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A competitive numerical method for a chemotherapy model of two HIV subtypes. (English) Zbl 1016.92015

Summary: A competitive Gauss-Seidel-type finite-difference method is developed for the solution of a nonlinear 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.

MSC:

92C50 Medical applications (general)
65L12 Finite difference and finite volume methods for ordinary differential equations
65F10 Iterative numerical methods for linear systems
37N25 Dynamical systems in biology
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References:

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