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• Two numerical methods are developed for solving the fractional-order HIV-1 infection model of CD4 + T-cells. • Two method (Bessel matrix method and Bessel quasilinearization method) are based on the novel Bessel polynomials. • Error and convergence analysis are studied. • Numerical applications and comparisons show that methods are effective. • In the comparison of the two methods used, the Bessel-QLM method gives better results. In this paper, two numerical methods based on the novel Bessel polynomials are developed to solve the fractional-order HIV-1 infection model of CD 4 + T-cells considering the impact of antiviral drug treatment. In first of these methods, by using the Bessel polynomial and collocation points, we transform the HIV problem into a system of nonlinear algebraic equations. And this method, which is the method of direct solution is called as Bessel matrix method. The second method, which is called the Bessel-QLM method converts firstly HIV problem to a sequence of linear equations by using the technique of quasilinearization and then the reduced problem is solved by the direct Bessel matrix method. Error and convergence analysis are studied for the Bessel method. Finally, the applications are made on the numerical examples and also the numerical results are compared with the results of other available techniques. It is observed from applications that the presented results are better than the results of other existing methods and also the Bessel-QLM method is more efficient than the direct Bessel method. [ABSTRACT FROM AUTHOR]

Based on some important biological meanings, we propose a class of HIV infection models incorporating both classical cell-free virus diffusion and direct cell-to-cell transmission. According to recent studies, the direct cell-to-cell transfer of HIV is a significantly more efficient mode of retroviral dissemination. In the first part of our analysis, we show that our model possesses non-negative solutions. Then, we derive sufficient conditions for the asymptotic stability of equilibriums. The analytical solutions are verified by simulation results. At the end of the paper, some important conclusions are given. [ABSTRACT FROM AUTHOR]