Modeling and Stability Analysis of SEIRS Model for Understanding the Tuberculosis Disease Dynamics

What is it about?

We study an SEIRS epidemiological model for the infectious disease Tuberculosis using differential equations. The entry of an infectious individual into a susceptible population leads to the spread of infection. There are chances of getting infected even after recovery, which has been taken into consideration. When the infection will establish itself or diminish is researched and validated by stability of equilibrium. The factor which gives the conclusion of equilibrium is the Basic Reproduction Number R_0. If R_0<1 then infection dies out and if R_0>1, the infection would establish itself.

Featured Image

Why is it important?

Tuberculosis, generally known as TB is a bacterial infectious disease caused by the bacteria named Mycobacterium Tuberculosis which was discovered by Dr. Robert Koch on March 24, 1882. Tuberculosis is transmitted if the infected person sneezes or coughs. TB affects the lungs majorly and then kidney, brain and spine also. The very dangerous part is the symptoms of TB are not many times visible. According to WHO, in India only, every year more than 1 Million cases of TB are being reported and more than 10 Million in all over the world.By considering the case of re infection we have studied SEIRS model using differential equations. The model can be validated by asymptotic stability of disease free equilibrium as well as the endemic equilibrium.