https://doi.org/10.1140/epjp/s13360-024-05605-1
Regular Article
Optimizing HIV/AIDS dynamics: stochastic control strategies with education and treatment
School of Mathematics, Sun Yat-Sen University, 510275, Guangzhou, People’s Republic of China
Received:
30
July
2024
Accepted:
29
August
2024
Published online:
11
September
2024
Human immunodeficiency virus (HIV) is a viral infection that infects CD4+ lymphocyte cells, and as a result, the body’s immune system is destroyed and unable to fight against the disease. Due to the attacks of HIV on the immune system, in the long run, the infection leads to Acquired Immune Deficiency Syndrome (AIDS). In the present manuscript, a stochastic model for the human immune deficiency virus (HIV) is formulated. Initially, it is shown that there exists a global positive solution to the model subject to a positive initial condition. To prove the stability results, the underlying stochastic equations are analyzed and the necessary Lyapunov functions have been formulated. The persistence of the diseases is investigated, and the necessary conditions are derived. Reducing the infection rate in the population requires a substantial cost and is more challenging; therefore, an optimal control system is derived by using a few control variables. To validate the theory and support the results, the model is simulated with the help of the standard stochastic method, followed by a comparative analysis at the end of the paper.
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