[MS02] Communicable Disease Modelling & Simulation

[MS02-02] Nonlinear Dynamics and Bifurcation Analysis of Tuberculosis Models

*Prashant Kumar Srivastava¹ (1. Indian Institute of Technology Patna, INDIA (India))

Keywords:

Tuberculosis,Reinfection,Nonlinear Dynamics,Bifurcation

In this talk, we shall first discuss challenges of the mathematical modeling of Tuberculosis. In this context, we shall emphasize a few features of the disease, such as, exogenous reinfection, endogenous reactivation, limited medical resources or treatment and behavioral response of the populations, which needs attention and understanding to control the TB disease. We shall provide some mathematical models and their outcomes, underlining the rich and complex nonlinear dynamical behavior exhibited by them. In addition, we shall also consider various time delays in the model system. These factors show that the dynamical behavior of the TB disease is significantly impacted in their presence and nonlinear dynamical behaviors, such as, existence of multiple equilibria, bi-stability, multi-stability, Hopf- bifurcation and Hopf-hopf Bifurcation are observed. We shall also validate our model with available data and further explore them numerically.