A key parameter in epidemiological modeling which characterizes the spread of an infectious disease is the generation time, or more generally the distribution of infectiousness as a function of time since infection. There is increasing evidence supporting a prolonged viral shedding window for COVID-19, but the transmissibility in this phase is unclear. Based on this, we develop a generalized Susceptible-Exposed-Infected-Resistant (SEIR) model including an additional compartment of chronically infected individuals who can stay infectious for a longer duration than the reported generation time, but with infectivity reduced to varying degrees. Using the incidence and fatality data from different countries, we first show that such an assumption also yields a plausible model in explaining the data observed prior to the easing of the lockdown measures (relaxation). We then test the predictive power of this model for different durations and levels of prolonged infectiousness using the incidence data after the introduction of relaxation in Switzerland, and compare it with a model without the chronically infected population to represent the models conventionally used. We show that in case of a gradual easing on the lockdown measures, the predictions of the model including the chronically infected population vary considerably from those obtained under a model in which prolonged infectiousness is not taken into account. Although the existence of a chronically infected population still remains largely hypothetical, we believe that our results provide tentative evidence to consider a chronically infected population as an alternative modeling approach to better interpret the transmission dynamics of COVID-19.