The disease COVID-19 is caused by the acute severe respiratory syndrome coronavirus 2 (SARS-CoV-2) and first diagnosed in Wuhan China, has whipped the entire world in its grip and threatened the mankind to the biggest ever extent. A within-host reaction-diffusion mathematical model describing the dynamics of SARS-CoV-2 in cancer patients has been considered in this research paper. Numerical simulation techniques based on the cubic B-splines collocation are proposed to the approximate the solutions of reaction-diffusion model taken into the consideration. The reduced collocation forms of the partial differential equations in the model are first being solved by the method of lines by reducing to the systems of first order ordinary differential equations which in turn are solved by the two methods viz. first by the well-known Runge-Kutta method of order 4 and secondly by the hybrid block method. The simulated results obtained by the two techniques are being analyzed and compared. It is found that Runge-Kutta method exhibits stability problem. However, hybrid block method produces good results but takes more computation time. The computed results are depicted for four different cases.