Epidemic spread and bifurcation effects in two-dimensional network models with viral dynamics.

Abstract

We extend a previous network model of viral dynamics to include host populations distributed in two space dimensions. The basic dynamical equations for the individual viral and immune effector densities within a host are bilinear with a natural threshold condition. In the general model, transmission between individuals is governed by three factors: a saturating function g( small middle dot) describing emission as a function of originating host virion level; a four-dimensional array B that determines transmission from each individual to every other individual; and a nonlinear function F, which describes the absorption of virions by a host for a given net arrival rate. A summary of the properties of the viral-effector dynamical system in a single host is given. In the numerical network studies, individuals are placed at the mesh points of a uniform rectangular grid and are connected with an m(2)xn(2) four-dimensional array with terms that decay exponentially with distance between hosts; g is linear and F has