Sliding mode dynamics and optimal control for HIV model

Abstract

<abstract><p>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.</p></abstract>

Stationary distribution and near‐optimal control of a stochastic reaction–diffusion HIV model

“…With the development of research, Zhong et al [9] and Sattentau [10] revealed that HIV‐infected cells can transfer the virus to a target cell through a special structure known as a virological synapse. Subsequently, several researchers have begun working on HIV models that incorporate virus‐to‐cell and cell‐to‐cell transmissions [11–14]. These models are primarily based on ordinary differential equations (ODEs).…”