Stochastic kinetics of reproduction of virions inside a cell

We analyze intracellular viral kinetics in the framework of the model incorporating viral genome replication, mRNA synthesis and degradation, protein synthesis and degradation, capsid assembly, and virion release from a cell. Due to the existence of the critical concentration of viral capsid proteins and other features of reproduction of virions inside a cell, the kinetics is demonstrated to exhibit three distinct initial stages. Specifically, (i) the exponential growth of the viral genome, mRNA and protein concentrations is followed by (ii) the transient stage to (iii) the steady-state regime. The formation of mature virions starts during the transient stage. Comparison of the kinetics, obtained by using the mass-action law and Monte Carlo (MC) technique, indicates that they are nearly identical during the initial exponential growth of the viral intermediates and also during the steady-state stage. The transition from the initial stage to the steady-state regime occurs however somewhat faster in the determenistic case even if the steady-state populations of virions and genomes are appreciable (e.g., about 250 and 500, respectively).