Vol. 30 No. 3 (2023)

Open Access

Articles

Article ID: 2412

NUMERICAL APPROXIMATION OF THE FINAL STATE OF AN INCOMPLETE DATA HEAT PROBLEM

by ABANI MAIDAOUAAli, DJIBO Moustapha, SALEY Bisso

Advances in Differential Equations and Control Processes, Vol.30, No.3, 2023;

We determine the state at an instant $T_0$ of a 2D heat problem whose initial condition is partially known on a part of the domain. We use a non-standard method to solve this problem numerically.

Open Access

Articles

Article ID: 2413

MATHEMATICAL ANALYSIS OF HEPATITIS B TRANSMISSION MODEL

by OUEDRAOGO Boukary, ZOROM Malicki, GOUBA Elisée

Advances in Differential Equations and Control Processes, Vol.30, No.3, 2023;

In this article, we present the transmission dynamics of the acute and chronic hepatitis B epidemic problem. To control the spread of hepatitis in a community, we first develop a mathematical model for the transmission of the virus of hepatitis B. After framing the mathematical model, we show the existence and uniqueness of the solution, then mathematically analyze the model and determine the disease-free equilibrium state of the model. Besides, we determine the basic reproduction number $\mathcal{R}_0$ for this model which is interpreted epidemiologically. Next, we study the local stability of the disease-free-equilibrium state and show that if $\mathcal{R}_0<1$, then, the disease-free equilibrium is asymptotically stable, otherwise unstable. Finally, a sensitivity analysis is performed to determine the relative importance of the model parameters to disease transmission and prevalence. The paper ends with the numerical simulation to illustrate the theoretical results.

Open Access

Articles

Article ID: 2414

EXISTENCE OF SOLUTIONS FOR NONLINEAR VOLTERRA FREDHOLM INTEGRODIFFERENTIAL EQUATION OF HIGHER ORDER VIA $S$-ITERATION METHOD

by Haribhau L. Tidke, Gajanan S. Patil

Advances in Differential Equations and Control Processes, Vol.30, No.3, 2023;

In this paper, we study the existence and other properties of the solution of the nonlinear Volterra Fredholm integrodifferential equation of higher order. The tool employed in the analysis is based on the application of the $S$-iteration method. Various properties such as dependence on initial data, closeness of solutions and dependence on parameters and functions involved therein are obtained using the $S$-iteration method. Examples are provided in support of findings.

Open Access

Articles

Article ID: 2415

ANALYTICAL AND NUMERICAL APPROACHES TO SOLVE A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS FOR THE SPREAD OF DENGUE FEVER OF WITH-IN-HOST MODEL

by D. Maheskumar, T. Jayakumar, S. Sujitha, E. VargeesKaviyan

Advances in Differential Equations and Control Processes, Vol.30, No.3, 2023;

In recent years, many mathematical models have been developed and investigated based on real-life issues in engineering, medicine, agriculture, and many other fields. Moreover, the numerical approach was used to solve it due to its intricacy. However, in reality, this methodology merely offers an approximate solution, which is close to an exact solution but not exact. This article demonstrates how to find the analytical solutions of the system of nonlinear ordinary differential equations precisely by considering the mathematical model for the spread of dengue fever of the with-in-host model. Furthermore, stability analysis and numerical simulation were also provided. Finally, graphs from the analytical method and numerical simulation are compared to assess the solutions of the system’s validity. This work may be helpful to many researchers in obtaining an analytical solution to the nonlinear dynamics

Open Access

Articles

Article ID: 2416

THE INVERSE LAPLACE TRANSFORM OF SOME COMPLEX EXPRESSIONS ARISING IN SOLAR ENERGY MODELS

by Abdelhalim Ebaid, Amjad A. Alsubaie

Advances in Differential Equations and Control Processes, Vol.30, No.3, 2023;

Recently, many mathematical models are proposed to describe storage of solar energy. Most of these models are governed by boundary value problems (BVPs). The explicit solutions of such BVPs depend in determining the inverse Laplace transform of complex expressions. This paper overcomes some of these difficulties arising on account of this. The results can be invested to construct the analytic solutions of solar energy models and also models of other fields in engineering sciences.