Spatial epidemic network models with viral dynamics

A mathematical model is presented for the spread of viral diseases within human or other populations in which both the dynamics of viral growth within individuals and the interactions between individuals are taken into account. We thus bridge the classical macroscopic approach to the growth and population dynamics of disease at the microscopic level. Each member, i, of the population of n individuals is represented by a vector function of time whose components are antibody numbers ai(t), and the virion level vi(t). These quantities evolve according to 2n differential equations, which are coupled via a transmission matrix B with element