Assessing the effects of vaccination on the dynamics of Tuberculosis
Marcio Rodrigues Sabino1, Hyun Mo Yang2 and Silvia Martorano Raimundo3
1,2
3
Universidade de Campinas, DMA, IMECC, Campinas, SP, Brazil,
[email protected]
[email protected]
Universidade de São Paulo, Faculdade de Medicina, DIM, São Paulo, SP, Brazil,
[email protected]
Keywords: Epidemic Model; Mathematical epidemiology; Tuberculosis; Infectious disease; DNA Vaccine.
This work proposes a mathematical model of the dynamics of the Tuberculosis (TB) to
investigate the use of some DNA vaccination (Genetic Vaccine) and usual chemotherapy
treatment as strategy for controlling the spread of the disease. The model is described by
nonlinear ordinary differential equations with seven subpopulations: susceptible individuals,
three subpopulations of latent individuals, infectious individuals, treated individuals with DNA
vaccine and vaccinated individuals with DNA and BCG vaccine. We present the analysis of the
trivial and the endemic equilibrium points using the Lyapunov functions to guarantee the global
stability of these points. Different situations for the dynamics of the model are determined by the
value of the reproductive rate Rvac. Estimations of the parameters were performed to determine
the recruitment rate for the period between 1980 and 2007 in Brazil.