An efficient therapy strategy under a novel HIV model. (English) Zbl 1229.92054
Summary: By incorporating the chemotherapy into a previous model describing the interaction of the immune system with the human immunodeficiency virus (HIV), this paper proposes a novel HIV virus spread model with control variables. Our goal is to maximize the number of healthy cells and, meanwhile, to minimize the cost of chemotherapy. In this context, the existence of an optimal control is proved. Experimental results show that, under this model, the spread of HIV virus can be controlled effectively.
MSC:
| 92C50 | Medical applications (general) |
| 92C60 | Medical epidemiology |
| 49N90 | Applications of optimal control and differential games |
References:
| [1] | DOI: 10.1016/j.cam.2005.02.004 · Zbl 1075.92030 · doi:10.1016/j.cam.2005.02.004 |
| [2] | DOI: 10.1093/imammb/3.4.229 · doi:10.1093/imammb/3.4.229 |
| [3] | Biometrics 35 (1) pp 295– (1979) · doi:10.2307/2529951 |
| [4] | DOI: 10.1109/MCS.2008.929281 · Zbl 1395.93561 · doi:10.1109/MCS.2008.929281 |
| [5] | DOI: 10.1007/s00285-003-0245-3 · Zbl 1057.92035 · doi:10.1007/s00285-003-0245-3 |
| [6] | Electronic Journal of Differential Equations 1998 (32) pp 1– (1998) |
| [7] | DOI: 10.1016/j.amc.2006.10.071 · Zbl 1113.92035 · doi:10.1016/j.amc.2006.10.071 |
| [8] | DOI: 10.1007/s002850050076 · Zbl 0876.92016 · doi:10.1007/s002850050076 |
| [9] | DOI: 10.1016/j.amc.2005.11.092 · Zbl 1096.92031 · doi:10.1016/j.amc.2005.11.092 |
| [10] | DOI: 10.1023/A:1016027113579 · Zbl 1035.49020 · doi:10.1023/A:1016027113579 |
| [11] | DOI: 10.1073/pnas.0510016103 · doi:10.1073/pnas.0510016103 |
| [12] | DOI: 10.1073/pnas.0711372105 · doi:10.1073/pnas.0711372105 |
| [13] | International Journal of Control, Automation and Systems 1 (3) pp 282– (2003) |
| [14] | DOI: 10.1134/S1064230706060050 · Zbl 1263.49032 · doi:10.1134/S1064230706060050 |
| [15] | DOI: 10.1109/TAC.2002.808494 · Zbl 1364.93838 · doi:10.1109/TAC.2002.808494 |
| [16] | DOI: 10.1016/j.mcm.2007.04.003 · Zbl 1134.92033 · doi:10.1016/j.mcm.2007.04.003 |
| [17] | DOI: 10.1016/j.jtbi.2005.05.004 · doi:10.1016/j.jtbi.2005.05.004 |
| [18] | Mathematics in Science and Engineering 162 (1982) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
