In this paper, we present a new axiomatic model of epidemic development, called HIT, which is consistent with the very special features of COVID19. This is a discrete-time linear switching model for predicting the dynamics of total number of infected persons and concentration of the asymptomatic virus holders in the population. A small number of its parameters can be tuned using the available real-time dynamic data on virus propagation. This model provides us with a rare possibility of online prediction of the future. As an example, we describe an application of this model to the online analysis of COVID19 epidemic in Belgium for eighty days in the period March - May, 2020. During this time, our predictions were exact, typically, within the accuracy of 0.5%. To the best of our knowledge, this is the first mathematical model predicting the evolution of epidemics under containment measures, which prevent development of immunity in the population.