model was considered which was an extension of the simple SIR model by adjoining a compartment (W) that tracks the pathogen concentration in the water. New infections arise both through exposure to contaminated water, as well as by the classical SIR person-person transmission pathway. The objective of optimal control is to effectively manage and minimize the transmission of waterborne diseases through strategic interventions and management strategies. The two controls were employed which represent immune boosting and pathogen suppressing drugs. The objective function is based on a combination of minimizing the number of infected individuals and the cost of the drug dose. Pontryagin's maximum principle has been used to characterize the optimal levels of the two controls. The optimal control is obtained by solving the optimality system which was composed of four nonlinear ODEs with initial conditions and four nonlinear adjoint ODEs with transversality conditions. The results show that the optimal combination of immune-boosting and pathogen-suppressing drugs required to achieve the set objective will depend on the relative cost of each of the control measures. The results were analysed and interpreted numerically using MATLAB.

 

Author(s) Details

G. Devipriya
Sri Krishna Adithya College of Arts & Science, Kovaipudur Coimbatore – 641042, India.

 

Please see the book here:- https://doi.org/10.9734/bpi/strufp/v10/1518

An Efficient Algorithm for Piecewise Approximate Analytical Solutions of High-order Reaction-Diffusion Singular Perturbation Problems with Boundary and Interior Layers | Chapter 3 | Mathematics and Computer Science: Research Updates Vol. 5

Singular perturbation problems (SPPs) manifest in various domains of applied mathematics and engineering, including control theory, fluid flow at high Reynolds or Hartmann numbers, heat and mass transfer, chemical reaction in spark ignition turbocharger engine, wave dynamics in coastal and ocean engineering, semiconductor devices, nuclear physics, etc. This study aims to present a reliable algorithm that can effectively generate accurate piecewise approximate analytical solutions for third- and fourth-order reaction-diffusion singular perturbation problems. These problems involve a discontinuous source term and exhibit both interior and boundary layers. The original problem was transformed into a system of coupled differential equations that are weakly interconnected. A zero-order asymptotic approximate solution was then provided, with known asymptotic analytical solutions for the boundary and interior layers, while the outer region solution was obtained analytically using an enhanced residual power series approach. This approach combined the standard residual power series method with the Padé approximation to yield a piecewise approximate analytical solution. It satisfies the continuity and smoothness conditions and offers higher accuracy than the standard residual power series method and other numerical methods like finite difference, finite element, hybrid difference scheme, and Schwarz method. The algorithm also provides error estimates, and numerical examples are included to demonstrate the high accuracy, low computational cost, and effectiveness of the method within a new asymptotic semi-analytical numerical framework. Finally, the study concluded that the proposed algorithm offers a convenient and reliable approach for effectively addressing high-order reaction-diffusion Singular Perturbation Boundary Value Problems (SPBVPs) with a discontinuous source term in a new asymptotic semi-analytical numerical framework. Future research will focus on extending the method’s capabilities to encompass nonlinear problems, a wider variety of higher-order SPBVPs with non-smooth variable coefficients and discontinuous source terms, and more applications with physical interpretation of the parameters and solution behaviour.

 

 

Author (s) Details

Essam R. El-Zahar
epartment of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia and Department of Basic Engineering Sciences, Faculty of Engineering, Menoufia University, Shebin El-Kom, 32511, Egypt.

 

Ghaliah F. Al-Boqami
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia.

 

Haifa S. Al-Juayd
Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, Al-Kharj, 11942, Saudi Arabia.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcsru/v5/5126

 

Monte Carlo Method for Pricing of Multi-Asset Rainbow Options| Chapter 7 | Recent Advances in Mathematical Research and Computer Science Vol. 10

When compared to other computer methods, the Monte Carlo method solution of the system stochastic differential equations in multidimensional instance offered numerous advantages. One of them is the possibility to solve boundary value issues at a single point (with accompanying processing savings), whereas deterministic approaches must simultaneously discover the answer at a large number of places. This trait is particularly important in problems such as option pricing, where the value of an option is only required at the moment of strike and for the current state of the market. In this study, we look at a multi-asset European option that is formally characterised by a system of stochastic differential equations. In this study, we use the Monte Carlo method's well-known "Random walk on spheres" (Rwos) technique to quantitatively evaluate the pricing of multi-asset rainbow options and compare the results to other known results.

Author(s) Details:

A. Rasulov
University of World Economy and Diplomacy, Tashkent, Uzbekistan.


M. Rakhmatov,
University of World Economy and Diplomacy, Tashkent, Uzbekistan.

Please see the link here: https://stm.bookpi.org/RAMRCS-V10/article/view/6275

Application of Differential Transformation Method for Solving Eighth-order Boundary Value Problems | Chapter 10 | Advanced Aspects of Engineering Research Vol. 15

 In this study, we solved linear and nonlinear eighth-order boundary value problems using the Differential Transformation Method. After that, the DTM error is determined, and the results are compared to those of other approaches like the modified implementation of the variational iteration method (MVAM), the homotopy perturbation method (HPM), and the modified Adomian decomposition method (MADM).

We compared the mistakes of each approach to the exact solutions. Many numerical examples were offered to demonstrate the precision and efficiency of the current method. The DTM showed to be more dependable than the data produced by other approaches.

Author (S) Details

Dr. Che Haziqah Che Hussin
Preparatory Centre of Science and Technology, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia.

Arif Mandangan
Faculty of Science and Natural Resources, Universiti Malaysia Sabah, Jalan UMS, 88400 Kota Kinabalu, Sabah, Malaysia.

View Book :- https://stm.bookpi.org/AAER-V15/article/view/1746