Some non-local diffussion processesmay be described by an integral operator such as ∫ 𝐾(𝑥, 𝑦)(𝑢(𝑦) − 𝑢(𝑥))𝑑𝑦. In the compartmental models in epidemilogy, the diffusion terms may be replaced by an integral term, similar to above, to describe the dispersion of population. Classical numerical approximations, like finite element methods or finite difference methods, lead to systems of equations with dense matrices. Wavelets are a kind of functions which have some properties that make them a very useful tool for discretizing the convolution operators getting sparse matrices, thus saving computing time and storage memory.