Eigenvalue method for the solution of multi-compartment model of HIV-AIDS transmission

Abstract

The aim of this study is to formulate a multi-compartment mathematical model regarding the transmission and dynamics of HIVAIDS. The model is formulated on the basis of a system of linear, ordinary differential equations and admits two locally and globally stable equilibria. Primarily, the existence and uniqueness of solution of the model are demonstrated which is then obtained analytically using the fundamental matrix method and eigenvalue approach. The obtained solution serves as the pedestal for studying the dynamics and spread of HIV-AIDS in general. Nevertheless, as an endorsement to the obtained results the simulations are also carried out with model outcomes being contrasted to the exact data of the disease in India.