Replication of viruses in a growing plaque: a reaction-diffusion model.

An understanding of the viral replication process commonly referred to as "plaque growth" is developed in the context of a reaction-diffusion model. The interactions among three components: the virus, the healthy host, and the infected host are represented using rates of viral adsorption and desorption to the cell surface, replication and release by host lysis, and diffusion. The solution to the full model reveals a maximum in the dependence of the velocity of viral propagation on its equilibrium adsorption constant, suggesting that conditions can be chosen where viruses which adsorb poorly to their hosts will replicate faster in plaques than those which adsorb well. Analytic expressions for the propagation velocity as a function of the kinetic and diffusion parameters are presented for the limiting cases of equilibrated adsorption, slow adsorption, fast adsorption, and large virus yields. Hindered diffusion at high host concentrations must be included for quantitative agreement with experimental data.