Abstract
The study of human immunodeficiency virus (HIV) has been the subject of massive scientific research in recent years. Some works have focused on the evolution of the virus mutations developed against the immune system or the combination design therapy. But most of these models are too complex to analyze in details and to design an optimal combination therapy. The main objective of this paper is to analyse the stability and optimal control of a HIV combination therapy nonlinear model, which takes into account the mutations and latent cells. We use a \(\mathcal {L}_1\) controller that stabilize the evolutionary dynamics of HIV disease. Because of the positive nature of the system, this problem can be solved with a scalable iterative algorithm that finds the best medication.Therefore, following recent work of V. Jonsson and R. Murray we introduce a similar algorithm to solve the combination therapy design problem. We obtain efficient results for this nonlinear model and thereby show that optimal control theory can be applied on more complex and realistic models.
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Kande, M., Jungers, R.M., Seck, D., Balde, M. (2020). A Scalable Engineering Combination Therapies for Evolutionary Dynamic of Macrophages. In: Seck, D., Kangni, K., Nang, P., Salomon Sambou, M. (eds) Nonlinear Analysis, Geometry and Applications. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-57336-2_8
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DOI: https://doi.org/10.1007/978-3-030-57336-2_8
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