Fig. 1

Compartmental model structure with pulse detection and isolation effect. The blue arrows indicate routine transfer. The red arrows indicate impulse transfer. The dotted line indicates that the patient discharges the virus into the environment and that susceptible people become infected by the virus in the environment. \(FO{I}_{V}=(c{p}_{SC}\frac{I+A}{N}+{\beta }_{SE}\frac{P}{N}){(1-f}_{S})p, FO{I}_{S}=c{p}_{SC}\frac{I+A}{N}+{\beta }_{SE}\frac{P}{N}\). We consider susceptible (\(S\)), exposed (\(E\)), symptomatic infected (\(I\)), asymptomatic infected (\(A\)), hospitalized (\(H\)), recovery (\(R\)), isolated (\({V}_{q}\), \({S}_{q}\), \({E}_{q}\)) individuals and the virus in the environment (\(P\)), more details of the model and the transitions between compartments are provided in the text and Table 1