Pandemic intensity monitoring, from the earliest stages of the pandemic outbreak, constitutes a critical scientific challenge with major societal stakes. The task is significantly complicated by the low quality of reported infection counts, stemming from emergency and crisis contexts, and by the need for regular (daily) updates, while the pandemic is still active. The present work first proposes a parametric Hidden Markov Model (HMM) aiming to account jointly for epidemic propagation mechanisms and for low-quality data, while imposing epidemiccompliant constraints on the time-varying reproduction number, considered as a proxy for pandemic intensity quantification. Second, and to avoid the arbitrary or expert-based tuning of the parameters of the HMM, data-driven automated selection procedures are devised relying on tailoring a stochastic Expectation-Maximization algorithm. Credibility interval-based estimation of the time-varying reproduction number, modeled as a hidden variable, is then obtained from Monte Carlo sampling. The potential of the tools devised here is illustrated on real Covid19 daily new infection counts from Johns Hopkins University repository.