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| Author(s): |
Marcio Rodrigues Sabino
Total Authors: 1
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| Document type: | Master's Dissertation |
| Press: | Campinas, SP. |
| Institution: | Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica |
| Defense date: | 2011-05-17 |
| Examining board members: |
Hyun Mo Yang;
Sidineia Barrozo;
Saulo Duarte Passos
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| Advisor: | Silvia Martorano Raimundo; Hyun Mo Yang |
| Abstract | |
The interest in modeling the transmission dynamics of the Tuberculosis(TB) is mainly due to the fact that TB is a major public health problem worldwide. According to World Health Organisation, TB is the leading cause of mortality from infectious diseases, accounting for more than 2 million deaths each year (WHO, 2007). Another reason, very important to this study is the discovery of "genetic vaccines" (or "DNA vaccine") by the research group of the researcher Celio Lopes Silva, coordinator of the Laboratory of genetic vaccines of the Faculty of Medicine of Ribeirao Preto, USP. The vaccine, still under experimentation and standardization, is a great promise for combating infectious diseases for which today there is no safe prevention, such as TB. This work presents epidemiological studies of TB, the main characteristics of the action of the vaccine on the epidemiology of the disease and then, a mathematical model formulation to describe the dynamics of TB transmission by using the genetic vaccine as a strategy for disease control. The basic assumption of the model is that vaccination is adopted not only as protection for susceptible individuals, but also as a treatment for infected and infectious individuals. An analysis of the general model is presented, by determining the equilibrium points of the system and the conditions of stability of these points: analytically for the trivial equilibrium point, and numerically for the endemic equilibrium point. By simplifying the general model, it was also possible to show analytically the global stability of the trivial and nontrivial equilibrium points with Lyapunov functions. Were estimated parameters of the model, using the data describing the scenario of TB in Brazil between 1980 and 2007. Finally, with these settings, critical values of vaccination for disease control were determined (AU) | |
| FAPESP's process: | 07/06093-0 - Effect of the Vaccination and Treatment on the Dynamics of Transmission of Tuberculosis |
| Grantee: | Marcio Rodrigues Sabino |
| Support Opportunities: | Scholarships in Brazil - Master |