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Our paper investigates distributions of exposed and infectious time periodsin an epidemic model and how applying a disease control strategy affects themodel's accuracy. While ordinary differential equations are widely used fortheir simplicity, they incorporate an exponential distribution for time spentexposed or infectious. This allows for a high probability of unrealisticallyshort exposed and infectious time periods. We propose that caution must betaken when applying intervention methods to basic models in order to avoidinaccurate predictions. Delay differential equations, which use a deltadistribution for exposed and infectious periods, can provide better realism butare more difficult to use and analyze. We introduce a multi-infectedcompartment model to interpolate between an ODE model with exponentialdistributions and a DDE model with delta distributions in order to investigatethe effect these distributions have on the dynamics of the system when anintervention method is also included. Using steady state stability andbifurcation analysis, this paper considers when simpler infectious diseasemodels can be used versus when more realistic time periods must beincorporated. We find that the placement of control measures on subpopulationsand the length of the time delay impacts the accuracy of the simpler models.

Intervention Strategies for Epidemics: Does Ignoring Time Delay Lead to Incorrect Predictions?