Kinetics of Infection-Driven Growth Model with Birth and Death

We propose a two-species infection model, in which an infected aggregate can gain one monomer from a healthy one due to infection when they meet together. Moreover, both the healthy and infected aggregates may lose one monomer because of self-death, but a healthy aggregate can spontaneously yield a new monomer. Consider a simple system in which the birth/death rates are directly proportional to the aggregate size, namely, the birth and death rates of the healthy aggregate of size k are J₁k and J₂k while the self-death rate of the infected aggregate of size k is J₃k. We then investigate the kinetics of such a system by means of rate equation approach. For the J₁>J₂ case, the aggregate size distribution of either species approaches the generalized scaling form and the typical size of either species increases wavily at large times. For the J₁=J₂ case, the size distribution of healthy aggregates approaches the generalized scaling form while that of infected aggregates satisfies the modified scaling form. For the J₁<J₂ case, the size distribution of healthy aggregates satisfies the modified scaling form, but that of infected aggregates does not scale.