Travelling waves of a nonlinear reaction-diffusion model of the hepatitis B virus

A mathematical model of viral hepatitis B that takes into account healthy cells, infected cells and free viruses is studied in this paper. This model takes into account spatial mobility of all the three populations group mentioned and also drug treatment, the Rough-Hurwitz criteria are used to determine the stability conditions of this model. The traveling wave solutions are obtained by the exp( - Φ ( ξ ) ) - expansion method in order to better appreciate the mechanism of infection by the hepatitis B virus and we obtain the bright, dark type profiles and show the effects of drug treatment on the amplitude of the solutions which, allows us to give more information on the treatment and control of the disease, we found that an increase in the dose of drug treatment promotes the development of healthy cells but that this increase significantly reduces the density of the viral population. Numerical simulations are carried out to verify the analytical predictions.