International Journal Of Mathematics And Computer Research

Stability Analysis of the Disease-Free Equilibrium State for Lymphatic Filariasis with Chemical and Biological Control on Vector

2024-12-03T08:26:48+00:00

In this paper, we develop a mathematical model to analyze the transmission dynamics and control strategies for Lymphatic Filariasis (LF), incorporating both chemical and biological control measures targeting the disease vector. The model is proven to be both mathematically and epidemiologically sound. By determining the basic reproduction number (\(R_0\)), we establish the conditions for local and global stability of the disease-free equilibrium (DFE). The model highlights the impact of Wolbachia bacteria on mosquito populations and the role of drug resistance and recovery in human populations. Our results demonstrate that reducing \(R_0\) below 1 is crucial to eradicating LF from an endemic population, and thus, preventive measures, including vector control, are essential. Further research is recommended to optimize the combined use of chemical and biological controls to achieve long-term stability and disease eradication.

Enhancing Image Encryption with Quadrant-Based Layered Multi-Key Systems

2024-12-03T08:30:07+00:00

The exponential growth of technology poses significant challenges to the robustness of current
encryption methods, such as AES and DES, which may become vulnerable soon. This research
introduces a novel approach, the Layered Multi-Key Encryption and Decryption System,
designed to enhance the security and efficiency of image encryption. The proposed system
employs Quadrant-Based Keys, a unique technique that divides an image into quadrants and
applies distinct keys to each section, creating an additional layer of complexity. By focusing on
color channels, this method ensures granular encryption, making unauthorized access
exceedingly difficult. Experimental results demonstrate that this system outperforms traditional
algorithms in terms of speed and security. However, the requirement to save keys in a .mat file
poses a slight limitation, as these keys are essential for decryption. This research paves the way
for next-generation encryption systems, offering a robust solution for secure image data
transmission and storage.

Nano (1,2)*-w πg Closed Sets and its Generalizations

2024-12-06T11:20:12+00:00

In this paper, we introduce the notions of nano (1,2)*-π-closed sets and nano (1,2)*-πg-closed sets, nano (1,2)*-wπg -closed sets and nano (1,2)*-rwg-closed sets use it to obtain a characterization and preservation theorems of quasi-normal spaces.

Special value of the odd zeta function ζ(3)

2024-12-10T07:22:37+00:00

Euler clarified even zeta special values which can be written as (rational number)power of π, but the odd zeta value is unknown. In this paper, the author will try to clarify the special value of with the aid of the Mathematical program.

(S, D) Magic Labeling of Subdivision of Some Special Trees

2024-12-10T11:00:03+00:00

Let G (connected, undirected, simple and non-trivial graph with p vertices and q edges. Let f be an injective function f: V(G) } and g be an injective function g: E(G) .Then the graph G is said to be (s, d) magic labeling if is a constant, for all . A graph G is called (magic graphif it admits magic labeling. In this paper the existence of (s, d) magic labeling of subdivision on some special trees are found.

Project Management Using Critical Path Method (CPM) and Project Evaluation and Review Technique (PERT)

2024-12-11T09:05:15+00:00

Project delivery within the established time line and project cost is one of the persistent issues in current project management practices. This work therefore aimed at assessing the appropriateness of Project Evaluation Review Technique and Critical Path Method in project management with a case study of a UNN lecture hall construction. Consequently, the research establishes the impact of these quantitative operations research tools on the efficient project management. Both of these project management techniques were explained and used in relation to the data that was obtained from the lecture hall construction project manager, concerning the project activities and the time taken for each of these activities. As indicated by the findings of this study, both the methods were posited to achieve success in project management where by relationship and connectivity of the activities that define a project life cycle persist as the key issues. As such, it was suggested that in view of the project critical activities determined by the CPM and/or PERT analyses, more resources and attention should be directed towards effective management of such activities to avoid the occasion of project delay as well as ensure the successful completion of projects.

Chickenpox Childhood Disease: An insight from Mathematical Modelling

2024-12-13T08:52:42+00:00

Chickenpox is an infectious disease that causes an itchy, blister-like rash on the skin and can spread through bodily fluids and body contact. This study presents a mathematical model for the transmission dynamics of chickenpox among children by considering the impact of vaccination and treatment. The qualitative analysis of the model reveals that the model has two equilibrium points, namely: the chickenpox-free and endemic equilibrium points. The disease-free equilibrium point is globally asymptotically stable whenever the basic reproduction number is less than unity (R0<1) and the endemic equilibrium point is globally stable whenever the reproduction number is greater than unity (R0>1). The normalized forward sensitivity index is also used to obtain the critical factors responsible for the transmission of chickenpox in the population. Furthermore, it reveals that parameters with negative indices will reduce the transmission of chickenpox when increased. The qualitative analysis of the model is supported by numerical simulation