A fractional order HIV/AIDS model based on the effect of screening of unaware infectives

Abstract

In this paper, a fractional order model for the spread of human immunodeficiency virus (HIV) infection is proposed to study the effect of screening of unaware infected individuals on the spread of the HIV virus. For this purpose, local asymptotic stability analysis of the disease‐free equilibrium is investigated. In addition, the model is studied for different values of the fractional order to show the relation between the variations of the reproduction number and the order of the proposed model. Finally, numerical solutions are simulated by using a predictor‐corrector method to illustrate the dynamics between susceptible individuals and unaware infected individuals.

A fractional differential equation model for the COVID-19 transmission by using the Caputo–Fabrizio derivative

“…If Picard's iteration q n+1 = Tq n is satisfied in all these conditions, then q n+1 = Tq n is T-stable. According to (8), the fractional model of COVID-19 (1) is connected with the subsequent iterative formula. Now consider the following theorem.…”

Laplace decomposition for solving nonlinear system of fractional order partial differential equations

“…In fact, many physical phenomena are dependent on time instant as well as at the earlier history of time are modeled by using fractional-order ordinary differential equations (FODEs), and thus FDEs have attained their importance in many fields of applied sciences. Due to the importance of FDEs, many researchers have made their focus on the analytical solution as well as the numerical solutions of FDEs [10][11][12]. In this regard numerous techniques have been discussed for the solutions of FPDEs such as homotopy analysis method (HAM), homotopy perturbation technique (HPM), Laplace transformation, variational technique with Pade approximation, corrected Fourier series, natural decomposition method [13][14][15][16], and fractional complex transformation [17].…”

Numerical Treatment of Time-Fractional Klein–Gordon Equation Using Redefined Extended Cubic B-Spline Functions

“…The subject of fractional-order differential equations has attracted considerable interest due to its applications in a wide range of fields, such as traffic flow, earthquakes and other physical phenomena, signal processing, finance, control theory, fractional dynamics, and mathematical modeling [1][2][3][4][5][6][7][8][9][10]. In recent years, the analytical and numerical study of fractional-order differential equations has become a dynamic area of research.…”