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MRSA_model.psc
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MRSA_model.psc
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#########################################################
# Dynamic Transmission Model of MRSA Cohorts. #
# Queue-based Steady State Populations #
# Author: Matthew Mietchen (matthew.mietchen@wsu.edu) #
#########################################################
# Descriptive Information for PML File
Modelname: MRSA Cohort
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 * (P_c1+P_i1) * (N_u1 / (P_c1 + P_u1 + P_p1 +P_i1))
R2:
N_c1 > N_u1
N_c1 * iota_N
R3:
N_c1 > N_u1
N_c1 * tau_N * ((P_c1+P_i1) / (P_c1 + P_u1 + P_p1 +P_i1))
# Reactions Governing Movement of Nurses (N) Cohort 2 #
R4:
N_u2 > N_c2
rho_N * sigma * (P_c2+P_i2) * (N_u2 / (P_c2 + P_u2 +P_p2 + P_i2))
R5:
N_c2 > N_u2
N_c2 * iota_N
R6:
N_c2 > N_u2
N_c2 * tau_N * ((P_c2+P_i2) / (P_c2 + P_u2 + P_p2+P_i2))
# Reactions Governing Movement of Nurses (N) Cohort 3 #
R7:
N_u3 > N_c3
rho_N * sigma * (P_c3+P_i3) * (N_u3 / (P_c3 + P_u3 + P_p3+P_i3))
R8:
N_c3 > N_u3
N_c3 * iota_N
R9:
N_c3 > N_u3
N_c3 * tau_N * ((P_c3+P_i3) / (P_c3 + P_u3 + P_p3 +P_i3))
# Reactions Governing Movement of Nurses (N) Cohort 4 #
R10:
N_u4 > N_c4
rho_N * sigma * (P_c4+P_i4) * (N_u4 / (P_c4 + P_u4 + P_p4 +P_i4))
R11:
N_c4 > N_u4
N_c4 * iota_N
R12:
N_c4 > N_u4
N_c4 * tau_N * ((P_c4+P_i4) / (P_c4 + P_u4 + P_p4+P_i4))
# Reactions Governing Movement of Nurses (N) Cohort 5 #
R13:
N_u5 > N_c5
rho_N * sigma * (P_c5+P_i5) * (N_u5 / (P_c5 + P_u5 + P_p5+P_i5))
R14:
N_c5 > N_u5
N_c5 * iota_N
R15:
N_c5 > N_u5
N_c5 * tau_N * ((P_c5+P_i5) / (P_c5 + P_u5 + P_p5+P_i5))
# Reactions Governing Movement of Nurses (N) Cohort 6 #
R16:
N_u6 > N_c6
rho_N * sigma * (P_c6+P_i6) * (N_u6 / (P_c6 + P_u6 + P_p6+P_i6))
R17:
N_c6 > N_u6
N_c6 * iota_N
R18:
N_c6 > N_u6
N_c6 * tau_N * ((P_c6+P_i6) / (P_c6 + P_u6 + P_p6+P_i6))
########################
# Reactions Governing Movement of the Doctor
R19:
D_u > D_c
rho_D * sigma * (P_c1+P_c2+P_c3+P_c4+P_c5+P_c6+P_i1+P_i2+P_i3+P_i4+P_i5+P_i6) * (D_u / (P_c1+P_c2+P_c3+P_c4+P_c5+P_c6 + P_u1+P_u2+P_u3+P_u4+P_u5+P_u6+ P_p1+P_p2+P_p3+P_p4+P_p5+P_p6+P_i1+P_i2+P_i3+P_i4+P_i5+P_i6))
R20:
D_c > D_u
D_c * iota_D
R21:
D_c > D_u
D_c * tau_D * ((P_c1+P_c2+P_c3+P_c4+P_c5+P_c6+P_i1+P_i2+P_i3+P_i4+P_i5+P_i6) / (P_c1+P_c2+P_c3+P_c4+P_c5+P_c6 + P_u1+P_u2+P_u3+P_u4+P_u5+P_u6 +P_p1+P_p2+P_p3+P_p4+P_p5+P_p6 + P_p1+P_p2+P_p3+P_p4+P_p5+P_p6+P_i1+P_i2+P_i3+P_i4+P_i5+P_i6))
########################
# Reactions Involving Uncontaminated Patients (P_u) Cohort 1 #
R22:
P_u1 > P_c1 + Acquisition
rho_N * psi * P_u1 * (N_c1/(N_u1 + N_c1))
R23:
P_u1 > P_c1 + Acquisition
rho_D * psi * P_u1 * (D_c / (D_u + D_c))
R24:
P_u1 > P_u1
theta * P_u1 * (1-nu)
R25:
P_u1 > P_c1 + Adm
theta * P_u1 * nu * (1-deltaP)
# Reactions Involving Uncontaminated Patients (P_u) Cohort 2 #
R26:
P_u2 > P_c2 + Acquisition
rho_N * psi * P_u2 * (N_c2/(N_u2 + N_c2))
R27:
P_u2 > P_c2 + Acquisition
rho_D * psi * P_u2 * (D_c / (D_u + D_c))
R28:
P_u2 > P_u2
theta * P_u2 * (1-nu)
R29:
P_u2 > P_c2 + Adm
theta * P_u2 * nu * (1-deltaP)
# Reactions Involving Uncontaminated Patients (P_u) Cohort 3 #
R30:
P_u3 > P_c3 + Acquisition
rho_N * psi * P_u3 * (N_c3/(N_u3 + N_c3))
R31:
P_u3 > P_c3 + Acquisition
rho_D * psi * P_u3 * (D_c / (D_u + D_c))
R32:
P_u3 > P_u3
theta * P_u3 * (1-nu)
R33:
P_u3 > P_c3 + Adm
theta * P_u3 * nu * (1-deltaP)
# Reactions Involving Uncontaminated Patients (P_u) Cohort 4 #
R34:
P_u4 > P_c4 + Acquisition
rho_N * psi * P_u4 * (N_c4/(N_u4 + N_c4))
R35:
P_u4 > P_c4 + Acquisition
rho_D * psi * P_u4 * (D_c / (D_u + D_c))
R36:
P_u4 > P_u4
theta * P_u4 * (1-nu)
R37:
P_u4 > P_c4 + Adm
theta * P_u4 * nu * (1-deltaP)
# Reactions Involving Uncontaminated Patients (P_u) Cohort 5 #
R38:
P_u5 > P_c5 + Acquisition
rho_N * psi * P_u5 * (N_c5/(N_u5 + N_c5))
R39:
P_u5 > P_c5 + Acquisition
rho_D * psi * P_u5 * (D_c / (D_u + D_c))
R40:
P_u5 > P_u5
theta * P_u5 * (1-nu)
R41:
P_u5 > P_c5 + Adm
theta * P_u5 * nu * (1-deltaP)
# Reactions Involving Uncontaminated Patients (P_u) Cohort 6 #
R42:
P_u6 > P_c6 + Acquisition
rho_N * psi * P_u6 * (N_c6/(N_u6 + N_c6))
R43:
P_u6 > P_c6 + Acquisition
rho_D * psi * P_u6 * (D_c / (D_u + D_c))
R44:
P_u6 > P_u6
theta * P_u6 * (1-nu)
R45:
P_u6 > P_c6 + Adm
theta * P_u6 * nu
########################
# Reactions Involving Contaminated Patients (P_c) Cohort 1 #
R46:
P_c1 > P_u1
mu*P_c1
R47:
P_c1 > P_c1 + Dis + Adm
theta * P_c1 * nu * (1-deltaP)
R48:
P_c1 > P_u1 + Dis
theta * P_c1 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 2 #
R49:
P_c2 > P_u2
mu*P_c2
R50:
P_c2 > P_c2 + Dis + Adm
theta * P_c2 * nu * (1-deltaP)
R51:
P_c2 > P_u2 + Dis
theta * P_c2 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 3 #
R52:
P_c3 > P_u3
mu * P_c3
R53:
P_c3 > P_c3 + Dis + Adm
theta * P_c3 * nu * (1-deltaP)
R54:
P_c3 > P_u3 + Dis
theta * P_c3 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 4 #
R55:
P_c4 > P_u4
mu * P_c4
R56:
P_c4 > P_c4 + Dis + Adm
theta * P_c4 * nu * (1-deltaP)
R57:
P_c4 > P_u4 + Dis
theta * P_c4 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 5 #
R58:
P_c5 > P_u5
mu * P_c5
R59:
P_c5 > P_c5 + Dis + Adm
theta * P_c5 * nu * (1-deltaP)
R60:
P_c5 > P_u5 + Dis
theta * P_c5 * (1-nu)
# Reactions Involving Contaminated Patients (P_c) Cohort 6 #
R61:
P_c6 > P_u6
mu * P_c6
R62:
P_c6 > P_c6 + Dis + Adm
theta * P_c6 * nu * (1-deltaP)
R63:
P_c6 > P_u6 + Dis
theta * P_c6 * (1-nu)
# CHG-related Reactions
R64:
P_c1 > P_p1
epsilonE * epsilonB * P_c1
R65:
P_u1 > P_p1
epsilonE * epsilonB * P_u1
R66:
P_p1 > P_u1
epsilonU * P_p1
R67:
P_c2 > P_p2
epsilonE * epsilonB * P_c2
R68:
P_u2 > P_p2
epsilonE * epsilonB * P_u2
R69:
P_p2 > P_u2
epsilonU * P_p2
R70:
P_c3 > P_p3
epsilonE * epsilonB * P_c3
R71:
P_u3 > P_p3
epsilonE * epsilonB * P_u3
R72:
P_p3 > P_u3
epsilonU * P_p3
R73:
P_c4 > P_p4
epsilonE * epsilonB * P_c4
R74:
P_u4 > P_p4
epsilonE * epsilonB * P_u4
R75:
P_p4 > P_u4
epsilonU * P_p4
R76:
P_c5 > P_p5
epsilonE * epsilonB * P_c5
R77:
P_u5 > P_p5
epsilonE * epsilonB * P_u5
R78:
P_p5 > P_u5
epsilonU * P_p5
R79:
P_c6 > P_p6
epsilonE * epsilonB * P_c6
R80:
P_u6 > P_p6
epsilonE * epsilonB * P_u6
R81:
P_p6 > P_u6
epsilonU * P_p6
## Admission for uncolonized from protected
R82:
P_p1 > P_u1
theta * P_p1 * (1-nu)
R35:
P_p2 > P_u2
theta * P_p2 * (1-nu)
R84:
P_p3 > P_u3
theta * P_p3 * (1-nu)
R85:
P_p4 > P_u4
theta * P_p4 * (1-nu)
R86:
P_p5 > P_u5
theta * P_p5 * (1-nu)
R87:
P_p6 > P_u6
theta * P_p6 * (1-nu)
## Admission for coloninized from protected
R88:
P_p1 > P_c1 + Adm
theta * P_p1 * nu * (1-deltaP)
R89:
P_p2 > P_c2 + Adm
theta * P_p2 * nu * (1-deltaP)
R90:
P_p3 > P_c3 + Adm
theta * P_p3 * nu * (1-deltaP)
R91:
P_p4 > P_c4 + Adm
theta * P_p4 * nu * (1-deltaP)
R92:
P_p5 > P_c5 + Adm
theta * P_p5 * nu * (1-deltaP)
R93:
P_p6 > P_c6 + Adm
theta * P_p6 * nu * (1-deltaP)
## Reactions involving infected individuals ##
## Reactions involving becoming infected ##
R94:
P_c1 > P_i1 + Acquisition2
deltaI * P_c1
R95:
P_c2 > P_i2 + Acquisition2
deltaI * P_c2
R96:
P_c3 > P_i3 + Acquisition2
deltaI * P_c3
R97:
P_c4 > P_i4 + Acquisition2
deltaI * P_c4
R98:
P_c5 > P_i5 + Acquisition2
deltaI * P_c5
R99:
P_c6 > P_i6 + Acquisition2
deltaI * P_c6
## Rate infected die ##
R100:
P_i1 > P_u1 + Deaths
deltaD * (1- nu)* P_i1
R101:
P_i1 > P_c1 + Deaths
deltaD * nu * P_i1
R102:
P_i2 > P_u2 + Deaths
deltaD * (1- nu)* P_i2
R103:
P_i2 > P_c2 + Deaths
deltaD * nu * P_i2
R104:
P_i3 > P_u3 + Deaths
deltaD * (1- nu)* P_i3
R105:
P_i3 > P_c3 + Deaths
deltaD * nu * P_i3
R106:
P_i4 > P_u4 + Deaths
deltaD * (1- nu)* P_i4
R107:
P_i4 > P_c4 + Deaths
deltaD * nu * P_i4
R108:
P_i5 > P_u5 + Deaths
deltaD * (1- nu)* P_i5
R109:
P_i5 > P_c5 + Deaths
deltaD * nu * P_i5
R110:
P_i6 > P_u6 + Deaths
deltaD * (1- nu)* P_i6
R111:
P_i6 > P_c6 + Deaths
deltaD * nu * P_i6
## Cured from Infection
R112:
P_i1 > P_u1
deltaC * P_i1
R113:
P_i2 > P_u2
deltaC * P_i2
R114:
P_i3 > P_u3
deltaC * P_i3
R115:
P_i4 > P_u4
deltaC * P_i4
R116:
P_i5 > P_u5
deltaC * P_i5
R117:
P_i6 > P_u6
deltaC * P_i6
# admission with infection
R118:
P_u1 > P_i1 + Adm
theta * P_u1 * nu * deltaP
R119:
P_c1 > P_i1 +Adm + Dis
theta * P_c1 * nu * deltaP
R120:
P_p1 > P_i1 + Adm
theta * P_p1 * nu * deltaP
R121:
P_i1 > P_i1 + Adm + Dis
#deltaD * P_i1 * nu * deltaP
0.0
R122:
P_u2 > P_i2 + Adm
theta * P_u2 * nu * deltaP
R123:
P_c2 > P_i2 + Adm + Dis
theta * P_c2 * nu * deltaP
R124:
P_p2 > P_i2 + Adm
theta * P_p2 * nu * deltaP
R125:
P_i2 > P_i2 + Adm + Dis
#deltaD * P_i2 * nu * deltaP
0.0
R126:
P_u3 > P_i3 + Adm
theta * P_u3 * nu * deltaP
R127:
P_c3 > P_i3 + Adm + Dis
theta * P_c3 * nu * deltaP
R128:
P_p3 > P_i3 + Adm
theta * P_p3 * nu * deltaP
R129:
P_i3 > P_i3 + Adm + Dis
#deltaD * P_i3 * nu * deltaP
0.0
R130:
P_u4 > P_i4 + Adm
theta * P_u4 * nu * deltaP
R131:
P_c4 > P_i4 + Adm + Dis
theta * P_c4 * nu * deltaP
R132:
P_p4 > P_i4 + Adm
theta * P_p4 * nu * deltaP
R133:
P_i4 > P_i4 + Adm + Dis
#deltaD * P_i4 * nu * deltaP
0.0
R134:
P_u5 > P_i5 + Adm
theta * P_u5 * nu * deltaP
R135:
P_c5 > P_i5 + Adm + Dis
theta * P_c5 * nu * deltaP
R136:
P_p5 > P_i5 + Adm
theta * P_p5 * nu * deltaP
R137:
P_i5 > P_i5 + Adm + Dis
#deltaD * P_i5 * nu * deltaP
0.0
R138:
P_u6 > P_i6 + Adm
theta * P_u6 * nu * deltaP
R139:
P_c6 > P_i6 + Adm + Dis
theta * P_c6 * nu * deltaP
R140:
P_p6 > P_i6 + Adm
theta * P_p6 * nu * deltaP
R141:
P_i6 > P_i6 + Adm + Dis
#deltaD * P_i6 * nu * deltaP
0.0
########################
### 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 = 2
P_u2 = 2
P_u3 = 3
P_u4 = 3
P_u5 = 3
P_u6 = 3
P_c1 = 1
P_c2 = 1
P_c3 = 0
P_c4 = 0
P_c5 = 0
P_c6 = 0
P_p1 = 0
P_p2 = 0
P_p3 = 0
P_p4 = 0
P_p5 = 0
P_p6 = 0
P_i1 = 0
P_i2 = 0
P_i3 = 0
P_i4 = 0
P_i5 = 0
P_i6 = 0
Acquisition = 0
Acquisition2 = 0
Deaths = 0
Adm=0
Dis=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 = 0.046 # successful colonization of an uncolonized patient probability
# Exit (death/discharge) rates
theta = 0.00949 # probability of death/discharge
#theta=0.0
# Admission Proportions
#nu = 0.0779 # proportion of admissions of colonized with MRSA
nu = 0.0
# 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
epsilonE = 0.125 # effectiveness of chg
epsilonU = 1.0 # rate protected people are returned to uncolonized
epsilonB = 0.0 # rate people are bathed in chg
#deltaI = 0.000343 # rate colonized become infected
deltaI = 0.0
#deltaD = 0.000403 # rate infected die
deltaD = 0.0
#deltaC = 0.002976 # rate infected cured
deltaC = 0.0
#deltaP = 0.32 # % infected from colonized
deltaP = 0.0