Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay

Abstract

This study is concerned with finding a numerical solution to the delay epidemic model with diffusion. This is not a simple task as variables involved in the model exhibit some important physical features. We have therefore designed an efficient numerical scheme that preserves the properties acquired by the given system. We also further develop Euler's technique for a delayed epidemic reaction-diffusion model. The proposed numerical technique is also compared with the forward Euler technique, and we observe that the forward Euler technique demonstrates the false behavior at certain step sizes. On the other hand, the proposed technique preserves the true behavior of the continuous system at all step sizes. Furthermore, the effect of the delay factor is discussed graphically by using the proposed technique.

Numerical Analysis for the Effect of Irresponsible Immigrants on HIV/AIDS Dynamics

“…Remark 1. The existence of the Schauder fixed point theorem can be guaranteed with the same conditions (17) and (18) with another state of relative compactness using the concepts of equicontinuity and the subsequent Arzela-Ascoli-Theorem.…”

“…The Nonstandard finite difference (NSFD) stochastic scheme retained all the important properties of the disease dynamical model. Jawaz et al studied a delay epidemic model with diffusion and developed Nonstandard finite difference (NSFD) based scheme to study HIV/AIDS, a delayed reaction-diffusion epidemic model [18]. Iqbal [22,23].…”

Modified Chebyshev collocation method for delayed predator–prey system

“…3 to Eq. (19) in order to obtain the approximate solutions. Let e 1N,M (t) and e 2N,M (t) be the estimation solutions of errors e 1N (t) and e 2N (t).…”

“…Nowadays, more and more attention is focused on the fractional predator-prey dynamical system. However, few of the fractional equations can be solved explicitly, but the broad application attracts many authors to devote themselves to numerical methods of these equations (see [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]). Very recently, many numerical methods have been developed for solving the fractional predator-prey dynamical system.…”

Positive solutions for integral boundary value problems of fractional differential equations with delay

“…They dealt with the existence of solutions under various boundary conditions by different methods. For details, one can refer to [20,[25][26][27] and the references therein.…”