Optimal control using linear feedback control and neutralizing antibodies for an HIV model with dynamical analysis

• Published in: Journal of applied mathematics & computing Vol. 68; no. 6; pp. 4361 - 4389
• Main Authors: Barik, Mamta, Chauhan, Sudipa, Misra, Om Prakash, Bhatia, Sumit Kaur
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 2022; Springer Nature B.V
• Subjects: Acquired immune deficiency syndrome; AIDS; Algorithms; Antibodies; Applied mathematics; Blocking; Computational Mathematics and Numerical Analysis; Control methods; Control systems; Curve fitting; Feedback control; HIV; Human immunodeficiency virus; Immune system; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Optimal control; Original Research; Stability analysis; Theory of Computation; Thresholds; Linear feedback control; Immune response; Graph theoretic approach; 34D23; Local bifurcation analysis; 34C23; 35F21; 34D20; Curve-fit; Local stability
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-022-01710-5

HIV (human immunodeficiency virus) is a dangerous virus that constantly diminishes an individual’s immune system by explicitly targeting CD4 cells, which are the body’s key protectors against disease by obstructing them to make duplicates of themselves. If left untreated, it can lead to AIDS (acquired immunodeficiency syndrome). The Treatment involves antiretroviral therapy which maintains the immunity to a specific level and thus helps in suppressing the virus replication. This paper emphasizes on the development of the model involving healthy and infected population, virus population, antibodies and CTL cells. The investigation encapsulates the local stability based on thresholds followed by the local bifurcation analysis based on
β
1
and
R
0
. The global stability analysis is done the using Graph- theoretic approach. Further the optimal control problem is discussed using Linear feedback control method which aims to reduce the viral load by keeping antibodies to a certain level. Numerical discussion includes surface plots of the thresholds based on various parameters, graphs showing the comparison between without control and with control especially for the virus population, infected population and antibodies which are our target. Finally, we have also shown the curve-fitting for our data using optimized Nedlar-Mean algorithm.