Estimating unreported cases of Covid-19 in a region or country presents a significant challenge, specially when they do not coincide with asymptomatic cases. This paper introduces a mathematical extension to deterministic models of total case growth, designed to describe the temporal evolution of unreported cases for each reported case of Covid-19. The proposed expression accounts for the growth of unreported cases in flat regions and their decline towards the end of an epidemic wave. We apply this extension to both a Gompertz growth model and a generalized Richards model, fitting these models to data from 30 countries/regions using Bayesian methods. The results show that fits from the extended models outperform those from the standalone Gompertz and generalized Richards models, as evidenced by superior values in the Bayesian Information Criterion (BIC) and R 2 metrics. In conclusion, the extended models offer a more accurate depiction of Covid-19 epidemic wave progression and provide short-term predictions of epidemic trends and criteria for identifying the end of an epidemic wave.