Global dynamics of cell mediated immunity in viral infection models with distributed delays

In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in \textit{vivo}. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection $R_{0}$ and for CTL response $R_{1}$ such that $R_{1}<R_{0}$. It is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of Lyapunov functional. More specifically, the uninfected equilibrium is globally asymptotically stable if $R_{0}\leq1$, an infected equilibrium without immune response is globally asymptotically stable if $R_{1}\leq1<R_{0}$ and an infected equilibrium with immune response is globally asymptotically stable if $R_{1}>1$. The immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if $R_{1}>1$.Comment: 16 pages, accepted by Journal of Mathematical Analysis and Application

Global stability of an SIS epidemic model with a finite infectious period

Assuming a general distribution for the sojourn time in the in- fectious class, we consider an SIS type epidemic model formulated as a scalar integral equation. We prove that the endemic equilibrium of the model is globally asymptotically stable whenever it exists, solving the conjecture of Hethcote and van den Driessche (1995) for the case of nonfatal diseases

Note on stability conditions for structured population dynamics models

We consider a characteristic equation to analyze asymptotic stability of a scalar renewal equation, motivated by structured population dynamics models. The characteristic equation is given by $$1=\int_{0}^{\infty}k(a)e^{-\lambda a}da,$$ where $k:\mathbb{R}_{+}\to\mathbb{R}$ can be decomposed into positive and negative parts. It is shown that if delayed negative feedback is characterized by a convex function, then all roots of the characteristic equation locate in the left half complex plane

Japanese Competitiveness in Liquid Crystal Display Industry - Analysis of Causes of its Decline, and Proposal of "Core National Management" (Japanese)

The liquid crystal display (LCD) is an original technology that was essentially researched and developed by Japan. Therefore, Japan took the leadership and created and nurtured the LCD industry. However, South Korea and Taiwan also entered the market and in recent years both have overtaken Japan. But why has the decline of Japanese competitiveness happened? There has been a decline in competitiveness not only in the LCD industry but also in semiconductors and many other industries. In order to clarify the causes of the decline, I analyze it from the viewpoint of architecture and knowledge management. The LCD industry uses larger glass substrates than other companies in order to produce larger LCD panels than other companies, and so it does not have the standardized sizes of the glass substrate and the standardized equipments, and has "integral architecture." In consequence, based on the case study of Sharp's Kameyama plant, it could be concluded that the origin of Japan's competitiveness arises from the "integration of tacit knowledge" in a closed innovation network. On the other hand, the products driving the LCD industry have in recent years changed from personal computers to LCD televisions. Sony, which does not have its own displays, has established a joint venture company with South Korea's Samsung Electronics, and conducts metanational management. In contrast, Sharp has a very large share of the Japanese LCD-TV market, but a small share globally. Then, Sharp bases the core of producing LCD panels in Japan, endeavors to maximize its enterprise value by assembling LCD televisions at five worldwide bases, and also by promoting OEM production of LCD panels. In this research, for strengthening Japan's competitiveness I propose "core national management." This includes three processes of integrating, which creates core knowledge locally through the integration of tacit knowledge; maximizing, which maximizes enterprise value on that basis; and allocating, which optimizes deployment of resources globally.

Convergence of a Logistic Type Ultradiscrete Model

We derive a piecewise linear difference equation from logistic equations with time delay by ultradiscretization. The logistic equation that we consider in this paper has been shown to be globally stable in the continuous and discrete time formulations. Here, we study if ultradiscretization preserves the global stability property, analyzing the asymptotic behaviour of the obtained piecewise linear difference equation. It is shown that our piecewise linear difference equation has a threshold property concerning global attractivity of equilibria, similar to the stable logistic equations with time delay