An SITR Analysis of Treatment Model of Hepatitis B Epidemic

This research article focuses on the formulation of a treatment model of hepatitis epidemic of type B. The dynamics of the model were studied and the local stability analyses of the equilibrium points of the model were investigated. Lyapunov functions were defined for the equilibrium points and their global stabilities were performed..........

Propagação de vírus informáticos baseada em modelos biológicos

A evolução digital proporcionou às sociedades uma facilidade extraordinária de comunicação. Com o número crescente de computadores e o aumento de acessos à internet, surgiu uma nova forma de criminologia, que cresceu em paralelo com o número de utilizadores. Desta forma, tornou-se comum a criação e difusão de vírus informáticos pelos chamados hackers. Neste trabalho estudam-se modelos de transmissão de vírus informáticos, usando modelos epidemiológicos. Começa-se por fazer uma revisão dos modelos existentes na literatura, de seguida sugerem-se alterações a esses modelos de forma a conseguir uma melhor aproximação à dinâmica real de transmissão de vírus informáticos. As simulações numéricas dos modelos permitem-nos inferir de que uma forma de controlar a transmissão de vírus informáticos é a diminuição da taxa de infeção, isto é, da taxa de transmissão do vírus. No último capítulo enumeram-se as conclusões do trabalho efetuado e indicam-se direções de trabalho futuro.The digital evolution in the last decades has provided extraordinary communications facilities. With the increasing number of computers and internet access, a new form of criminology has emerged, which grew in parallel with the number of users. In this way, it became common the creation and dissemination of computer viruses by the so-called hackers. This work studies models for computer viruses transmission, based on epidemiological models. We start by doing a review of the existing models in the literature, then suggest changes to these models, in order to get a better approximation to the real dynamics of transmission of computer viruses. The numerical simulations of the models allow us to infer that a way to control the transmission of computer viruses is to decrease the infection rate, i.e. the rate of transmission of the virus. In the last chapter, we list the findings of the work carried out and suggest directions of future work

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems