Forward Bifurcation and Stability Analysis

Abstract

Bifurcation is an indispensable tool to describe the behavior of the system at steady states. Recently, the forward bifurcation showed the existence of both local and global stability of equilibrium points obtained from epidemiological models. It is known that the computing process to show the global stability of endemic equilibrium is tricky. But, in this chapter, we incorporate the principles that support the simplification of computation and give the exact existence of global stability of endemic equilibrium point. The most important issue is the application of forward bifurcation diagram obtained from endemic equilibrium and basic reproduction number. For illustration purposes, the mathematical modeling of HBV transmission dynamics is built in this study. The generated HBV model’s well-posedness is confirmed, and the equilibrium points are determined. Additionally, a next-generation matrix approach is used to calculate the basic reproduction number from infected compartments, and numerical simulations are used to demonstrate the occurrence of forward bifurcation at R0=1. If R0<1, the disease-free equilibrium point is both locally and globally asymptotically stable, and if R0>1, the endemic equilibrium is both locally and globally asymptotically stable. The MATLAB platform is used to facilitate numerical simulation.