Kyung Hee University · Mathematics
Professor Shahram Rezapour's research lab specializes in the development and analysis of fractional-order mathematical models for infectious diseases, with a strong emphasis on novel fractional derivatives such as Caputo–Fabrizio and generalized Caputo types. The lab focuses on the theoretical and computational study of epidemic dynamics—particularly for HIV, COVID-19, childhood diseases, and waterborne infections—using advanced analytical techniques like fixed point theory, homotopy analysis, Laplace transforms, and iterative methods. A key strength lies in proving existence, uniqueness, and stability of solutions, combined with numerical simulations using real-world data to enhance public health modeling. The lab also explores fractal-fractional integral formulations to improve model accuracy and applicability in complex biological systems.
Figures are computed from collected data and may differ slightly.
Abstract By using the fractional Caputo–Fabrizio derivative, we investigate a new version for the mathematical model of HIV. In this way, we review the existence and uniqueness of the solution for the model by using fixed point theory. We solve the equation by a combination of the Laplace transform and homotopy analysis method. Finally, we provide some numerical analytics and comparisons of the results.
We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results
Abstract A newly proposed p -Laplacian nonperiodic boundary value problem is studied in this research paper in the form of generalized Caputo fractional derivatives. The existence and uniqueness of solutions are fully investigated for this problem using some fixed point theorems such as Banach and Schauder. This work is supported with an example to apply all obtained new results and validate their applicability.
Waterborne diseases are illnesses caused by pathogenic bacteria that spread through water and have a negative influence on human health. Due to the involvement of most countries in this vital issue, accurate analysis of mathematical models of such diseases is one of the first priorities of researchers. In this regard, in this paper, we turn to a waterborne disease model for solution’s existence, HU-stability, and computational analysis. We transform the model to an analogous fractal-fractional i
We present a fractional-order epidemic model for childhood diseases with the new fractional derivative approach proposed by Caputo and Fabrizio. By applying the Laplace Adomian decomposition method (LADM), we solve the problem and the solutions are presented as infinite series converging to the solution. We prove the existence, uniqueness, and stability of the solution by using the fixed point theory. Also, we provide some numerical results to illustrate the effectiveness of the new derivative.
We provide a SEIR epidemic model for the spread of COVID-19 using the Caputo fractional derivative. The feasibility region of the system and equilibrium points are calculated and the stability of the equilibrium points is investigated. We prove the existence of a unique solution for the model by using fixed point theory. Using the fractional Euler method, we get an approximate solution to the model. To predict the transmission of COVID-19 in Iran and in the world, we provide a numerical simulati
Abstract We present a new mathematical model for the transmission of Zika virus between humans as well as between humans and mosquitoes. In this way, we use the fractional-order Caputo derivative. The region of the feasibility of system and equilibrium points are calculated, and the stability of equilibrium point is investigated. We prove the existence of a unique solution for the model by using the fixed point theory. By using the fractional Euler method, we get an approximate solution to the m
Abstract We study a fractional-order model for the anthrax disease between animals based on the Caputo–Fabrizio derivative. First, we derive an existence criterion of solutions for the proposed fractional $\mathcal {CF}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>CF</mml:mi></mml:math> -system of the anthrax disease model by utilizing the Picard–Lindelof technique. By obtaining the basic reproduction number $\mathcal{R}_{0}$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/
Abstract In this paper, we study the rubella disease model with the Caputo–Fabrizio fractional derivative. The mathematical solution of the liver model is presented by a three-step Adams–Bashforth scheme. The existence and uniqueness of the solution are discussed by employing fixed point theory. Finally some numerical simulations are showed to underpin the effectiveness of the used derivative.
Nonlinear phenomena observed in diverse scientific disciplines, including fluid dynamics, plasma physics, and biology, are frequently described by partial differential equations (PDEs). Among these PDEs, the Chaffee-Infante equation holds considerable importance and finds applications in various scientific and engineering domains. The focus of this research article revolves around the exploration of closed-form solitary wave solutions for this significant nonlinear evolution equation (NLEE) thro
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