Numerical simulation of the intracellular dynamics of HBV/Malaria co-infection with immune control and treatment

Abstract

In this paper, we proposed an intracellular mathematical model to describe the dynamics of the co-infection of hepatitis B virus (HBV) and malaria co-infection by taking into account the immune response and treatment. We established the wellposedness of the model by proving the existence, positivity and boundedness of solution of the problem. The basic reproduction number of HBV only model in the hepatocyte and malaria only model, both in the hepatocyte and erythrocyte were obtained, and when combined gives the basic reproduction number of the co-infection model. The local stability of the disease free equilibrium is obtained using characteristic equation. We showed condition under which the disease-free equilibrium with treatment effect exists and is asymptotically stable. Finally, we noticed from the numerical result that when the immune response is large, strong and faster and treatment is effective than the rate at which both infections replicate in the hepatocytes and erythrocytes, HBV only infected hepatocytes and malaria only infected hepatocytes and erythrocytes can be controlled with malaria resurfacing after some time as indicated by the oscillation in the malaria infected erythrocytes. There will be resistance in the co-infected hepatocytes and this may cause liver dysfunction.