  Our paper investigates distributions of exposed and infectious time periods
in an epidemic model and how applying a disease control strategy affects the
model's accuracy. While ordinary differential equations are widely used for
their simplicity, they incorporate an exponential distribution for time spent
exposed or infectious. This allows for a high probability of unrealistically
short exposed and infectious time periods. We propose that caution must be
taken when applying intervention methods to basic models in order to avoid
inaccurate predictions. Delay differential equations, which use a delta
distribution for exposed and infectious periods, can provide better realism but
are more difficult to use and analyze. We introduce a multi-infected
compartment model to interpolate between an ODE model with exponential
distributions and a DDE model with delta distributions in order to investigate
the effect these distributions have on the dynamics of the system when an
intervention method is also included. Using steady state stability and
bifurcation analysis, this paper considers when simpler infectious disease
models can be used versus when more realistic time periods must be
incorporated. We find that the placement of control measures on subpopulations
and the length of the time delay impacts the accuracy of the simpler models.
