The numerical solution of epidemic models on moving domains using combined masses

The application of a moving mesh finite difference method, based on mass conservation, is described for epidemic models, integrating cross- and self-diffusion to represent social distancing and self-isolation. A significant feature of the models is the moving boundary which describes the spread of the disease in the domain. Numerical illustrations emphasise the influence of social interactions on transmission and infection rates. Notably, simulations show containment of disease spread within a small initial infected radius despite a high reproductive parameter. The results affirm the efficacy of the moving mesh approach for multi-population systems in epidemic models.