Stabilization of HIV/AIDS model by receding horizon control

This work concerns the stabilization of uninfected steady state of an ordinary differential equation system modeling the interaction of the HIV virus and the immune system of the human body. The control variable is the drug dose, which, in turn, affects the rate of infection of CD4⁺ T cells by HIV virus. The feedback controller is constructed by a variant of the receding horizon control (RHC) method. Simulation results are discussed.     

Stability of a general adaptive immunity virus dynamics model with multistages of infected cells and two routes of infection

This paper studies an (n+4)-dimensional nonlinear virus dynamics model that characterizes the interactions of the viruses, susceptible host cells, n-stages of infected cells, B cells and cytotoxic T lymphocyte (CTL) cells. Both viral and cellular infections have been incorporated into the model. The infected-susceptible and virus-susceptible infection rates as well as the generation and removal rates of all compartments are described by general nonlinear functions. Five threshold parameters are computed, which insure the existence of the equilibria of the model under consideration. A set of conditions on the general functions has been established, which is sufficient to investigate the global dynamics of the model. The global asymptotic stability of all equilibria is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations of the model with specific forms of the general functions.     

Dynamics and control in an $$({\varvec{n}}+{\varvec{2}})$$ ( n + 2 ) -neuron BAM network with multiple delays

Nonlinear Dynamics - The issues of the stability and bifurcation for a delayed BAM network involving two neurons in the I-layer and arbitrary neurons in the J-layer are concerned in the present...     

HIV dynamics: Analysis and robust multirate MPC-based treatment schedules

Analysis and control of human immunodeficiency virus (HIV) infection have attracted the interests of mathematicians and control engineers during the recent years. Several mathematical models exist and adequately explain the interaction of the HIV infection and the immune system up to the stage of clinical latency, as well as viral suppression and immune system recovery after treatment therapy. However, none of these models can completely exhibit all that is observed clinically and account the full course of infection. Besides model inaccuracies that HIV models suffer from, some disturbances/uncertainties from different sources may arise in the modelling. In this paper we study the basic properties of a 6-dimensional HIV model that describes the interaction of HIV with two target cells, CD4⁺ T cells and macrophages. The disturbances are modelled in the HIV model as additive bounded disturbances. Highly Active AntiRetroviral Therapy (HAART) is used. The control input is defined to be dependent on the drug dose and drug efficiency. We developed treatment schedules for HIV infected patients by using robust multirate Model Predictive Control (MPC)-based method. The MPC is constructed on the basis of the approximate discrete-time model of the nominal model. We established a set of conditions, which guarantee that the multirate MPC practically stabilizes the exact discrete-time model with disturbances. The proposed method is applied to the stabilization of the uninfected steady state of the HIV model. The results of simulations show that, after initiation of HAART with a strong dosage, the viral load drops quickly and it can be kept under a suitable level with mild dosage of HAART. Moreover, the immune system is recovered with some fluctuations due to the presence of disturbances.     

Stability of general virus dynamics models with both cellular and viral infections and delays

We consider general virus dynamics model with virus‐to‐target and infected‐to‐target infections. The model is incorporated by intracellular discrete or distributed time delays. We assume that the virus‐target and infected‐target incidences, the production, and clearance rates of all compartments are modeled by general nonlinear functions that satisfy a set of reasonable conditions. The non‐negativity and boundedness of the solutions are studied. The existence and stability of the equilibria are determined by a threshold parameter. We use suitable Lyapunov functionals and apply LaSalle's invariance principle to prove the global asymptotic stability of the all equilibria of the model. We confirm the theoretical results by numerical simulations. Copyright © 2017 John Wiley & Sons, Ltd.     

Multirate sampling and input-to-state stable receding horizon control for nonlinear systems

In this paper, a robust receding horizon control for multirate sampled-data nonlinear systems with bounded disturbances is presented. The proposed receding horizon control is based on the solution of Bolza-type optimal control problems for the approximate discrete-time model of the nominal system. “Low measurement rate” is assumed. It is shown that the multistep receding horizon controller that stabilizes the nominal approximate discrete-time model also practically input-to-state stabilizes the exact discrete-time system with disturbances.     

Variable permeability effect on buoyancy-induced inclined boundary layer flow in a saturated porous medium with variable wall temperature

The analysis is carried out for buoyancy-induced boundary layer flow adjacent to an inclined heated surface in a saturated porous medium incorporating the variation of permeability and thermal conductivity due to paking particles with non-uniform temperature. The surface temperature is assumed to vary as a power function of the axial coordinate measured from the leading edge of the surface. Both the streamwise and normal component of the buoyancy force are retained in the momentum equations. Numerical solutions are obtained in the cases of uniform and nonuniform permeability and various values of the inclination parameter ξ (x) = (Ra _x cos ϕ)^1/3 tan ϕ by using finite difference method. The problem is solved using nonsimilarity solutions for the case of variable wall temperature. Results for the details of the velocity and temperature fields as well as local Nusselt number have been presented.     

Global properties of a class of virus infection models with multitarget cells

In this paper, we propose a class of virus infection models with multitarget cells and study their global properties. We first study three models with specific forms of incidence rate function, then study a model with a more general nonlinear incidence rate. The basic model is a (2n+1)-dimensional nonlinear ODEs that describes the population dynamics of the virus, n classes of uninfected target cells, and n classes of infected target cells. Model with exposed state and model with saturated infection rate are also studied. For these models, Lyapunov functions are constructed to establish the global asymptotic stability of the uninfected and infected steady states of these models. We have proven that if the basic reproduction number is less than unity then the uninfected steady state is globally asymptotically stable, and if the basic reproduction number is greater than unity then the infected steady state is globally asymptotically stable. For the model with general nonlinear incidence rate, we construct suitable Lyapunov functions and establish the sufficient conditions for the global stability of the uninfected and infected steady states of this model.     

Global stability of delay-distributed viral infection model with two modes of viral transmission and B-cell impairment

This paper formulates a virus dynamics model with impairment of B-cell functions. The model incorporates two modes of viral transmission: cell-free and cell-to-cell. The cell-free and cell-cell incidence rates are modeled by general functions. The model incorporates both, latently and actively, infected cells as well as three distributed time delays. Nonnegativity and boundedness properties of the solutions are proven to show the well-posedness of the model. The model admits two equilibria that are determined by the basic reproduction number R₀. The global stability of each equilibrium is proven by utilizing Lyapunov function and LaSalle's invariance principle. The theoretical results are illustrated by numerical simulations. The effect of impairment of B-cell functions and time delays on the virus dynamics are studied. We have shown that if the functions of B-cell is impaired, then the concentration of viruses is increased in the plasma. Moreover, we have observed that increasing the time delay will suppress the viral replication.