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

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