Related papers: Stability and Optimal Control of a Delayed HIV Mod…
Mathematical modeling of biological systems is crucial to effectively and efficiently developing treatments for medical conditions that plague humanity. Often, systems of ordinary differential equations are a traditional tool used to…
We model the interaction between the immune system and tumor cells including a time delay to simulate the time needed by the latter to develop a chemical and cell mediated response to the presence of the tumor. The results are compared with…
This paper investigates the effect of drug treatment on the standard within-host HIV model, assuming that therapy occurs periodically. It is shown that eradication is possible under these periodic regimes, and we quantitatively characterize…
An increasing number of control techniques are introduced to HIV infection problem to explore the options of helping clinical testing, optimizing drug treatments and to study the drug resistance situations. In such cases, complete/accurate…
In this paper, we consider the impact of time delay by media on the control of the disease. We set up a class of SISM epidemic model with the time delay and the cumulative density of awareness caused by media. The sufficient condition of…
In this paper, we propose a delayed cytokine-enhanced viral infection model incorporating saturation incidence and immune response. We compute the basic reproduction numbers and introduce a convex cone to discuss the impact of non-negative…
A ternary reaction-diffusion model for early HIV infection dynamics, incorporating logistic growth of target cells, is introduced. According to in vitro and in vivo studies, random movement of target cells, infected cells, and virions and a…
We consider a class of monotone systems in which the control signal multiplies the state. Among other applications, such bilinear systems can be used to model the evolutionary dynamics of HIV in the presence of combination drug therapy. For…
An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and…
In the framework of homogeneous susceptible-infected-recovered (SIR) models, we use a control theory approach to identify optimal pandemic mitigation strategies. We derive rather general conditions for reaching herd immunity while…
The origin of the unusual incubation period distribution in the development of AIDS is largely unresolved. A key factor in understanding the observed distribution of latency periods, as well as the occurrence of infected individuals not…
In this article, the feasibility of using optimal control theory will be studied to develop control theoretic methods for personalized treatment of HCV patients. The mathematical model for HCV progression includes compartments for healthy…
We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The…
We propose a mathematical spatiotemporal epidemic SICA model with a control strategy. The spatial behavior is modeled by adding a diffusion term with the Laplace operator, which is justified and interpreted both mathematically and…
We investigate feedback control of linear quantum systems subject to feedback-loop time delays. In particular, we examine the relation between the potentially achievable control performance and the time delays, and provide theoretical…
We consider a Human Immunodeficiency Virus (HIV) model with a logistic growth term and continue the analysis of the previous article [6]. We now take the viral diffusion in a two-dimensional environment. The model consists of two ODEs for…
We analyze the stabilization of unstable steady states by delayed feedback control with a periodic time-varying delay in the regime of a high-frequency modulation of the delay. The average effect of the delayed feedback term in the control…
We study optimal proportional feedback controllers for spatially invariant systems when the controller has access to delayed state measurements received from different spatial locations. We analyze how delays affect the spatial locality of…
We study the stability of unstable steady states in scalar retarded time-delayed systems subjected to a variable-delay feedback control. The important aspect of such a control problem is that time-delayed systems are already…
Competition within the immune system may degrade immune control of viral infections. We formalize the evolution that occurs in both HIV-1 and the immune system quasispecies. Inclusion of competition in the immune system leads to a novel…