Numerical Analysis For A Reaction-Diffusion Model In HIV Transmission

This paper is concerned with finite difference solutions of a reaction-diffusion model in the transmission of human immunodeficiency virus (HIV).The reaction-diffusion system is discretized by the finite difference method,and the investigation is devoted to the finite difference system for both the time-dependent problem and its corresponding steady-state problem. The existence (and uniqueness) of a nonnegative finite difference solution and threemonotone iterative algorithms for the computation of the solutions are given. The asymptotic behavior of the time-dependent solution in relation to the steady-state solution is discussed. It is shown that the time-dependent problem has a unique nonnegative solution, while the steady-state problem might have the different nonnegative solutions depending on the parameters in the problem. These different non-negative solutions can be computed from the monotone iterative algorithms by choosing the different initial iterations. The asymptotic behavior result leads to convergence of the time-dependent solution to a unique steady-state solution. Some numerical results are given to demonstrate the theoretical analysis results.