Department of Mathematics & Statistics

An infection-age-structured modelling for Monkey-Pox disease dynamics incorporating control measures

2025-04-07T11:45:34Z

An infection-age-structured modelling for Monkey-Pox disease dynamics incorporating control measures AZUABA, Emmanuel Monkey-pox is known as pathogens affecting livestock animals and humans and belongs to the orthopox virus. The pathogen causes lymph nodes to swell and increasing transmission risk associated with factors involving introduction of virus to the oral mucosa. In this paper, we developed an Age-Structured model for Monkey-pox disease in a population with vital dynamics, incorporating standard incidence rate and vaccination. We showed the existence and uniqueness of the solution of the model. We obtained the Disease-Free Equilibrium state and shown the effective reproduction number of the model. We proved the conditions for Local and Global Stability of the Disease-Free Equilibrium (DFE) State and we found that the disease free equilibrium state is locally asymptotically stable if G(0)  1 (RE < 1) and Globally Asymptotically Stable (GAS) in Ω if RE ≤ 1 while unstable if RE ≥ 1.

Research Updates in Mathematics and Computer Science Vol. 6

2024-07-03T08:47:11Z

Research Updates in Mathematics and Computer Science Vol. 6 OHWADUA, Emmanuel The study of the stability of solutions to differential equations is a fundamental and ongoing area of research in mathematics and applied sciences with numerous applications, and it provides a framework for analysing the behaviour of dynamical systems and predicting their long-term behaviour. For a numerical solution to be useful it must be both consistent and stable, and such a solution can be said to be stable if small errors in the initial data or in the numerical approximation do not grow unbounded as the computations progresses. In this paper, the stability of finite difference methods for time-dependent Schrodinger equation with Dirichlet boundary conditions on a staggered mesh was considered with explicit and implicit discretization. It is demonstrated that the solution is conditionally stable for the explicit finite difference technique and unconditionally stable for the implicit finite difference methods using the numerical algorithm's matrix representation. We will utilize a 1D harmonic oscillator problem to demonstrate this behaviour. Chapter 9: Stability of Finite Difference Solution of 1D Time-Dependent Schrodinger Wave Equation

NINTH ORDER BLOCK HYBRID INTEGRATORS FOR DIRECT NUMERICAL SOLUTION OF SECOND ORDER DIFFERENTIAL EQUATIONS

2024-06-24T15:01:26Z

NINTH ORDER BLOCK HYBRID INTEGRATORS FOR DIRECT NUMERICAL SOLUTION OF SECOND ORDER DIFFERENTIAL EQUATIONS JOSEPH, Folake A ninth order numerical scheme is develped in this work to directly solve second order initial and boundary value problems and via the method of lines for the semi descritization and solution for second order partial differential equations. These schemes are developed via the collocation technique and unified to form a single block of hybrid integrators. The derived method is investigated for its consistency, zero-stability and convergence and found to satisfy these characteristics. Numerical examples shows that the derived method is fond to be efficient in terms of implimentation and less computer time and in terms of accuracy when compared to existing methods in literature.

A CONTINOUS COLLOCATION FORMULATION OF TWO-STEP IMPLICIT BLOCK METHOD FOR SECOND ORDER ODEs USING LEGENDRE BASIS FUNCTION

2024-06-24T14:59:37Z

A CONTINOUS COLLOCATION FORMULATION OF TWO-STEP IMPLICIT BLOCK METHOD FOR SECOND ORDER ODEs USING LEGENDRE BASIS FUNCTION JOSEPH, Folake