The Mathematics of Infectious Diseases
SIAM Review
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According the World Health Organization, one third of the world's population is infected with tuberculosis (TB), leading to between two and three million deaths each 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 .In the recent year, 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. The papers will apply Lyapunov 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. The theory of Lyapunov stability function is a general rule and method to examine and determine the stability characteristics of a dynamic system. There are two functions of Lyapunov theory: (a)the Lyapunov indirect method which solves the dynamics differential equations of the constructing system then determines its stability properties, and (b)the Lyapunov direct method which determine the system stability directly via constructing a Lyapunov Energy Function V(x) of the dynamic mathematic model for tuberculosis. Here we will analyse the complex dynamic mathematic model of tuberculosis epidemic and determine its stability property by using the popular Matlab/Simulink software and relative software packages.