Dynamic modeling of viral infections in spherical organs

A general mathematical model of viral infections inside a spherical organ is presented. Transported quantities are used to represent external cells or viral particles that penetrate the organ surface to either promote or combat the infection. A diffusion mechanism is considered for the migration of transported quantities to the inner tissue of the organ. Cases that include the generation of latent infected cells and the delivery of anti-viral treatment are analyzed. Different anti-viral mechanisms are modeled in the context of spatial variation. Equilibrium conditions are also calculated to determine the radial profile after the infection progresses and therapy is delivered for a long period of time. The dynamic and equilibrium solutions obtained in this paper provide insight into the temporal and spatial evolution of viral infection for optimal therapies.