Dynamical behaviorism of hepatitis B epidemic model with crowley-martin perspective
Abstract
Hepatitis B Virus (HBV) poses a significant global health threat due to its ability to cause chronic liver inflammation, leading to severe complications such as cirrhosis and liver cancer. This study presents a novel epidemic model of Hepatitis B virus that integrates a constant vaccination strategy alongside the Crowley-Martin perspective. In this study, we investigate the dynamic properties of a hepatitis B epidemic model, focusing on key metrics such as the basic reproduction number (RN), which indicates the average number of secondary infections produced by one infected individual in a fully susceptible population. We analyze stability characteristics to determine how the system behaves over time, ensuring that populations remain bounded and non-negative. Using the Bendixson theorem, we confirm that the disease-free equilibrium point is globally asymptotically stable, meaning that if the system starts without the disease, it will remain disease-free over time. Our analysis also reveals a transcritical bifurcation at RN = 1, indicating a critical threshold where the dynamics of the system change; below this threshold, the disease cannot sustain itself, while above it, the disease can persist. For RN > 1, we establish the globally asymptotic stability of the endemic equilibrium point, where the disease persists in the population, using Dulac’s criteria. To validate our theoretical findings, we
employ numerical simulations using the Non-Standard Finite Difference (NSFD) scheme. The phase
plane analysis at h = 0:1 demonstrates superior efficiency and high accuracy in establishing the global
asymptotic stability of E∗, outperforming traditional methods such as the Runge-Kutta (RK4) and Euler
methods.
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