  We here propose to model active and cumulative cases data from COVID-19 by a
continuous effective model based on a modified diffusion equation under
Lifshitz scaling with a dynamic diffusion coefficient. The proposed model is
rich enough to capture different aspects of a complex virus diffusion as
humanity has been recently facing. The model being continuous it is bound to be
solved analytically and/or numerically. So, we investigate two possible models
where the diffusion coefficient associated with possible types of contamination
are captured by some specific profiles. The active cases curves here derived
were able to successfully describe the pandemic behavior of Germany and Spain.
Moreover, we also predict some scenarios for the evolution of COVID-19 in
Brazil. Furthermore, we depicted the cumulative cases curves of COVID-19,
reproducing the spreading of the pandemic between the cities of S\~ao Paulo and
S\~ao Jos\'e dos Campos, Brazil. The scenarios also unveil how the lockdown
measures can flatten the contamination curves. We can find the best profile of
the diffusion coefficient that better fit the real data of pandemic.
