Theoretical study of diffusive model of HIV-1 infection and its analytical solution

T his article studied a mathematical model for the diffusive human immunodeficiency virus-type 1 (HIV-1) infection combining with stem cell therapy. The HIV-1 infection is a chronic disease and the viral replication continues if the patient stopes use the antiretroviral therapy (cART). Therefore, it is important to seek the cure of HIV-1 infection and some medical trials showed the cure by stem cell therapy and there are others failure to achieve the cure of HIV-1 with same treatments. The novelty of this paper is constructing a mathematical model with adding diffusion terms to study the effect of spread of virus and other cells in the body. Theoretical analysis such as boundedness, positivity, stability (local/global) of the HIV-1 model is presented. The model is solved analytically by the tanh expansion method. The results show that the tanh expansion method is a very useful technique, that can give a good prediction of the effect of stem cell therapy on infected cells on the spread of the virus. The results further demonstrated that the best way to control the disease is by limiting the spread of the virus; more so than the spread of other components.