Epidemiological models are complex structures where unobserved variables, like asymptomatic and pre-symptomatic infected individuals can have a great role in the dynamics of the disease. In this presentation we discuss the stochastic modelling of an outbreak of Covid-19 in a small population on which asymptomatic and pre-symptomatic individuals and public health interventions are explicitly modelled either as a branching process or through a compartmentalised stochastic model. These principles are used to model and analyse the Newfoundland Covid-19 first outbreak and the effect of public health interventions. We also discuss the use of dynamic programming to optimise public health interventions depending of if the objective is contain or mitigation of the epidemiological process.