We present an enhanced approach to solving the combined non-linear time-dependent Burgers-Fisher equation, which is widely used in mathematical biology and has a broad range of applications. Our proposed method employs a modified version of the finite element method, specifically the virtual element method, which is a robust numerical approach. We introduce a virtual process and an Euler-backward scheme for discretization in the spatial and time directions, respectively. Our numerical scheme achieves optimal error rates based on the degree of our virtual space, ensuring high accuracy. We evaluate the efficiency and flexibility of our approach by providing numerical results on both convex and non-convex polygonal meshes. Our findings indicate that the proposed method is a promising tool for solving non-linear time-dependent equations in mathematical biology
