This paper extends the Lee-Carter model for single- and multi-populations to account for pandemic jump effects of vanishing kind, allowing for a more comprehensive and accurate representation of mortality rates during a pandemic, characterised by a high impact at the beginning and gradually vanishing effects over subsequent periods. While the Lee-Carter model is effective in capturing mortality trends, it may not always be able to account for large, unexpected jumps in mortality rates caused by pandemics or wars. Existing models allow either for transient jumps with an effect of one period only or persistent jumps. However, there is no literature on estimating mortality time series with jumps having an effect over a small number of periods, as is typically observed in pandemics. The Bayesian approach allows to quantify the uncertainty around the parameter estimates. Empirical data from the COVID-19 pandemic show the superiority of the proposed approach, compared to models with a transitory shock effect.