Stability Analysis of an SVLI Epidemic Model
Immunization with the Bacillus Calmette-Guérin \(\left(BCG \right)\) vaccine is currently used in many parts of the world as a means of preventing tuberculosis even though it remains a highly controversial method of preventing tuberculosis disease. We develop a deterministic mathematical model for the transmission dynamics of tuberculosis to monitor the effect of BCG vaccine, which may wane over time and which is not 100 % effective, on tuberculosis epidemiology. The analysis of the presented model has provided conditions to guarantee the eradication of the disease in terms of three major parameters incorporated into the model; the vaccination coverage level, the waning rate and the efficacy of the vaccine.
KeywordsBacillus Calmette-Guérin (BCG) vaccine Deterministic model Equilibria Reproduction number Stability Tuberculosis
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