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 \textcolor{red}{with finding} the numerical solution of delay epidemic model with diffusion which is not a simple task as variables involved in the model exhibit some important physical features. Therefore we design an efficient numerical scheme which preserves the properties acquired by the given system. We also develop forward Euler technique for delayed epidemic reaction-diffusion model. The proposed numerical technique is also compared with the forward Euler technique and observe that forward Euler technique demonstrates the false behavior at certain step sizes. On the other hand, proposed technique preserves the true behavior of the continuous system at all step sizes. Furthermore, the effect of delay factor is discussed graphically by using proposed technique.