A Hybrid Method with RDTM for Solving the Biological Population Model

In this paper, we establish an analytical solution to the non-linear biological population model using a hybrid method that combines a reduced differential transform method with a resummation method based on Yang transform and a Padé approximant. The proposed method significantly improves the approximate solution series and broadens the convergence field, It is also dependent on a few straightforward steps, and does not depend on a perturbation parameter or produce secular terms. Three examples are given to test the effectiveness, accuracy, and performance of the suggested method. The results and graph demonstrate that the suggested method is successful and more accurate than other methods. In addition, PYRDTM is a useful tool with great potential for solving nonlinear BPM. Keywords: Biological population model, Yang transform, RDTM, Padé approximation, accuracy. DOI: 10.7176/MTM/12-2-01 Publication date:September 30th 2022

Analytical Solutions for Simulation of Mathematical Modelling of Liposomal Drug Release to Tumor by Adomian Decomposition Method.

In this paper,  the  system of partial differential equations of the  thermo sensitive liposome-mediated drug delivery  model is solved analytically by applied the Adomian decomposition method with the appropriate initial and boundary  condition as well. Also, to determine the effectiveness of suggested models, simulated results were in comparison to the corresponding experimental information , and an important agreement was reached . So that a quantitative analysis is finally done by numerical simulation by adopting the values of all typical parameters to clarify the drug concentrations behavior with increasing time in different cases. Keywords: Local drug ; Drug delivery ; cancer stem cells ; Adomian decomposition method ; Different locations

A New Approximate Analytical Solutions for Two- and Three-Dimensional Unsteady Viscous Incompressible Flows by Using the Kinetically Reduced Local Navier-Stokes Equations

In this work, the kinetically reduced local Navier-Stokes equations are applied to the simulation of two- and three-dimensional unsteady viscous incompressible flow problems. The reduced differential transform method is used to find the new approximate analytical solutions of these flow problems. The new technique has been tested by using four selected multidimensional unsteady flow problems: two- and three-dimensional Taylor decaying vortices flow, Kovasznay flow, and three-dimensional Beltrami flow. The convergence analysis was discussed for this approach. The numerical results obtained by this approach are compared with other results that are available in previous works. Our results show that this method is efficient to provide new approximate analytic solutions. Moreover, we found that it has highly precise solutions with good convergence, less time consuming, being easily implemented for high Reynolds numbers, and low Mach numbers

Development and simulation of a mathematical model representing the dynamics of type 1 diabetes mellitus with treatment

The research aims to understand and study type 1 diabetes and its response to treatment using a mathematical model. We employ a novel method that combines the Shehu transformation with the Akbari–Ganji approach and the Padé approximation to derive approximate solutions for this model. The research findings convincingly show the effectiveness of the method used. The results show a positive impact of the investigated treatment on individuals with type 1 diabetes. Strong agreement is observed between the results obtained from this model's solutions and those of previous studies, confirming the accuracy and reliability of the simulation method employed. This method is considered a successful simulation technique for future studies, enhancing our understanding of the effects of treatments on individuals with type 1 diabetes. From a practical standpoint, the study's results can offer valuable insights to healthcare professionals, enabling them to make more informed decisions regarding treatment strategies. These insights have the potential to optimize treatment plans, potentially leading to improved health outcomes for patients. Furthermore, this research paves the way for further advanced studies in the field of medical modeling and simulation

A Novel Algorithm for Studying the Effects of Squeezing Flow of a Casson Fluid between Parallel Plates on Magnetic Field

In this paper, the magneto hydrodynamic (MHD) squeezing flow of a non-Newtonian, namely, Casson, fluid between parallel plates is studied. The suitable one of similarity transformation conversion laws is proposed to obtain the governing MHD flow nonlinear ordinary differential equation. The resulting equation has been solved by a novel algorithm. Comparisons between the results of the novel algorithm technique and other analytical techniques and one numerical Range-Kutta fourth-order algorithm are provided. The results are found to be in excellent agreement. Also, a novel convergence proof of the proposed algorithm based on properties of convergent series is introduced. Flow behavior under the changing involved physical parameters such as squeeze number, Casson fluid parameter, and magnetic number is discussed and explained in detail with help of tables and graphs

A New Analytical-Approximate Solution for the Viscoelastic Squeezing Flow Between Two Parallel Plates

In this paper, a new approach is used to study analytically the axisymmetric fluid squeezed between two parallel plates. This new approach depends mainly on the coefficients of powers series resulting from integrating nth order differential equation with known data. We obtianed an analytical-approximate solution for the squeezing flow between two parallel plates. The steady non-linear governing partial differential equations are converted by using the suitable similarity transformation into ordinary differential equation. In addition, some theorems are introduced to prove the convergence of a new approach theoretically and explain the verifications of these theorems computationally. The results domenstrate this new approach is efficient and reasonable which compare with the results of the other methods

SARS-CoV-2 vaccination modelling for safe surgery to save lives: data from an international prospective cohort study

Background: Preoperative SARS-CoV-2 vaccination could support safer elective surgery. Vaccine numbers are limited so this study aimed to inform their prioritization by modelling. Methods: The primary outcome was the number needed to vaccinate (NNV) to prevent one COVID-19-related death in 1 year. NNVs were based on postoperative SARS-CoV-2 rates and mortality in an international cohort study (surgical patients), and community SARS-CoV-2 incidence and case fatality data (general population). NNV estimates were stratified by age (18-49, 50-69, 70 or more years) and type of surgery. Best- and worst-case scenarios were used to describe uncertainty. Results: NNVs were more favourable in surgical patients than the general population. The most favourable NNVs were in patients aged 70 years or more needing cancer surgery (351; best case 196, worst case 816) or non-cancer surgery (733; best case 407, worst case 1664). Both exceeded the NNV in the general population (1840; best case 1196, worst case 3066). NNVs for surgical patients remained favourable at a range of SARS-CoV-2 incidence rates in sensitivity analysis modelling. Globally, prioritizing preoperative vaccination of patients needing elective surgery ahead of the general population could prevent an additional 58 687 (best case 115 007, worst case 20 177) COVID-19-related deaths in 1 year. Conclusion: As global roll out of SARS-CoV-2 vaccination proceeds, patients needing elective surgery should be prioritized ahead of the general population