Positivity Preserving Technique for the Solution of HIV/AIDS Reaction Diffusion Model With Time Delay - Jawaz, Muhammad; Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Rehman, Muhammad Aziz-ur (Frontiers in Physics, 2020)
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.