Modelling and analysis of a within-host model of hepatitis B and D co-infections

Abstract

The Hepatitis delta virus (HDV) is a defect RNA virus that requires the presence of the hepatitis B virus (HBV) for cellular infection. A co-infection may result in a more severe acute disease and a higher risk of developing acute liver failure compared with those infected with HBV alone. At the present time, there has been very little to the modeling of HDV. The derivation and analysis of such a mathematical model poses difficulty as it requires the inclusion of (HBV). In this paper, a within-host model for the co-interaction of HDV and HBV is presented and rigorously analyzed. We calculate the basic reproduction number (Ro), the disease-free equilibrium, boundary equilibrium, which we define as the existence of one disease along with the complete eradication of the other disease, and the co-infection equilibrium. We determine stability criteria for the disease-free and boundary equilibrium. We also use the optimal control theory to assess the disease control. Numerical simulations have been presented to illustrate analytical results.

Keywords

• Hepatitis D, Hepatitis B, Immune system, Basic reproduction number, Optimal control.