A numerical efficient splitting method for the solution of HIV time periodic reaction–diffusion model having spatial heterogeneity

• Published in: Physica A 2023-01, Vol.609, p.128385, Article 128385
• Main Authors: Raza, Nauman, Arshed, Saima, Bakar, Abu, Shahzad, Aamir, Inc, Mustafa
• Format: Article
• Language: English
• Subjects: Basic reproduction number; HIV; Nonstandard operator splitting method; Positivity; Reaction–diffusion model
• ISSN: 0378-4371; 1873-2119
• DOI: 10.1016/j.physa.2022.128385

This study examines a novel reaction–diffusion model for the existence and treatment of acquired immunodeficiency syndrome. This model is a spatial extension of the recent HIV model and human immunodeficiency viruses cause this disorder. The most significant barrier to eradicating this virus is latency and the virus’ subsequent viral reservoir in CD4+ T cells. A nonstandard operator splitting strategy is proposed to approximate the solution of the time-periodic reaction–diffusion model. The main advantages of employing this approach over other techniques are its low computational costs, high accuracy and ease of implementation. The results are truly solid and match those available in the literature. The nature of the solution for the threshold parameter is demonstrated graphically using numerical results. Finally, the M-matrix theory and the positivity of the proposed scheme are discussed. •The existence and treatment of acquired immunodeficiency syndrome, the disease caused by human immunodeficiency viruses is investigated.•The nonstandard finite difference method is suggested to estimate the solution of the time-periodic reaction–diffusion model.•The physical explanations are presented for the obtained results.•The obtained results are given by 3D figures.