Modeling Complex Systems: A Case Study of Compartmental Models in Epidemiology

Figure 8

Continuous compartmental models forecast a deterministic second wave of infections. The shaded region of the plot shows the time period for which the spreading rate is reduced as a result of policy interventions. The blue curve shows the number of infections according to a continuous SIR model: after the interventions are removed, the infections rise again. The scatter plot trajectories show the number of infections in a stochastic SIR model, with each marker type corresponding to a single realization of the model. The trajectories marked by pink circles and yellow squares show that elimination is possible and that a second wave need not occur. Due to the stochastic nature of disease spread, interventions cannot be held in place for a predetermined amount of time but rather must be calibrated to real-time observations. For instance, for the cases of the pink circles and yellow squares, the interventions could be lifted earlier than they were in this simulation, while for the blue triangles, the interventions would need to be kept in place for longer. Simulation details and parameters can be found in Appendix D.