Analysis of a fractional-order model for acute and chronic hepatitis-B transmission with Mittag-Leffler kernels

Abstract

This study explores the dynamic characteristics of a fractional-order model for the hepatitis B virus (HBV) epidemic. We present the existence, uniqueness, and Ulam-Hyers stability of solutions for a fractional-order HBV model utilizing the Atangana-Baleanu-Caputo fractional operator with Mittag-Leffler kernels. For the fractional numerical simulations, we employ the Adams-Moulton numerical scheme. The results from the numerical solutions indicate that the parameter χ\chi (order of derivative) plays a crucial role, highlighting the importance of the two infection stages (acute and chronic) within the model. We observed the relationship between the basic reproduction number, the HBV transmission rate, the birth-rate, and the acutely infected individuals to the chronic stage.

Keywords

• stability analysis
• fractional order
• acute infection
• chronic infection
• mittag-leffler kernel
• 34d23
• 37n25
• 92-10