Global dynamics of delayed HCV/HBV co-infection model with antibody immunity

Hepatitis B virus (HBV) and hepatitis C virus (HCV) infect liver cells (hepatocytes) and are responsible for most cases of chronic liver disease. HCV/HBV co-infected patients have a greater risk of severe liver disease, cirrhosis and liver cancer than mono-infected patients. In this paper, we develop a within-host HCV/HBV co-infection model with distributed delays and antibody immunity. The model involves nine delay differential equations (DDEs) that reflect the interactions between uninfected cells, latent HCV-infected cells, active HCV-infected cells, latent HBV-infected cells, active HBV-infected cells, free HCV particles, free HBV particles, HCV-specific antibodies, and HBV-specific antibodies. We test the nonnegativity and boundedness of the solutions. We compute all steady states and affirm the global stability. We confirm the results through numerical simulations. We found that time delays decrease the basic reproduction numbers leading to the stability of uninfected steady state. Also, fewer treatment efficacies will be required when employing a model with time delays. Moreover, increasing the stimulation rate of antibody immunity increases the densities of uninfected cells during co-infection.