. 2021 Jun 28;31(6):917–932. doi: 10.1007/s10389-021-01611-0

Table 5.

Sub-compartment exchanges in SCM, in order of execution in each daily time step

Process	Daily cohorts	Compartment exchanges
Transmission	T_I < = d < = T_F	See Text.
Asymptomatic & hidden	d = 0	Given X new local cases: [X_SF, X_AF, X_SU, X_AU] is ~ multinomial (X, [(1-P_A).(1-P_U), P_A.(1-P_U), P_U(1-P_A), P_A.P_U])
Overseas arrivals	d = 0	Overseas reported (symptomatic) cases XSO treated as newly infected T_S days earlier. Matched by asymptomatic cases XAO ~ BIN(XSO,P_A/(1-P_A)). For arrivals: Before March 17: X_SFO = XSO, X_AF = X_AF + XAO. From March 17 to March 28: X_SSQO = XSO, X_ASQ = XAO. After March 28: X_SQ = XSO, X_AQ = XAO.
Hotel quarantine breakdown	d = 0	Hotel quarantine evasions QE ~ BIN(XSQ,P_Q). X_SQ = X_SQ – QE, X_SU = X_SU + QE.
Source detected	d > = 1	DXST = additional symptomatic cases with detected sources. DXAT = additional asymptomatic cases with detected sources. (See text for derivation). X_ST = X_ST + DXST, X_SF = X_SF – DXST. X_AT = X_AT + DXAT, X_AF = X_AF – DXAT.
Contact tracing	d > = 1	CST ~ BIN(X_ST,P_T). X_ST = X_ST – CST, X_SSQ = X_SSQ + CST. CAT ~ BIN(X_AT,P_T). X_AT = X_AT – CAT, X_ASQ = X_ASQ + CAT.
Detection of overseas cases	d = T_S	X_D = X_D + X_SFO + X_SSQO, X_SFO = 0, X_SSQO = 0. YDET = YDET + X_SFO + X_SSQO + X_SQO
Detection of cases in self-quarantine	d > = T_S	DSQ ~ BIN(X_SSQ,P_DSQ). X_SSQ = X_SSQ – DSQ, X_D = X_D + DSQ. YDET = YDET + DSQ, YDETL = YDETL + DSQ.
Detection of cases in community	d > = Ts	DSF ~ BIN(X_SF,P_DC). X_SF = X_SF– DSF, X_D = X_D + DSF. DST ~ BIN(X_ST,P_DC). X_ST = X_ST– DST, X_D = X_D + DST. YDET = YDET + DSF + DST, YDETL = YDETL + DSF + DST.
Hospitalisation	d = T_H	For each of X = X_SF, X_SSQ, X_ST, X_SU, X_D, X_SQ DH ~ BIN(X,P_H). X_SH = X_SH + DH, YH = YH + DH. For CC = SF, SSQ, ST, SU, D: X_CC = X_CC – DH. For CC = SF, SSQ, ST, SU: YDET = YDET + DH, YDETL = YDETL + DH.
Fatally ill	d = T_D	DFI ~ BIN(X_SH,P_M). X_SH = X_SH – DFI, X_FI = X_FI + DFI.
Death	T_D < = d < = T_M	DD ~ BIN(X_FI,P_D). X_FI = X_FI – DD, X_M = X_M + DD. YM = YM + DD.
Recovery	T_C < = d < = T_M	DRD ~ BIN(X_D,P_R). X_D = X_D – DRD, X_RD = X_RD + DRD. DRH ~ BIN(X_SH,P_R). X_SH = X_SH – DRH, X_RD = X_RD + DRH. YRD = YRD + DRD + DRH.