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The asymptotical stability of a dynamic system uppercasewith structural damping

100%
Hou X.
International Journal of Applied Mathematics and Computer Science
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2003
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tom 13
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nr 2
131-138
EN
A dynamic system with structural damping described by partial differential equations is investigated. The system is first converted to an abstract evolution equation in an appropriate Hilbert space, and the spectral and semigroup properties of the system operator are discussed. Finally, the well-posedness and the asymptotical stability of the system are obtained by means of a semigroup of linear operators.
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Survival probabilities for HIV infected patients through semi-Markov processes

75%
Masala G., Cannas G., Micocci M.
Biometrical Letters
|
2014
|
tom 51
|
nr 1
13-36
EN
In this paper we apply a parametric semi-Markov process to model the dynamic evolution of HIV-1 infected patients. The seriousness of the infection is rendered by the CD4+ T-lymphocyte counts. For this purpose we introduce the main features of nonhomogeneous semi-Markov models. After determining the transition probabilities and the waiting time distributions in each state of the disease, we solve the evolution equations of the process in order to estimate the interval transition probabilities. These quantities appear to be of fundamental importance for clinical predictions. We also estimate the survival probabilities for HIV infected patients and compare them with respect to certain categories, such as gender, age group or type of antiretroviral therapy. Finally we attach a reward structure to the aforementioned semi-Markov processes in order to estimate clinical costs. For this purpose we generate random trajectories from the semi-Markov processes through Monte Carlo simulation. The proposed model is then applied to a large database provided by ISS (Istituto Superiore di Sanità, Rome, Italy), and all the quantities of interest are computed.
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