A Transmission Rate Estimator & Controller for Infectious Disease SIR Models - Constant Case

A widely studied susceptible S(t), infectious I(t), and removed R(t) (SIR) family of deterministic, lumped-parameter models of directly transmitted infectious diseases is considered to estimate the transmission rate assumed to be piecewise constant via a linear, extended-state observer. Then, although the transmission rate is not a control signal in the traditional sense, the application of feedback control design offers guidance in implementing mitigating actions that curb the disease spread. A linearized model at each measurement point is used for offline observer design with the transmission rate treated as an unknown but constant disturbance. The observer-based controller simulations in discrete time explore heuristic policies that may be implemented by public health and government organizations.