A major impact of viruses on humans is that they cause a variety of diseases including AIDS, flu, cancer, the common cold, and most recently, COVID-19. For many of the diseases, there are no vaccines or treatments. To develop the therapeutics, it is necessary to understand the growth of viruses in their native environment, host cells. The complexity of this environment adds difficulties to the comprehension of the viruses. Most research efforts focus on the molecular mechanisms behind the virus-host cell interactions and organ or the clinical level response of infected subjects, but relatively less attention has been paid to the middle of the spectrum, the spread of virus infection over multiple infection cycles, especially in a manner that is both dynamic and quantitative. To help mitigate the gap in our knowledge, we develop here experimental and computational methods to research the viral dynamics of two positive-strand RNA viruses within and beyond the single cycle.First, viral protein expression dynamics were measured utilizing a recombinant reporter strain of human rhinovirus A16 (RV-A16) infecting HeLa cells as an example. Rhinovirus is a positive-strand RNA virus, and its infection causes the common cold, which is frequent in both adults and children. No antiviral has been approved to treat rhinovirus infection, so researchers are interested in host factors involved in rhinovirus infection as potential therapeutic targets. In our study, infected cells were automatically imaged over time to detect the fluorescence level from the reporter virus, which is a measurement of viral protein expression. A set of parameters were defined to describe the timing and magnitude of the viral protein expression dynamics. The numbers of fluorescent positive cells detected in the same frames over differently treated cells depict the susceptibility under different conditions. Cells treated with a translation inhibitor had a lower susceptibility and those that were infected were slower in the timing of viral protein expression. Cells in different stages of the cell cycle were similarly susceptible to infection and displayed similar viral protein dynamics. Serum starvation reduced the susceptibility but did not change the viral protein expression in the first cycle of infection. However, for the second cycle, the infection in serum-starved cells was earlier. If the mechanisms behind the serum related phenomena can be identified, drugs to promote resistance to or slow the spread of rhinovirus might be discovered. The discovery of the phenomena would not be possible without the study of the multi-cycle dynamics of the rhinovirus with this reporter strain. The second example was the single-cycle and multi-cycle virus growth dynamics of another positive-strand RNA virus, the Zika virus. We are concerned about the Zika virus because its infection in pregnant women increases the risk of defects in newborns. Two strains of the Zika virus that belong to different lineages were used to infect the Vero cells respectively. Their infection dynamics not only characterize the distinction between the two lineages but also help identify optimization strategies for vaccine production. In single-cycle infections, the infection of African strain resulted in slower virus production till 20 hours post-infection (h.p.i.) but higher final virus titer. These agree with the viral protein expression measured by immunocytochemical staining and fluorescent microscopy that cells infected by the African strain had a lower fluorescent positive rate and a lower mean intensity at the early stage. For multi-cycle infections, both strains had similar dynamics, but the African strain had a higher titer. The African strain had a lower extracellular degradation rate in comparison to the Asian strain. Finally, the growth curves of the Zika virus were fitted by ordinary differential equation (ODE) models using three models of delay: fixed, exponential-distributed, and gamma-distributed. For single-cycle growth, the fixed delay model recapitulated the growth of both strains without contradicting cell death curves. The models did not perform ideally for multi-cycle growth. The fixed and exponential-distributed delay models worked the best for the African and the Asian strains, respectively. Sensitivity analysis revealed that changing the degradation of the virus has the largest effect on the titer, which is worth noticing in vaccine production. The models promote our comprehension of the growth kinetics of the Zika virus and can be applied to understand the effect of antivirals and optimize vaccine production processes. Overall, the methods here demonstrated the potential of image-based quantitative measurements and mathematical models in analyzing single-cycle and multi-cycle positive-strand RNA virus infection. This work also provides a basis for further quantitative studies of virus-host interaction at the tissue level.