Numerical and bifurcation analysis of spatio-temporal delay epidemic model

Abstract

HIV/AIDS is a distressing and incurable disease of the human beings. In this article, we have proposed a numerical structure for the HIV/AIDS compartmental model with diffusion and delay process. The proposed scheme has the proficiency to preserve the positivity of the state variables. Also, the proposed scheme leads to the consistency and stability. Two equilibrium states of the model have been described. Moreover, the stability of the scheme is examined at these two states. The contribution of the basic reproductive number R0, in stability analysis is also investigated. The bifurcation value of the infection parameter γ, for different situations of τ is also investigated. Graphical solutions with the aid of computer simulations are presented to clarify the paramount features of the proposed numerical design.