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Gamma.psc
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Gamma.psc
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###########################################################
# Dynamic Transmission Model of MRSA in a Meta-population #
# Leaky-Pod Model #
# Queue-based Steady State Populations #
# Author: Matthew Mietchen (matthew.mietchen@wsu.edu) #
###########################################################
# Descriptive Information for PML File
Modelname: MRSA Meta-population Expanded
Description: PML Implementation of MRSA transmission model
# Set model to run with numbers of individuals
Species_In_Conc: False
Output_In_Conc: False
#### Model Reactions ####
# Reactions Governing Movement of Nurses (N) Cohort 1 #
R1:
N_u1 > N_c1
rho_N * sigma * N_u1 * (P_c1 / (P_c1 + P_u1)) * gamma
R2:
N_u1 > N_c1
rho_N * sigma * N_u1 * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R3:
N_u1 > N_c1
rho_N * sigma * N_u1 * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R4:
N_u1 > N_c1
rho_N * sigma * N_u1 * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R5:
N_u1 > N_c1
rho_N * sigma * N_u1 * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R6:
N_u1 > N_c1
rho_N * sigma * N_u1 * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
R7:
N_c1 > N_u1
N_c1 * iota_N
R8:
N_c1 > N_u1
N_c1 * tau_N * (P_c1 / (P_c1 + P_u1)) * gamma
R9:
N_c1 > N_u1
N_c1 * tau_N * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R10:
N_c1 > N_u1
N_c1 * tau_N * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R11:
N_c1 > N_u1
N_c1 * tau_N * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R12:
N_c1 > N_u1
N_c1 * tau_N * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R13:
N_c1 > N_u1
N_c1 * tau_N * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
# Reactions Governing Movement of Nurses (N) Cohort 2 #
R14:
N_u2 > N_c2
rho_N * sigma * N_u2 * (P_c2 / (P_c2 + P_u2)) * gamma
R15:
N_u2 > N_c2
rho_N * sigma * N_u2 * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R16:
N_u2 > N_c2
rho_N * sigma * N_u2 * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R17:
N_u2 > N_c2
rho_N * sigma * N_u2 * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R18:
N_u2 > N_c2
rho_N * sigma * N_u2 * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
R19:
N_u2 > N_c2
rho_N * sigma * N_u2 * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
R20:
N_c2 > N_u2
N_c2 * iota_N
R21:
N_c2 > N_u2
N_c2 * tau_N * (P_c2 / (P_c2 + P_u2)) * gamma
R22:
N_c2 > N_u2
N_c2 * tau_N * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
R23:
N_c2 > N_u2
N_c2 * tau_N * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R24:
N_c2 > N_u2
N_c2 * tau_N * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R25:
N_c2 > N_u2
N_c2 * tau_N * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R26:
N_c2 > N_u2
N_c2 * tau_N * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
# Reactions Governing Movement of Nurses (N) Cohort 3 #
R27:
N_u3 > N_c3
rho_N * sigma * N_u3 * (P_c3 / (P_c3 + P_u3)) * gamma
R28:
N_u3 > N_c3
rho_N * sigma * N_u3 * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R29:
N_u3 > N_c3
rho_N * sigma * N_u3 * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R30:
N_u3 > N_c3
rho_N * sigma * N_u3 * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
R31:
N_u3 > N_c3
rho_N * sigma * N_u3 * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
R32:
N_u3 > N_c3
rho_N * sigma * N_u3 * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R33:
N_c3 > N_u3
N_c3 * iota_N
R34:
N_c3 > N_u3
N_c3 * tau_N * (P_c3 / (P_c3 + P_u3)) * gamma
R35:
N_c3 > N_u3
N_c3 * tau_N * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R36:
N_c3 > N_u3
N_c3 * tau_N * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
R37:
N_c3 > N_u3
N_c3 * tau_N * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R38:
N_c3 > N_u3
N_c3 * tau_N * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R39:
N_c3 > N_u3
N_c3 * tau_N * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
# Reactions Governing Movement of Nurses (N) Cohort 4 #
R40:
N_u4 > N_c4
rho_N * sigma * N_u4 * (P_c4 / (P_c4 + P_u4)) * gamma
R41:
N_u4 > N_c4
rho_N * sigma * N_u4 * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R42:
N_u4 > N_c4
rho_N * sigma * N_u4 * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
R43:
N_u4 > N_c4
rho_N * sigma * N_u4 * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
R44:
N_u4 > N_c4
rho_N * sigma * N_u4 * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R45:
N_u4 > N_c4
rho_N * sigma * N_u4 * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R46:
N_c4 > N_u4
N_c4 * iota_N
R47:
N_c4 > N_u4
N_c4 * tau_N * (P_c4 / (P_c4 + P_u4)) * gamma
R48:
N_c4 > N_u4
N_c4 * tau_N * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R49:
N_c4 > N_u4
N_c4 * tau_N * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R50:
N_c4 > N_u4
N_c4 * tau_N * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
R51:
N_c4 > N_u4
N_c4 * tau_N * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R52:
N_c4 > N_u4
N_c4 * tau_N * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
# Reactions Governing Movement of Nurses (N) Cohort 5 #
R53:
N_u5 > N_c5
rho_N * sigma * N_u5 * (P_c5 / (P_c5 + P_u5)) * gamma
R54:
N_u5 > N_c5
rho_N * sigma * N_u5 * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
R55:
N_u5 > N_c5
rho_N * sigma * N_u5 * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
R56:
N_u5 > N_c5
rho_N * sigma * N_u5 * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R57:
N_u5 > N_c5
rho_N * sigma * N_u5 * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R58:
N_u5 > N_c5
rho_N * sigma * N_u5 * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R59:
N_c5 > N_u5
N_c5 * iota_N
R60:
N_c5 > N_u5
N_c5 * tau_N * (P_c5 / (P_c5 + P_u5)) * gamma
R61:
N_c5 > N_u5
N_c5 * tau_N * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R62:
N_c5 > N_u5
N_c5 * tau_N * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R63:
N_c5 > N_u5
N_c5 * tau_N * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R64:
N_c5 > N_u5
N_c5 * tau_N * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
R65:
N_c5 > N_u5
N_c5 * tau_N * (P_c6 / (P_c6 + P_u6)) * ((1 - gamma) / 5)
# Reactions Governing Movement of Nurses (N) Cohort 6 #
R66:
N_u6 > N_c6
rho_N * sigma * N_u6 * (P_c6 / (P_c6 + P_u6)) * gamma
R67:
N_u6 > N_c6
rho_N * sigma * N_u6 * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
R68:
N_u6 > N_c6
rho_N * sigma * N_u6 * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R69:
N_u6 > N_c6
rho_N * sigma * N_u6 * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R70:
N_u6 > N_c6
rho_N * sigma * N_u6 * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R71:
N_u6 > N_c6
rho_N * sigma * N_u6 * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R72:
N_c6 > N_u6
N_c6 * iota_N
R73:
N_c6 > N_u6
N_c6 * tau_N * (P_c6 / (P_c6 + P_u6)) * gamma
R74:
N_c6 > N_u6
N_c6 * tau_N * (P_c2 / (P_c2 + P_u2)) * ((1 - gamma) / 5)
R75:
N_c6 > N_u6
N_c6 * tau_N * (P_c3 / (P_c3 + P_u3)) * ((1 - gamma) / 5)
R76:
N_c6 > N_u6
N_c6 * tau_N * (P_c4 / (P_c4 + P_u4)) * ((1 - gamma) / 5)
R77:
N_c6 > N_u6
N_c6 * tau_N * (P_c5 / (P_c5 + P_u5)) * ((1 - gamma) / 5)
R78:
N_c6 > N_u6
N_c6 * tau_N * (P_c1 / (P_c1 + P_u1)) * ((1 - gamma) / 5)
########################
# Reactions Governing Movement of the Doctor
R79:
D_u > D_c
rho_D * sigma * D_u * (P_c1 + P_c2 + P_c3 + P_c4 + P_c5 + P_c6 / (P_c1 + P_c2 + P_c3 + P_c4 + P_c5 + P_c6 + P_u1 + P_u2 + P_u3 + P_u4 + P_u5 + P_u6))
R80:
D_c > D_u
D_c * iota_D
R81:
D_c > D_u
D_c * tau_D * (P_c1 + P_c2 + P_c3 + P_c4 + P_c5 + P_c6 / (P_c1 + P_c2 + P_c3 + P_c4 + P_c5 + P_c6 + P_u1 + P_u2 + P_u3 + P_u4 + P_u5 + P_u6))
########################
# Reactions Involving Uncontaminated Patients (P_u) Cohort 1 #
R82:
P_u1 > P_c1 + Acquisition
rho_N * psi * P_u1 * (N_c1 / (N_c1 + N_u1)) * gamma
R83:
P_u1 > P_c1 + Acquisition
rho_N * psi * P_u1 * (N_c2 / (N_c2 + N_u2)) * ((1 - gamma) / 5)
R84:
P_u1 > P_c1 + Acquisition
rho_N * psi * P_u1 * (N_c3 / (N_c3 + N_u3)) * ((1 - gamma) / 5)
R85:
P_u1 > P_c1 + Acquisition
rho_N * psi * P_u1 * (N_c4 / (N_c4 + N_u4)) * ((1 - gamma) / 5)
R86:
P_u1 > P_c1 + Acquisition
rho_N * psi * P_u1 * (N_c5 / (N_c5 + N_u5)) * ((1 - gamma) / 5)
R87:
P_u1 > P_c1 + Acquisition
rho_N * psi * P_u1 * (N_c6 / (N_c6 + N_u6)) * ((1 - gamma) / 5)
R88:
P_u1 > P_c1 + Acquisition
rho_D * psi * P_u1 * (D_c / (D_c + D_u))
R89:
P_u1 > P_u1
theta * P_u1 * (1-nu)
R90:
P_u1 > P_c1
theta * P_u1 * nu
# Reactions Involving Uncontaminated Patients (P_u) Cohort 2 #
R91:
P_u2 > P_c2 + Acquisition
rho_N * psi * P_u2 * (N_c2 / (N_c2 + N_u2)) * gamma
R92:
P_u2 > P_c2 + Acquisition
rho_N * psi * P_u2 * (N_c1 / (N_c1 + N_u1)) * ((1 - gamma) / 5)
R93:
P_u2 > P_c2 + Acquisition
rho_N * psi * P_u2 * (N_c3 / (N_c3 + N_u3)) * ((1 - gamma) / 5)
R94:
P_u2 > P_c2 + Acquisition
rho_N * psi * P_u2 * (N_c4 / (N_c4 + N_u4)) * ((1 - gamma) / 5)
R95:
P_u2 > P_c2 + Acquisition
rho_N * psi * P_u2 * (N_c5 / (N_c5 + N_u5)) * ((1 - gamma) / 5)
R96:
P_u2 > P_c2 + Acquisition
rho_N * psi * P_u2 * (N_c6 / (N_c6 + N_u6)) * ((1 - gamma) / 5)
R97:
P_u2 > P_c2 + Acquisition
rho_D * psi * P_u2 * (D_c / (D_c + D_u))
R98:
P_u2 > P_u2
theta * P_u2 * (1-nu)
R99:
P_u2 > P_c2
theta * P_u2 * nu
# Reactions Involving Uncontaminated Patients (P_u) Cohort 3 #
R100:
P_u3 > P_c3 + Acquisition
rho_N * psi * P_u3 * (N_c3 / (N_c3 + N_u3)) * gamma
R101:
P_u3 > P_c3 + Acquisition
rho_N * psi * P_u3 * (N_c2 / (N_c2 + N_u2)) * ((1 - gamma) / 5)
R102:
P_u3 > P_c3 + Acquisition
rho_N * psi * P_u3 * (N_c1 / (N_c1 + N_u1)) * ((1 - gamma) / 5)
R103:
P_u3 > P_c3 + Acquisition
rho_N * psi * P_u3 * (N_c4 / (N_c4 + N_u4)) * ((1 - gamma) / 5)
R104:
P_u3 > P_c3 + Acquisition
rho_N * psi * P_u3 * (N_c5 / (N_c5 + N_u5)) * ((1 - gamma) / 5)
R105:
P_u3 > P_c3 + Acquisition
rho_N * psi * P_u3 * (N_c6 / (N_c6 + N_u6)) * ((1 - gamma) / 5)
R106:
P_u3 > P_c3 + Acquisition
rho_D * psi * P_u3 * (D_c / (D_c + D_u))
R107:
P_u3 > P_u3
theta * P_u3 * (1-nu)
R108:
P_u3 > P_c3
theta * P_u3 * nu
# Reactions Involving Uncontaminated Patients (P_u) Cohort 4 #
R109:
P_u4 > P_c4 + Acquisition
rho_N * psi * P_u4 * (N_c4 / (N_c4 + N_u4)) * gamma
R110:
P_u4 > P_c4 + Acquisition
rho_N * psi * P_u4 * (N_c2 / (N_c2 + N_u2)) * ((1 - gamma) / 5)
R111:
P_u4 > P_c4 + Acquisition
rho_N * psi * P_u4 * (N_c3 / (N_c3 + N_u3)) * ((1 - gamma) / 5)
R112:
P_u4 > P_c4 + Acquisition
rho_N * psi * P_u4 * (N_c1 / (N_c1 + N_u1)) * ((1 - gamma) / 5)
R113:
P_u4 > P_c4 + Acquisition
rho_N * psi * P_u4 * (N_c5 / (N_c5 + N_u5)) * ((1 - gamma) / 5)
R114:
P_u4 > P_c4 + Acquisition
rho_N * psi * P_u4 * (N_c6 / (N_c6 + N_u6)) * ((1 - gamma) / 5)
R115:
P_u4 > P_c4 + Acquisition
rho_D * psi * P_u4 * (D_c / (D_c + D_u))
R116:
P_u4 > P_u4
theta * P_u4 * (1-nu)
R117:
P_u4 > P_c4
theta * P_u4 * nu
# Reactions Involving Uncontaminated Patients (P_u) Cohort 5 #
R118:
P_u5 > P_c5 + Acquisition
rho_N * psi * P_u5 * (N_c5 / (N_c5 + N_u5)) * gamma
R119:
P_u5 > P_c5 + Acquisition
rho_N * psi * P_u5 * (N_c2 / (N_c2 + N_u2)) * ((1 - gamma) / 5)
R120:
P_u5 > P_c5 + Acquisition
rho_N * psi * P_u5 * (N_c3 / (N_c3 + N_u3)) * ((1 - gamma) / 5)
R121:
P_u5 > P_c5 + Acquisition
rho_N * psi * P_u5 * (N_c4 / (N_c4 + N_u4)) * ((1 - gamma) / 5)
R122:
P_u5 > P_c5 + Acquisition
rho_N * psi * P_u5 * (N_c1 / (N_c1 + N_u1)) * ((1 - gamma) / 5)
R123:
P_u5 > P_c5 + Acquisition
rho_N * psi * P_u5 * (N_c6 / (N_c6 + N_u6)) * ((1 - gamma) / 5)
R124:
P_u5 > P_c5 + Acquisition
rho_D * psi * P_u5 * (D_c / (D_c + D_u))
R125:
P_u5 > P_u5
theta * P_u5 * (1-nu)
R126:
P_u5 > P_c5
theta * P_u5 * nu
# Reactions Involving Uncontaminated Patients (P_u) Cohort 6 #
R127:
P_u6 > P_c6 + Acquisition
rho_N * psi * P_u6 * (N_c6 / (N_c6 + N_u6)) * gamma
R128:
P_u6 > P_c6 + Acquisition
rho_N * psi * P_u6 * (N_c2 / (N_c2 + N_u2)) * ((1 - gamma) / 5)
R129:
P_u6 > P_c6 + Acquisition
rho_N * psi * P_u6 * (N_c3 / (N_c3 + N_u3)) * ((1 - gamma) / 5)
R130:
P_u6 > P_c6 + Acquisition
rho_N * psi * P_u6 * (N_c4 / (N_c4 + N_u4)) * ((1 - gamma) / 5)
R131:
P_u6 > P_c6 + Acquisition
rho_N * psi * P_u6 * (N_c5 / (N_c5 + N_u5)) * ((1 - gamma) / 5)
R132:
P_u6 > P_c6 + Acquisition
rho_N * psi * P_u6 * (N_c1 / (N_c1 + N_u1)) * ((1 - gamma) / 5)
R133:
P_u6 > P_c6 + Acquisition
rho_D * psi * P_u6 * (D_c / (D_c + D_u))
R134:
P_u6 > P_u6
theta * P_u6 * (1-nu)
R135:
P_u6 > P_c6
theta * P_u6 * nu
########################
# Reactions Involving Contaminated Patients (P_c) Cohort 1 #
R136:
P_c1 > P_u1
mu * P_c1
R137:
P_c1 > P_c1
theta * P_c1 * nu
R138:
P_c1 > P_u1
theta * P_c1 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 2 #
R139:
P_c2 > P_u2
mu * P_c2
R140:
P_c2 > P_c2
theta * P_c2 * nu
R141:
P_c2 > P_u2
theta * P_c2 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 3 #
R142:
P_c3 > P_u3
mu * P_c3
R143:
P_c3 > P_c3
theta * P_c3 * nu
R144:
P_c3 > P_u3
theta * P_c3 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 4 #
R145:
P_c4 > P_u4
mu * P_c4
R146:
P_c4 > P_c4
theta * P_c4 * nu
R147:
P_c4 > P_u4
theta * P_c4 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 5 #
R148:
P_c5 > P_u5
mu * P_c5
R149:
P_c5 > P_c5
theta * P_c5 * nu
R150:
P_c5 > P_u5
theta * P_c5 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 6 #
R151:
P_c6 > P_u6
mu * P_c6
R152:
P_c6 > P_c6
theta * P_c6 * nu
R153:
P_c6 > P_u6
theta * P_c6 * (1-nu)
########################
### Parameter Values ###
## Time Values are in HOURS ##
# Compartments #
N_u1 = 1
N_u2 = 1
N_u3 = 1
N_u4 = 1
N_u5 = 1
N_u6 = 1
N_c1 = 0
N_c2 = 0
N_c3 = 0
N_c4 = 0
N_c5 = 0
N_c6 = 0
D_u = 1
D_c = 0
P_u1 = 3
P_u2 = 3
P_u3 = 3
P_u4 = 3
P_u5 = 3
P_u6 = 3
P_c1 = 0
P_c2 = 0
P_c3 = 0
P_c4 = 0
P_c5 = 0
P_c6 = 0
Acquisition = 0
# Contact Rates and Contamination Probabilities #
rho_N = 3.973 # nurse direct care tasks per patient per hour
rho_D = 0.181 # doctor direct care tasks per patient per hour
sigma = 0.054 # hand contamination probability
psi = 0.0464 # successful colonization of an uncolonized patient probability
#gamma = 1.0 proportion of time a nurse is in the assigned/original cohort
gamma = 0.1667
# Exit (death/discharge) rates
theta = 0.00949 # probability of death/discharge
# Admission Proportions
nu = 0.0779 # proportion of admissions of colonized with MRSA
# Handwashing and Gown/Glove Change Rates
iota_N = 6.404 #11.92 nurse direct care tasks per hour with 56.55% compliance and 95% efficacy
iota_D = 1.748 #3.25 doctor direct care tasks per hour with 56.55% compliance and 95% efficacy
tau_N = 2.728 #3.30 nurse gown/glove changes per hour with 82.66% compliance
tau_D = 0.744 #0.90 doctor gown/glove changes per hour with 82.66% compliance
mu = 0.002083 # natural decolonization rate median 20 days per Star*ICU trial