Effect of antibodies and latently infected cells on HIV dynamics with differential drug efficacy in cocirculating target cells

In this paper, we investigate the qualitative behaviors of three viral infection models with two types of cocirculating target cells. The models take into account both antibodies and latently infected cells. The incidence rate is represented by bilinear, saturation and general function. For the first two models, we have derived two threshold parameters, R0 and R1 which completely determined the global properties of the models. Lyapunov functions are constructed and LaSalle's invariance principle is applied to prove the global asymptotic stability of all equilibria of the models. For the third model, we have established a set of conditions on the general incidence rate function which are sufficient for the global stability of the equilibria of the model. Theoretical results have been checked by numerical simulations.The Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah.http://link.springer.com/journal/108192018-06-30hb2017Electrical, Electronic and Computer Engineerin

Global co-dynamics of viral infections with saturated incidence

Several mathematical models of two competing viruses (or viral strains) that have been published in the literature assume that the infection rate is determined by bilinear incidence. These models do not show co-existence equilibrium; moreover, they might not be applicable in situations where the virus concentration is high. In this paper, we developed a mathematical model for the co-dynamics of two competing viruses with saturated incidence. The model included the latently infected cells and three types of time delays: discrete (or distributed): (ⅰ) The formation time of latently infected cells; (ⅱ) The activation time of latently infected cells; (ⅲ) The maturation time of newly released virions. We established the mathematical well-posedness and biological acceptability of the model by examining the boundedness and nonnegativity of the solutions. Four equilibrium points were identified, and their stability was examined. Through the application of Lyapunov's approach and LaSalle's invariance principle, we demonstrated the global stability of equilibria. The impact of saturation incidence, latently infected cells, and time delay on the viral co-dynamics was examined. We demonstrated that the saturation could result in persistent viral coinfections. We established conditions under which these types of viruses could coexist. The coexistence conditions were formulated in terms of saturation constants. These findings offered new perspectives on the circumstances under which coexisting viruses (or strains) could live in stable viral populations. It was shown that adding the class of latently infected cells and time delay to the coinfection model reduced the basic reproduction number for each virus type. Therefore, fewer treatment efficacies would be needed to keep the system at the infection-free equilibrium and remove the viral coinfection from the body when utilizing a model with latently infected cells and time delay. To demonstrate the associated mathematical outcomes, numerical simulations were conducted for the model with discrete delays

The Kirchhoff Index of Hypercubes and Related Complex Networks

The resistance distance between any two vertices of G is defined as the network effective resistance between them if each edge of G is replaced by a unit resistor. The Kirchhoff index Kf(G) is the sum of resistance distances between all the pairs of vertices in G. We firstly provided an exact formula for the Kirchhoff index of the hypercubes networks Qn by utilizing spectral graph theory. Moreover, we obtained the relationship of Kirchhoff index between hypercubes networks Qn and its three variant networks l(Qn), s(Qn), t(Qn) by deducing the characteristic polynomial of the Laplacian matrix related networks. Finally, the special formulae for the Kirchhoff indexes of l(Qn), s(Qn), and t(Qn) were proposed, respectively

A dual-loop model predictive voltage control/sliding-mode current control for voltage source inverter operation in smart microgrids

The design of a robust controller for the voltage source inverter is essential for reliable operation of distributed energy resources in future smart microgrids. The design problem is challenging in the case of autonomous operation subsequent to an islanding situation. In this article, a dual-loop controller is proposed for voltage source inverter control. The outer loop is designed for microgrid voltage and frequency regulation based on the model predictive control strategy. This outer loop generates reference inverter currents for the inner loop. The inner loop is designed using a sliding-mode control strategy, and it generates the pulse-width modulation voltage commands to regulate the inverter currents. A standard space vector algorithm is used to realize the pulse-width modulation voltage commands. Performance evaluation of the proposed controller is carried out for different loading scenarios. It is shown that the proposed dual-loop controller provides the specified performance characteristics of an islanded microgrid with different loading conditions.http://www.tandfonline.com/loi/uemp20hb201

Synchronization of Switched Interval Networks and Applications to Chaotic Neural Networks

This paper investigates synchronization problem of switched delay networks with interval parameters uncertainty, based on the theories of the switched systems and drive-response technique, a mathematical model of the switched interval drive-response error system is established. Without constructing Lyapunov-Krasovskii functions, introducing matrix measure method for the first time to switched time-varying delay networks, combining Halanay inequality technique, synchronization criteria are derived for switched interval networks under the arbitrary switching rule, which are easy to verify in practice. Moreover, as an application, the proposed scheme is then applied to chaotic neural networks. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical results

A Dual-loop Model Predictive Voltage Control/Sliding-mode Current Control for Voltage Source Inverter Operation in Smart Microgrids

The design of a robust controller for the voltage source inverter is essential for reliable operation of distributed energy resources in future smart microgrids. The design problem is challenging in the case of autonomous operation subsequent to an islanding situation. In this article, a dual-loop controller is proposed for voltage source inverter control. The outer loop is designed for microgrid voltage and frequency regulation based on the model predictive control strategy. This outer loop generates reference inverter currents for the inner loop. The inner loop is designed using a sliding-mode control strategy, and it generates the pulse-width modulation voltage commands to regulate the inverter currents. A standard space vector algorithm is used to realize the pulse-width modulation voltage commands. Performance evaluation of the proposed controller is carried out for different loading scenarios. It is shown that the proposed dual-loop controller provides the specified performance characteristics of an islanded microgrid with different loading conditions.http://www.tandfonline.com/loi/uemp20hb201