Journal of Mathematical Analysis and Modeling

A GUMBORO-SALMONELLA CO-INFECTION MATHEMATICAL MODEL WITH OPTIMAL CONTROL

2024-07-11T17:07:55+00:00

Poultry production contributes immensely to the economic growth of a country. For instance in Kenya, 20
tonnes of poultry meat worth 3.5 billion kenya shillings and 1.3 billion eggs worth 9.7 billion Kenya Shillings
come from this sector. However, the sector is greatly threatened by poultry diseases among them, Gum-
boro(IBD) and Salmonella as inadequate knowledge exists of optimal control strategies for various poultry
co-infections. In this research, a Gumboro-Salmonella co-infection mathematical model with optimal control
is developed using a system of ODEs to perform an optimal control analysis. The analysis was done by for-
mulating an optimal control problem and using Pontryagin’s maximum principle to solve it. The Numerical
simulation results showed that the best Gumboro-Salmonella co-infection control strategy involved combining
all the interventions

Numerical Investigation of Turbulent Convection Flow in a Rectangular Closed Cavity

2024-04-07T21:31:08+00:00

Natural turbulent convection in closed cavities has many practical applications in the field of engineering
such as the design of electronic computer chips, atomic installation and industrial cooling among others. In
particular, it enables in achieving a desired micro-climate and efficient ventilation in a building. Recent studies
show that turbulent flow is affected by variations in Rayleigh numbers, aspect ratio, and heater position
among others. Temperature is kept constant in all these studies hence inadequate literature on the effects
of temperature on a turbulent flow. In this study, aspect ratio and Rayleigh numbers are kept constant at
2 and 1012 respectively and natural turbulent convection flow in a closed rectangular cavity is investigated
numerically as the operating temperature is varied from 285.5K to 293K. The rectangular cavity’s lower wall
was heated and cooling done at the top face wall while the rest of the vertical walls were kept in adiabatic
condition. Material properties such as density of the fluid kept on changing at any given temperature. The
thermal profile data generated influenced the nature of the turbulent flow. The non-linear averaged continuity,
momentum, and energy equation terms were modeled by the SST k − ω model to generate streamlines,
isotherms, and velocity magnitude for a different operating temperature and presented graphically. The finite
difference method and FLUENT were used to solve two SST k − ω model equations, vortices, and energy with
boundary conditions. It was discovered that, as the operating temperature increased turbulence decreased
due to a decrease in the velocity of the elements and vortices became more parallel and smaller.

The importance of quarantine: A bifurcation analysis and modeling of the transmission dynamics of Covid 19

2024-09-01T18:39:25+00:00

The research aims to construct a mathematical model for COVID 19 that includes features six compartments to evaluate the positive effects of quarantine measures. The model categorizes individuals into the
following classes: susceptible, exposed, quarantined, asymptomatic cases, symptomatic cases, and recovered
(SEQI1
I2R). Several assumptions regarding positivity and boundness are identified to ensure that the solution
originated within a certain class and that the basic reproduction number is analyzed. Of course, the existence
of an endemic equilibrium is argued, which provides an understanding of the long-term persistence of the
disease. More precisely, to enhance our understanding of the model’s dynamics, we have analyzed both the
local and global asymptotic stability of the disease-free equilibrium. Moreover, to assess the global stability
of the system, we employ a Lyapunov function which provides a comprehensive mathematical evaluation. At
the same time, our findings show evidence of a backward bifurcation which is recognized as a possible result
of the clinical transition from an asymptomatic state to symptom one.

Fixed Point Results in Archimedean Type Neutrosophic b-Metric Spaces

2024-06-17T16:06:31+00:00

This paper defines Archimedean, Caristi-Krirk balls, and Neutrosophic b metric space (Nb-MS). Using
the Archimedean idea and complete Nb-MS, we have shown the existence of a shared fixed point using
two self-mappings and an upper semicontinuous function. We have demonstrated the existence of a fixed point by employing a k-continuous self-map and an upper semi-continuous function in conjunction with the Archimedean notion and complete Nb-MS. Furthermore, we have proven the completeness of the space by using Archimedean, Nb-MS, and a k-continuous self-map.
MSC 2010: 47H10.

Statistical approximation for functions of two variables by Bernstein-Chlodowsky Polynomials on a triangular domain

2024-09-01T18:36:45+00:00

Statistical approximation of continuous functions of two variables by means of Bernstein-Chlodowsky polynomials on a triangular domain is studied. Further, weighted approximation of continuous functions of two variables on a triangular domain is investigated in statistical sense. Finally, we study the approximation results in terms of ideal convergence.

New proof and variants of a referenced logarithmic-power integral

2024-10-01T17:22:55+00:00

This article contributes to mathematical analysis by (i) presenting an elegant proof of a specific integral, (ii) demonstrating its connection with an existing result, and (iii) introducing previously unexplored
variants.

An efficient fourth-order method for direct integration of second-order ordinary differential equations

2024-10-22T14:57:17+00:00

This paper presents a novel fourth-order block method for the direct integration of second-order differential equations. The method is derived from a basis function that combines a third-order polynomial with the sum of sine and cosine functions. By leveraging this unique basis function, the proposed method maintains computational efficiency while achieving fourth-order accuracy. It outlines the method's derivation and analyzes its stability and accuracy properties. Numerical experiments demonstrate its e ffectiveness and efficiency compared to existing techniques. The results indicate that the proposed fourth-order block method off ers signi cant advantages in accuracy and computational cost, making it promising for directly integrating

Modeling the Transmission Dynamics of Avian Influenza in Cattle

2024-06-23T19:55:57+00:00

Avian Influenza (AI) poses a critical threat to cattle production worldwide, resulting in significant yield losses and economic damages. Despite the severity of AI, comprehensive modeling studies on its transmission dynamics within cattle populations remain limited. In this study, we present a mathematical model to describe the spread of AI among cattle. The model is based on the Susceptible-Infectious-Recovered (SIR) framework, adapted to capture the unique characteristics of AI transmission. The disease-free equilibrium of the model was computed, and the basic reproduction number for AI was calculated using the next-generation matrix method. Sensitivity analysis was conducted using normalized forward sensitivity method to determine the impact of various parameters on the basic reproduction number ($\mathcal{R}_0$). Analytical and numerical analyses indicate that increased contact rates between susceptible cattle and infected virus significantly raise the transmission rate of AI, impacting cattle health and productivity. Sensitivity analysis highlights that the recruitment rates of cattle and infection rates are the most influential parameters affecting $\mathcal{R}_0$. Control measures such as introducing AI-resistant cattle breeds and improving farm management practices to reduce infection rates may be used to mitigate the disease spread. This study enhances the understanding of AI transmission dynamics, providing valuable insights for developing targeted control strategies to protect cattle health and improve production.

Fixed Point Theorem on C ∗-algebra-valued Suprametric Spaces

2024-04-21T18:59:39+00:00

The present study’s objective is to propose a C∗-algebra-valued suprametric spaces to provide an appro priate generalization concerning both suprametric spaces and C ∗-algebra-valued metric spaces. The concepts of convergence, Cauchy sequence, and completeness are then examined through suprametric space with C ∗-algebra and illustrated with an example. Furthermore, the Banach fixed point theorem, established in pursuance of the same metric, is employed to determine the existence and uniqueness of the solution to an integral equation.