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# Modeling of HIV/AIDS Transmission and Its Analysis

Author: XuYing
Tutor: XuGenQi
School: Tianjin University
Course: Operational Research and Cybernetics
Keywords: Vertical infection Therapeutic vaccine Age of infection Age of onset C0 semigroup Posedness
CLC: R311
Type: Master's thesis
Year: 2007
Downloads: 145
Quote: 0
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### Abstract

 AIDS as the history of modern medicine 's most interesting and most fear an epidemic , and shocked the world with its rapid spread of potential disease ferocious , can not be treated as well as extremely serious harm , therefore , an urgent task facing humanity from popular epidemiology, virology, immunology, and social psychology careful study of AIDS , to improve the treatment level and propose defensive measures . Analysis and mathematical modeling to study the spread of the disease law , the mode of transmission of AIDS is the theoretical basis of the prediction and control of AIDS . This paper is in the past on the basis of HIV / AIDS model , establish a dynamic of HIV / AIDS model , this paper established model containing ordinary differential equations and partial differential equations coupled equations to describe equations , differential and integral the coupling of the equation . AIDS patient characteristics , from epidemiology, virology, immunology, social psychology angle analysis more comprehensive consideration of the different development stages of HIV / AIDS , vertical infection , AIDS patients with infectious , AIDS patients hope restored to the incubation period of these and many other factors , to make up for the early stage of the model ignored vertical infection , AIDS patients with infectious as well as AIDS patients may be restored to the incubation period of the lack of these three factors . In addition, this article introduced in the incubation period of the infection age ; introduced the onset of the period , the age of onset , HIV / AIDS in the incubation period , the incidence of the development process described by partial differential equations . Employing the derived equations , we directly introduced : the AIDS cause an increase in mortality , the total population of the community attenuation . To a clearer understanding of the impact of AIDS on the socio-demographic , in the case of the birth rate equal to the natural mortality , considering the evolution of linear equations , using the method of functional analysis and bounded linear operator semigroup theoretical analysis system posedness of the problem , and prove that there is a positive solution of the system equations . This article is from the dynamic point of view to study the spread of AIDS , and the impact on human health , this research and analysis method is general and can be extended to other systems modeling and analysis , both on the theoretical and practical application have significance.

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