A competitive numerical method for a chemotherapy model of two HIV subtypes

摘要

A competitive Gauss–Seidel-type finite-difference method is developed for the solution of a non-linear deterministic model associated with the transmission dynamics of two HIV subtypes in the presence of antiretroviral therapy. The model suggests the optimal level of drug therapy coverage necessary to eradicate the disease in a given population. Unlike the standard fourth-order Runge–Kutta method (RK4), which fails when certain parameter values and time-steps are used in the discretization of the model, the new implicit finite-difference method to be developed gives stable convergent numerical results for any time-step.