Global Stability and Numerical Analysis of a Compartmental Model of the Transmission of the Hepatitis A Virus (HAV): A Case Study in Tunisia

This paper deals with the transmission and spread of the hepatitis A virus in central west Tunisia (the city of Thala). The target of this framework is to determine the global stability of a SEIRD epidemiological model where the infectious compartment is split into symptomatic and asymptomatic compartments. We study the global stability of the equilibrium state using the Lyapunov function which depends on the value of the basic reproduction number R_0 . Therefore, we prove that when R_0<1 , the disease-free equilibrium (DFE) is globally stable, but when R_0>1 , the DFE is unstable, and therefore the the endemic equilibrium is globally stable.