New Insights into an Epidemic SIR Model for Control and Public Health Intervention

A susceptible, infectious, removed (SIR) model for the spread of directly transmitted disease caused by pathogens such as bacteria, viruses, and fungi is considered. The nonlinear state equations are feedback linearizable resulting in second order dynamics that can be controlled to achieve constant setpoint tracking. Although the model’s transmission rate $\beta$(t) is not a control input in the traditional sense, feedback control is used to synthesize a ‘gold standard’ $\beta^{o}(t)$ to assist institutions in visualizing what could be achieved via timely implementation of public health interventions, economic and other measures which are known to influence the transmission rate and curb the spread. Control goals may be an improvement in state performance, such as a reduction in the population fraction that is removed, or minimization of the peak fraction of the population that is infected, or minimization of the quarantine window weighed against the economic cost on society, or the avoidance altogether of a second peak. The examination of limiting state behaviors gives further insight into the model and what actions to take in a pandemic. Simulations illustrate several scenarios including performance impact from a time delay in the implemented actions.