The dynamics of fractional order Hepatitis B virus model with asymptomatic carriers

Asymptomatic carriers play an important role in modelling infectious diseases. Asymptomatic infected people have no symptoms but can infect other people and spread the disease among other people. The laboratory confirmed that asymptomatic hepatitis B may infect individuals and may generate other infected cases. Due to this significant role of asymptomatic carriers, we are considering a new mathematical model for hepatitis B virus with asymptomatic carriers to study its dynamic analysis. First, we briefly discussed the formulation of the model, and then used the Caputo derivative to generalize the model. Using the definition of fractional stability analysis, we study the results of the model, and show that the model is locally asymptotically stable for disease-free cases when R-0 < 1. We also give the result so that the model is globally asymptotically stable when R-0 < 1. The endemic equilibrium of the model is obtained when R-0 >1, which demonstrates the existence of a unique endemic equilibrium. Additionally, we use a new numerical scheme that is introduced for fractional differential equations to get numerical results. We use a number of fractional order values and present the graphical results of the model. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.

Automated summary

Asymptomatic carriers play a significant role in modeling infectious diseases and can impact disease transmission. A new mathematical model for hepatitis B virus with asymptomatic carriers was proposed, incorporating fractional differential equations for dynamic analysis. The model's results indicate local and global asymptotic stability, with an endemic equilibrium observed at a specific threshold value. Additionally, a new numerical scheme was utilized to obtain numerical results for various fractional order values.