The SEIIR model is a compartment model with five populations, the susceptible, exposed, symptomatic and asymptomatic infectious, and recovered groups S, E, Is , Ia and R. It characterizes infectious diseases with a significant group of individuals that remain asymptomatic upon infection, but can still infect others. Since the SEIIR model has no analytical solution for the time course of its populations, we discretize it in time using finite differences and apply explicit time integration schemes to solve it. We distinguish two cases, the special case where the disease dynamics of the symptomatic and asymptomatic groups are similar, and the general case where the disease dynamics are different. To illustrate the features of the SEIIR model, we simulate the early COVID-19 outbreak in the Netherlands, one of the first countries that systematically estimated asymptomatic transmission using seroprevalence studies. The learning objectives of this chapter on computational SEIIR modeling are to