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Updated: Jul 31, 2025

Humanized NOD/SCID/IL2rγnull (hu-NSG) Mouse Model for HIV Replication and Latency Studies
Published on: January 7, 2019
Sliding mode dynamics and optimal control for HIV model
Dan Shi1, Shuo Ma1, Qimin Zhang1,2
1School of Mathematics and Information Science, North Minzu University, Yinchuan 750021, China.
Abstract:
Considering the drug treatment strategy in both virus-to-cell and cell-to-cell transmissions, this paper presents an HIV model with Filippov control. Given the threshold level $ N_t $, when the total number of infected cells is less or greater than threshold level $ N_t $, the threshold dynamics of the model are studied by using the Routh-Hurwitz Criterion. When the total number of infected cells is equal to $ N_t $, the sliding mode equations are obtained by Utkin equivalent control method, and the dynamics are studied. In addition, the optimal control strategy is introduced for the case that the number of infected cells is greater than $ N_t $. By dynamic programming, the Hamilton-Jacobi-Bellman (HJB) equation is constructed, and the optimal control is obtained. Numerical simulations are presented to illustrate the validity of our results.
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