Liapunov functions applied to biomathematic model of dynamic system for tuberculosis

According to the Centers for Disease Control and Prevention (CDC) in 2008, nearly one-third of the world´s population is infected with Tuberculosis (TB), which kills almost 1.6 million people per year. TB is now the second most common cause of death from infectious disease in the world after human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS). Tuberculosis is a leading cause of infectious mortality. Although anti-biotic treatment is available and there is vaccine, tuberculosis levels are rising in many areas of the world. Mathematical models have been used to study tuberculosis in the past and have influenced policy; the spread of HIV and the emergence of drug-resistant TB strains motivate the use of mathematical models today. The Biomathmetics has become the main important trend of research dirction which has applied to the epidemic models of disease mechanism, spreading regulation, and stategy of disease preventing in the field of medical and public health. Here we review and compare the mathematical models of tuberculosis dynamics in the literature and apply Liapunov stability function V(x) to construct a dynamic mathematics models for tuberculosis and to meet the above-mentioned TB disease mechanism, spreading regulation, and stategy of disease preventing in the medical field.