Homotopy Perturbation Method for Pneumonia–HIV Co-Infection

It is well known that HIV (human immunodeficiency virus) weakens the immune system of individuals, resulting in risk of other infections, such as pneumonia. The most frequent viral pneumonia seen in individuals infected with HIV is cytomegalovirus (CMV). In this paper, pneumonia–HIV co-infection is modeled through the formulation of a mathematical compartmental model consisting of nine compartments. Some of the basic properties of the model are established, such as the positivity, boundedness of the system, equilibrium points, and computation of the basic reproduction number. After obtaining the solution, the homotopy perturbation method (HPM) is applied, as it is known for its convergence properties. It is observed that the HPM gives an accurate analytical solution that indicates various important factors that are responsible for the spread of cytomegalovirus pneumonia in HIV-infected populations, and this is justified through a plot made by using MATLAB 2020a.