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General_Spatial_Model.jl
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General_Spatial_Model.jl
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#=
General model: Model parameterized for two locations (Schleswig-Holstein & Saxony)
- Julia version: 1.6.1
- Authors: Kristan A. Schneider, H. Christian Jr. Tsoungui Obama, Nessma Adil M. Y.
- Date created: 2021-09-06
- Date last modified: 2022-20-10
=#
using Pkg
using Plots ### if not instaled run: import Pkg; Pkg.add("Plots")
using DifferentialEquations ### if not instaled run: import Pkg; Pkg.add("DifferentialEquations")
using LinearAlgebra ### if not instaled run: import Pkg; Pkg.add("LinearAlgebra")
using CSV ### if not instaled run: import Pkg; Pkg.add("CSV")
using DataFrames ### if not instaled run: import Pkg; Pkg.add("DataFrames")
# Simulation time
tmax = 850
# Number of locations (location index l = 1 -> Schleswig-Hoöstein, l = 2 -> Saxony)
r = 2
# Number of vaccines
V = 3
# Number of aga strata
s = 4
# Number of variants
M = 3
# Matrix of sub-populaitioon sizes r x s matrix (rows: location), (columns: age groups)
PopSize =[129579 400794 1498110 909046; # Schleswig Holstein
180370 533194 1970270 1401510] # Saxony
# Total Population size
N = sum(PopSize)
# Initial infections vector of length r
ininf=[[ 0. ; 0. ; 0.5 ; 0.],
[ 0. ; 0. ; 0.5 ; 0.]]
# Erlang states
nE = [5 5 5; 5 5 5; 5 5 5; 5 5 5] # Matrix of latent Erlang states per age group (row) and viral variant (col)
nP = [5 5 5; 5 5 5; 5 5 5; 5 5 5] # Matrix of prodromal Erlang states per age group (row) and viral variant (col)
nI = [5 5 5; 5 5 5; 5 5 5; 5 5 5] # Matrix of fully infectious Erlang states per age group (row) and viral variant (col)
nL = [5 5 5; 5 5 5; 5 5 5; 5 5 5] # Matrix of late infectious Erlang states per age group (row) and viral variant (col)
# Durations of disease stages
DE = [3.5 3.5 3.5; 3.5 3.5 3.5; 3.5 3.5 3.5; 3.5 3.5 3.5] # Duration in latent phase per age group (row) and viral variant (col)
DP = [1.0 1.0 1.0; 1.0 1.0 1.0; 1.0 1.0 1.0; 1.0 1.0 1.0] # Duration in prodromal phase per age group (row) and viral variant (col)
DI = [5.0 5.0 5.0; 5.0 5.0 5.0; 5.0 5.0 5.0; 5.0 5.0 5.0] # Duration in infectious phase per age group (row) and viral variant (col)
DL = [5.0 5.0 5.0; 5.0 5.0 5.0; 5.0 5.0 5.0; 5.0 5.0 5.0] # Duration in late infectious phase per age group (row) and viral variant (col)
# Infectiousness at disease stages
cP = [0.5, 0.5, 0.5] # Contagiousness for prodromal per viral variant
cI = [1.0, 1.0, 1.0] # Contagiousness for fully infectious per viral variant
cL = [0.5, 0.5, 0.5] # Contagiousness for late infectious per viral variant
# Basic reproduction number
R0 = [3., 3*1.3, 3*1.3*1.4] # Vector of size M
tR0max = 300.0 # Time at which the seasonal fluctuation of R0 reaches its maximum
Amp = 0.43 # Seasonal amplitude
lamex = [1.0 1.3] # External force of infection (this will be split to the age groups in the respective locations according to their contact behavior)
# Time each viral variant was introduced in each location rxM matrix
mutint = [-20 290 475 ; -20 290 475]
# Severity of infection
## Fraction of sick individuals per age group (row) and viral variant (col) sxM Matrix
fsick = [0.15 0.15 0.15; 0.30 0.30 0.30; 0.65 0.65 0.65; 0.7 0.7 0.7]
## Fraction of partially immunized sick individuals per age group (row) and viral variant (col) sxM Matrix
fsickPI = [[0.10 0.11 0.10; 0.11 0.12 0.11; 0.12 0.13 0.12 ],
[0.25 0.22 0.25; 0.26 0.23 0.26; 0.27 0.24 0.27 ],
[0.55 0.60 0.55; 0.56 0.61 0.56; 0.57 0.62 0.57 ],
[0.60 0.60 0.60; 0.60 0.60 0.60; 0.60 0.60 0.60 ]]
## Fraction of dead individuals per age group (row) and viral variant (col) sxM Matrix
fdead = [0.0001 0.0002 0.0004; 0.0001 0.0002 0.0004; 0.0010 0.0011 0.0012; 0.24 0.24 0.24]
## Fraction of dead partially immunized individuals per age group (vector-element): entry is MxV Matrices per viral variant (row) and vaccine (col))
fdeadPI = [[0.0 0.0 0.0 ; 0.0 0.0 0.0 ;0.0 0.0 0.00],
[5.0e-6 5.5e-6 5.0e-6 ; 1.0e-5 1.6e-5 1.0e-5 ;2.0e-5 2.5e-5 2.0e-5],
[0.000055 0.00006 0.000055; 0.000055 0.00006 0.000055;0.000055 0.00006 0.000055],
[0.004 0.0045 0.004 ; 0.004 0.0045 0.004 ;0.004 0.0045 0.004 ]]
# Fraction of sick individuals that die
fsickdead = fsick .* fdead
# Fraction of partially immunized sick individuals that die per age group
fsickdeadPI = fsickPI
for a = 1:s
fsickdeadPI[a] = fsickPI[a] .* fdeadPI[a]
end
# Vaccination onset
# Array of dimension V (number of vaccines prducts) x s (age strata) x l (locations) describes when the VC start, per age group (row) and location (col)
tvax= [[ 850 490 400 310 ],
[850 850 400 360 ],
[850 850 430 430 ]]
## Waiting time for vaccination
## Vector of size V (number of vaccines) - in each entry r x s matrix with location (row) and age group (col)
## If vaccination rate changes for any vaccine, location, or age group the vector needs to be redefined
Dvax1= [[ 1 1 1 280 ; 1 1 1 280 ],
[ 1 1 1 1 ; 1 1 1 1 ],
[ 1 1 1 1 ; 1 1 1 1 ]]
Dvax2= [[ 1 1 1 160 ; 1 1 1 160 ],
[ 1 1 1 400 ; 1 1 1 400],
[ 1 1 1 1 ; 1 1 1 1 ]]
Dvax3= [[ 1 1 240 160 ; 1 1 240 160],
[ 1 1 240 400 ; 1 1 240 400],
[ 1 1 1 1 ; 1 1 1 1 ]]
Dvax4= [[ 1 1 240 140 ; 1 1 240 140 ],
[ 1 1 240 340 ; 1 1 240 340 ],
[ 1 1 240 400 ; 1 1 240 400 ]]
Dvax5= [[ 1 170 220 140 ; 1 170 220 140 ],
[ 1 1 360 380 ; 1 1 360 380 ],
[ 1 1 240 400 ; 1 1 240 400]]
## Vector of waiting times for vaccination
Dvaxlist = [Dvax1, Dvax2, Dvax3, Dvax4, Dvax5, Dvax5]
## Times vaccination rates change corresponding to matrices Dvax1, ...,Dvax5
tvaxchange = [360, 400, 430, 490, 590]
# Vector with proportion of vaccinable individuals per location and entries being vectors of length s (age groups)
propvax = [[0.0 ; 0.35 ; 0.90 ; 0.95],
[0.0 ; 0.25 ; 0.70 ; 0.85]]
# Vaccine effect for each vaccine: fS [fS(Im), fS(PI), fS(NI)], fE [fE(Inf), fE(PI)], fE(NI)] , fP, ... as vector of length V with entries being 5 x 3 matrices (rows stages, columns IM, PI, NI)
f= [[0.25 0.7 0.05; 0. 0.5 0.5; 0. 0.5 0.5; 0. 0.5 0.5; 0. 0.5 0.5],
[0.3 0.65 0.05; 0. 0.5 0.5; 0. 0.5 0.5; 0. 0.5 0.5; 0. 0.5 0.5],
[0.3 0.65 0.05; 0. 0.5 0.5; 0. 0.5 0.5; 0. 0.5 0.5; 0. 0.5 0.5]]
# Waiting time for vaccine to immunize for age strata (rows) and vaccines (cols)
DA = [30 50 15; 30 50 15; 30 50 15; 30 50 15]
# Vaccine protection from variants (MxV Matrix with viral variants (row), vaccine (col)
g = [0.66 0.66 0.66; 0.70 0.70 0.70; 0.70 0.70 0.70]
h = [0.0 0.0 0.0 ; 0.0 0.0 0.0 ; 0.0 0.0 0.0]
## Effect of partial immunity on transmission
## During prodromal phase m x v matrix
pPmv = [ 0.66 0.70 0.66
0.66 0.70 0.66
0.66 0.70 0.66]
## During fully infectious phase m x v matrix
pImv = [ 0.66 0.70 0.66
0.66 0.70 0.66
0.66 0.70 0.66]
## During late infectious phase m x v matrix
pLmv = [ 0.66 0.70 0.66
0.66 0.70 0.66
0.66 0.70 0.66]
#############################
## Case isolation
#############################
Qmax = [200 200] # Vector of length r: maximum capacity per location per 100.000
fiso = [0.65 0.65] # Probability of being isolated per location, vector of length r
tiso1 = [10. 10.] # Time isolation starts per location
tiso2 = [tmax tmax] # Time isolation ends per location
phome = 0.75 # Contacts prevented at home islolation
#############################
# General contact reduction
## The contact matrix and the contact reductions need to be implemented to generate the contact matrices X(t),
## this can be done individuzally and the code hence needs to be adjusted properly.
##t0 = 0.0 -> Feb. 25, 2020 - First reported case in Germany.
#############################
## Times for weather adjustment
tw1 = 380 # Mar. 11, 2021
tw2 = 430 # Apr. 30, 2021
tw3 = 520 # Jul. 29, 2021
tw4 = 540 # Aug. 18, 2021
## Weather adjustment
w_adj = [20, -30]
## Times contact reductions change (NN such time points) in both Schleswig-Holstein (SH) and Saxony (Sax)
t1 = 36. # Apr. 02, 2020 - First lockdown
t2 = 85. # May 20, 2020 - Relaxation
t3 = 97. # Jun. 01, 2020 - summer vacations (SH)
t3a = 137. # Jul. 11, 2020 - summer vacations
t4 = 170. # Aug. 13, 2020 - end summer vacations (SH)
t4a = 180. # Aug. 23, 2020 - end summer vacations (Sax)
t5 = 190. # Sep. 02, 2020 - week measures
t6 = 245. # Oct. 27, 2020 - soft lockdown
t7 = 280. # Dec. 01, 2020 - hard christmas lockdown
t8 = 303. # Dec. 24, 2020 -
t9 = 355. # Feb. 14, 2021 -
t10 = 425. # Apr. 25, 2021 - emergency break
t11 = 490. # Jun. 29, 2021 - End emergency break
t12 = 540 # Aug. 18, 2021 - 3G rule (SH)
t12a = 552 # Aug. 30, 2021 - 3G rule (Sax)
t13 = 621 # Nov. 07, 2021 - 2G rule
t14 = 636 # Nov. 22, 2021 - hypothetical school closures
t15 = tmax # End of simulation
## Interval of school vacation (summer vacation)
tschool = [501 537; 866 904; 1100 1150]
## Time Emergency Break (EB) starts
tEB = t10
## Time emergency break ends
tEBstop = t11
## Time Emergency Break (EB) starts again (use for hypothetical roll back of EB)
tEB2 = tmax
## Time emergency break stops again
tEBstop2 = tmax
## Breaking time of general contact reductions
conttime = copy([0, t1, t2, t3, t3a, t4, t4a, t5, t6, t7, t8, t9, t10, t11, t12, t12a, t13, t14, t15])
## Contact reduction per break point for Home, Others, School, Work
## NN x 6 matrix with amount of contacts being reduced Home, Home_old (oldest age group), Others, Others_old (Oldest age group), School, Work at various time points
## Contact reductions SChleswig-Holstein
ContRedl1 = [0.35 0.05 0.80 0.2 0.90 0.6; #t1: Apr. 01, 2020 - First lockdown
0.15 0.05 0.60 0.20 0.75 0.40; #t2: May 20, 2020 - Relexation
0.00 0.00 0.50 0.10 1.00 0.20; #t3: Jun. 01, 2020 - summer vacations (SH)
0.00 0.00 0.50 0.10 1.00 0.20; #t3a: Jul. 11, 2020 - summer vacations (Sax)
0.10 0.00 0.60 0.20 0.5 0.40; #t4: Aug. 13, 2020 - end summer vctations (SH)
0.10 0.00 0.60 0.20 0.5 0.40; #t4a: Aug. 23, 2020 - end summer vctations (Sax)
0.15 0.15 0.7 0.2 0.75 0.60; #t5: Sep. 02, 2020 - week measures
0.30 0.20 0.7 0.6 1.0 0.70; #t6: Oct. 27, 2020 - soft lockdown
0.30 0.20 0.80 0.6 1.0 0.70; #t7: Dec. 01, 2020 - hard christmas lockdown
0.35 0.25 0.85 0.75 1.00 0.85; #t8: Dec. 24, 2020 -
0.25 0.20 0.7 0.6 0.75 0.75; #t9: Feb. 14, 2021 -
0.00 0.00 0.0 0.0 0.0 0.00; #t10: Apr. 25, 2021 - emergency break
0.10 0.05 0.50 0.30 0.50 0.25; #t11: Jun. 29, 2021 - End emergency break
0.35 0.15 0.85 0.40 0.75 0.80; #t12: Aug. 13, 2021 - 3G rule (SH)
0.35 0.15 0.85 0.40 0.75 0.80; #t12a: Aug. 23, 2021 - 3G rule (Sax)
0.30 0.15 0.85 0.40 0.75 0.80; #t13: Nov. 07, 2021 - 2G rule
0.30 0.15 0.85 0.40 0.75 0.80; #t14: Nov. 22, 2021 - hypothetical schools closed
0.30 0.15 0.85 0.40 0.75 0.80] #t15: End of simulation
## Contact reductions Saxony
ContRedl2 = [0.25 0.05 0.80 0.20 0.90 0.75; #t1: Apr. 01, 2020 - First lockdown (SH)
0.15 0.05 0.60 0.20 0.75 0.50; #t2: May. 20, 2020 - Relexation
0.15 0.05 0.60 0.20 0.75 0.50; #t3: Jun. 01, 2020 - summer vacations (SH)
0.00 0.00 0.40 0.10 1.00 0.20; #t3a: Jul. 11, 2020 - summer vacations (For Saxony)
0.00 0.00 0.40 0.10 1.00 0.20; #t4: Aug. 13, 2020 - end summer vctations (SH)
0.10 0.00 0.40 0.10 0.75 0.35; #t4a: Aug. 23, 2020 - end summer vctations (For Saxony)
0.10 0.15 0.5 0.2 0.75 0.40; #t5: Sep. 02, 2020 - week measures
0.25 0.20 0.7 0.6 1.0 0.70; #t6: Oct. 27, 2020 - soft lockdown
0.30 0.20 0.80 0.6 1.0 0.75; #t7: Dec. 01, 2020 - hard christmas lockdown
0.40 0.35 0.90 0.75 1.00 0.85; #t8: Dec. 24, 2020 -
0.15 0.20 0.6 0.30 0.75 0.55; #t9: Feb. 14, 2021 -
0.00 0.00 0.00 0.00 0.00 0.00; #t10: Apr. 25, 2021 - Emergency break
0.10 0.05 0.50 0.30 0.50 0.25; #t11: Jun. 29, 2021 - End emergency break
0.10 0.05 0.50 0.30 0.50 0.25; #t12: Aug. 13, 2021 - 3G rule (SH)
0.30 0.15 0.75 0.40 0.75 0.65; #t12a: Aug. 23, 2021 - 3G rule (For Saxony)
0.30 0.15 0.75 0.40 0.75 0.70; #t13: Nov. 07, 2021 - 2G rule
0.30 0.15 0.75 0.40 0.75 0.70; #t14: Nov. 22, 2021 - hypothetical schools closed
0.30 0.15 0.75 0.40 0.75 0.70] #t15: End of simulation
## Incidence threshold values (per 100,000) triggering EB contact reductions (NN1 time points)
Incid_Trig = [10.0, 50.0, 100.0, 180.0]
## Incidence based contact reductions for emergency break ((NN1+1) x 6 matrix)
ContRedIndl1 = [ 0.00 0.00 0.50 0.10 0.25 0.30;
0.25 0.05 0.60 0.20 0.50 0.55;
0.30 0.10 0.85 0.60 0.75 0.65;
0.40 0.20 0.95 0.75 0.75 0.85;
0.40 0.35 0.95 0.75 1.00 0.85]
# Contact reductions -- each row corresp. to one time break point
ContRedIndl2 = [ 0.00 0.00 0.50 0.10 0.00 0.10;
0.25 0.05 0.60 0.20 0.50 0.55;
0.30 0.10 0.75 0.60 0.75 0.60;
0.40 0.20 0.80 0.60 0.75 0.70;
0.40 0.35 0.90 0.70 1.0 0.85] # Contact reductions -- each row corresp. to one time break point
# Contact behavior (case of Schleswig-Holstein & Saxony)
## Contacts at home
XHome = [[57182.980566158 43021.4787255984 224322.150383509 7446.1535646188;
43021.4787255984 379370.801549785 624597.388617006 26625.2175224807;
224322.150383509 624597.388617006 1776834.58696149 118774.7602034845;
7446.1535646188 26625.2175224807 118774.7602034845 0.0], # SH
[79596.9578768004 59670.1545553057 316718.948302366 10879.2828759017;
59670.1545553057 498783.452279101 857476.742458246 37149.740100271;
316718.948302366 857476.742458246 2300267.00642317 167112.764198724;
10879.2828759017 37149.740100271 167112.764198724 0.0]] # Sax
## Contacts at home for elderlies (60+ years)
XHomeOld = [[0.0 0.0 0.0 0.0;
0.0 0.0 0.0 0.0;
0.0 0.0 0.0 118774.7602034845;
0.0 0.0 118774.7602034845 596735.273075845], # SH
[0.0 0.0 0.0 0.0;
0.0 0.0 0.0 0.0;
0.0 0.0 0.0 167112.764198724;
0.0 0.0 167112.764198724 929687.783717516]] # Sax
## Contacts at other places
XOthers = [[66995.5203024599 42793.7453631786 169869.314815012 48051.0137233581;
42793.7453631786 554486.415402645 431019.891346432 87809.1926752048;
169869.314815012 431019.891346432 2721693.85772205 364259.230987248;
48051.0137233581 87809.1926752048 364259.230987248 0.0], # SH
[93255.712707728 58506.6810461036 225611.786474497 71708.4624301757;
58506.6810461036 720841.254898603 558368.007685395 128927.44601176;
225611.786474497 558368.007685395 3590070.11109356 508889.14474428;
71708.4624301757 128927.44601176 508889.14474428 0.0]] # Sax
## Contacts at other places for elderlies (60+ years)
XOthersOld = [[0.0 0.0 0.0 0.0;
0.0 0.0 0.0 0.0;
0.0 0.0 0.0 364259.230987248;
0.0 0.0 364259.230987248 623116.499388776], # SH
[0.0 0.0 0.0 0.0;
0.0 0.0 0.0 0.0;
0.0 0.0 0.0 508889.14474428;
0.0 0.0 508889.14474428 938471.397922117] # Sax
]
## contact in schools
XSchool = [[172012.212131109 36706.3010421756 39840.225707455 1.00596813447136e-61;
36706.3010421756 549815.334488166 340758.175881302 11634.0815791544;
39840.225707455 340758.175881302 218292.24073141 2162.61699834293;
1.00596813447136e-61 11634.0815791544 2162.61699834293 4028.52342131705], # SH
[239435.731886248 48269.3527789394 58055.4103544699 1.40027683818057e-61;
48269.3527789394 717540.837032603 430805.120551977 16965.0358447184;
58055.4103544699 430805.120551977 278508.169137414 3282.90903617846;
1.40027683818057e-61 16965.0358447184 3282.90903617846 6880.9276104271]] # Sax
## contacts at work
XWork = [[0.0 0.0 0.0 1.69321587350173e-37;
0.0 94714.980163013 200768.524913529 729.622036802347;
0.0 200768.524913529 4779074.03812527 24296.6296756034;
1.69321587350173e-37 729.622036802347 24296.6296756034 252.854648862366], # SH
[0.0 0.0 0.0 2.35690464584158e-37;
0.0 113681.13069066 249481.133139123 912.003442533374;
0.0 249481.133139123 6451490.20291225 33713.5321437912;
2.35690464584158e-37 912.003442533374 33713.5321437912 372.325133342623]] # Sax
## Fraction of general contacts reduced at home, others, school, work at each breaking point
redu=[vcat([0 0 0 0 0 0],ContRedl1,[0 0 0 0 0 0]),vcat([0 0 0 0 0 0],ContRedl2,[0 0 0 0 0 0])]
## Fraction of contacts reduced during emergency break at home, others, school, work at each breaking point
reduinz=[ContRedIndl1,ContRedIndl2]
# General contact reduction
## Proportion of the population per location moving to work at given location
## sxs matrix a_kl prop. of pop. that moves from loc k to l for work
mobilwork = [0.99 0.01;
0.01 0.99]
# Proportion of the population moving to others (vacation, etc.) per location
## sxs matrix a_kl prop. of pop. that moves from loc k to l for others purposes (vacation, etc.)
mobilother = [1.0 0.0;
0.0 1.0]
Xmat = Array{Union{Missing, Any}}(missing, length(conttime))
XmatEB = Array{Union{Missing, Any}}(missing, (length(Incid_Trig)+1)^r)
XmatNoSch= Array{Union{Missing, Any}}(missing, (length(Incid_Trig)+1)^r)
for t = 1:length(conttime)
Contmat = zeros(s*r,s*r)
for l in 1:r
A = XHome[l] .* (1-redu[l][t,1])+ XHomeOld[l] .* (1-redu[l][t,2])+ XOthers[l] .* (1-redu[l][t,3]) .* mobilother[l,l]+ XOthersOld[l] .* (1-redu[l][t,4]) .* mobilother[l,l]+ XSchool[l] .* (1-redu[l][t,5]) + XWork[l] .* (1-redu[l][t,6]) .* mobilwork[l,l]
Contmat[(l-1)*s+1:l*s,(l-1)*s+1:l*s] = N^2 ./(repeat(PopSize[l,1:s],inner=(1,s)) .* repeat(PopSize[l,1:s],inner=(1,s))') .*A
for m in (l+1):r
B = XOthers[l] .* (1-redu[l][t,3]) .* mobilother[l,m] + XOthersOld[l] .* (1-redu[l][t,4]) .* mobilother[l,m] + XWork[l] .* (1-redu[l][t,6]) .* mobilwork[l,m]
C = XOthers[m] .* (1-redu[m][t,3]) .* mobilother[m,l] + XOthersOld[m] .* (1-redu[m][t,4]) .* mobilother[m,l] + XWork[m] .* (1-redu[m][t,6]) .* mobilwork[m,l]
C1 = (B+C)/2
C1 = N^2 .* C1 ./ (repeat(PopSize[l,1:s],inner=(1,s)) .* repeat(PopSize[m,1:s],inner=(1,s))')
Contmat[(l-1)*s+1:l*s,(m-1)*s+1:m*s] = C1
Contmat[(m-1)*s+1:m*s,(l-1)*s+1:l*s] = C1'
end
end
Xmat[t] = Contmat
end
inctr = (length(Incid_Trig)+1)
AA = zeros(Int64, inctr^r,r)
AA[1:inctr,1] = 1:inctr
for l = 2:r
AA[1:inctr^l,1:(l-1)] = repeat(AA[1:inctr^(l-1),1:(l-1)],outer=(inctr,1))
AA[1:inctr^l,l] = repeat(1:inctr,inner=inctr^(l-1))
end
base = inctr .^(0:(r-1))
# Contact reduction for emergency break (EB)
for t = 1:inctr^r
ind = AA[t,:]
Contmat = zeros(s*r,s*r)
for l in 1:r
A = XHome[l] .* (1-reduinz[l][ind[l],1])+ XHomeOld[l] .* (1-reduinz[l][ind[l],2])+ XOthers[l] .* (1-reduinz[l][ind[l],3]) .* mobilother[l,l]+ XOthersOld[l] .* (1-reduinz[l][ind[l],4]) .* mobilother[l,l]+ XSchool[l] .* (1-reduinz[l][ind[l],5]) + XWork[l] .* (1-reduinz[l][ind[l],6]) .* mobilwork[l,l]
Contmat[(l-1)*s+1:l*s,(l-1)*s+1:l*s] = N^2 ./(repeat(PopSize[l,1:s],inner=(1,s)) .* repeat(PopSize[l,1:s],inner=(1,s))') .*A
for m in (l+1):r
a = max(ind[l],ind[m])
if a ==inctr ### if maximum incidence is surpassed 20 km restriction area, only work related travel
B = XWork[l] .* (1-reduinz[l][a,6]) .* mobilwork[l,m]
C = XWork[m] .* (1-reduinz[m][a,6]) .* mobilwork[m,l]
else
B = XOthers[l] .* (1-reduinz[l][a,3]) .* mobilother[l,m] + XOthersOld[l] .* (1-reduinz[l][a,4]) .* mobilother[l,m] + XWork[l] .* (1-reduinz[l][a,6]) .* mobilwork[l,m]
C = XOthers[m] .* (1-reduinz[m][a,3]) .* mobilother[m,l] + XOthersOld[m] .* (1-reduinz[m][a,4]) .* mobilother[m,l] + XWork[m] .* (1-reduinz[m][a,6]) .* mobilwork[m,l]
end
C1 = (B+C)/2
C1 = N^2 .* C1 ./ (repeat(PopSize[l,1:s],inner=(1,s)) .* repeat(PopSize[m,1:s],inner=(1,s))')
Contmat[(l-1)*s+1:l*s,(m-1)*s+1:m*s] = C1
Contmat[(m-1)*s+1:m*s,(l-1)*s+1:l*s] = C1'
end
end
XmatEB[t] = Contmat
end
# Contact reduction during EB assuming no school (Summer vacations)
for t = 1:inctr^r ## no school
ind = AA[t,:]
Contmat = zeros(s*r,s*r)
for l in 1:r
A = XHome[l] .* (1-reduinz[l][ind[l],1])+ XHomeOld[l] .* (1-reduinz[l][ind[l],2])+ XOthers[l] .* (1-reduinz[l][ind[l],3]) .* mobilother[l,l]+ XOthersOld[l] .* (1-reduinz[l][ind[l],4]) .* mobilother[l,l] + XWork[l] .* (1-reduinz[l][ind[l],6]) .* mobilwork[l,l]
Contmat[(l-1)*s+1:l*s,(l-1)*s+1:l*s] = N^2 ./(repeat(PopSize[l,1:s],inner=(1,s)) .* repeat(PopSize[l,1:s],inner=(1,s))') .*A
for m in (l+1):r
a = max(ind[l],ind[m])
if a ==inctr ### if maximum incidence is surpassed 20 km restriction area, only work related travel
B = XWork[l] .* (1-reduinz[l][a,6]) .* mobilwork[l,m]
C = XWork[m] .* (1-reduinz[m][a,6]) .* mobilwork[m,l]
else
B = XOthers[l] .* (1-reduinz[l][a,3]) .* mobilother[l,m] + XOthersOld[l] .* (1-reduinz[l][a,4]) .* mobilother[l,m] + XWork[l] .* (1-reduinz[l][a,6]) .* mobilwork[l,m]
C = XOthers[m] .* (1-reduinz[m][a,3]) .* mobilother[m,l] + XOthersOld[m] .* (1-reduinz[m][a,4]) .* mobilother[m,l] + XWork[m] .* (1-reduinz[m][a,6]) .* mobilwork[m,l]
end
C1 = (B+C)/2
C1 = N^2 .* C1 ./ (repeat(PopSize[l,1:s],inner=(1,s)) .* repeat(PopSize[m,1:s],inner=(1,s))')
Contmat[(l-1)*s+1:l*s,(m-1)*s+1:m*s] = C1
Contmat[(m-1)*s+1:m*s,(l-1)*s+1:l*s] = C1'
end
end
XmatNoSch[t] = Contmat
end
###############################################################
###### Derived parameters
###############################################################
# Maximum capacity per 100,000 per location
Qmax = Qmax .* sum(PopSize,dims=2) ./100000 # maximum capacity per 100000 per location
X = copy(Xmat[1])
lamexvec = zeros(r,s)
for l = 1:r
XX = copy(Xmat[1])[((1:s) .+(l-1)*s),((1:s) .+(l-1)*s)]
lamexvec[l,:] = (zeros(s) .+1)*lamex[l]
end
mutinttimes = sort(unique(collect(Iterators.flatten(mutint))))
lamexmat = fill(zeros(r,s,M), length(mutinttimes))
for t=1:length(mutinttimes)
pick= sum(mutint .<= mutinttimes[t],dims=2)
lamexmat0=zeros(r,s,M)
for l=1:r
lamexmat0[l,:,pick[l]] = collect(Iterators.flatten(lamexvec[l,:] .* N ./PopSize[l,:]))
end
lamexmat[t]= lamexmat0
end
lamexmat[2] =lamexmat[2] ./2
lamexmat[3] =lamexmat[3]
# Rates beta
cPmat = repeat(cP,inner=(1,s))'
cImat = repeat(cI,inner=(1,s))'
cLmat = repeat(cL,inner=(1,s))'
betaP = cPmat
betaI = cImat
betaL = cLmat
nEP = nE + nP
nEPI = nEP + nI
nEPIL = nEPI + nL
# Number of infected, dead, and recoverd compartments per age
CnumInf = sum(nEPIL .*(2*(V+1)).+2,dims=2)
# Total Number of compartments per age
Cnum = sum(nEPIL .*(2*(V+1)).+2,dims=2) .+(3*V+2)
# Erl[s+1] number of compartments for each location
Erl = accumulate(+,[0 transpose(Cnum)])
# Matrix with indices of S(U) per age group (row) per loction (col)
IndSU = repeat(transpose(collect(0:(r-1))).*Erl[s+1],outer=(s,1))
IndSU = IndSU .+ repeat(Erl[1:s].+1,outer=(1,r))
# Index where the first Erlang states start
Erl1 = accumulate(+,[0 transpose(Cnum)])[1:s] .+(3*V+3)
IndE1Uam = zeros(Int64,s,M,r)
for l = 1:r
IndE1Uam[1:s,1:M,l] = hcat(zeros(Int64, s,1), accumulate(+,nEPIL .*(2*(V+1)).+2,dims=2))[:,1:M] .+ Erl1 .+ (l-1)*Erl[s+1]
end
#Index of states E1Uaml
# Arrays of transition rates for (U) compartments
rates = Array{Union{Missing, Any}}(missing, s, M)
for a = 1:s
local delta
for m = 1:M
eps1 = nE[a,m] .*repeat([1/DE[a,m]],nE[a,m])
phi = nP[a,m] .*repeat([1/DP[a,m]],nP[a,m])
gamma = nI[a,m] .*repeat([1/DI[a,m]],nI[a,m])
delta = nL[a,m] .*repeat([1/DL[a,m]],nL[a,m])
rates[a,m] = vcat(eps1, phi, gamma, delta)
end
end
# Next generation matrix
cPIL = Array{Union{Missing, Any}}(missing, s, M)
for a = 1:s
for m = 1:M
cEnew = repeat([0],nE[a,m])
cPnew = repeat([cP[m]],nP[a,m])
cInew = repeat([cI[m]],nI[a,m])
cLnew = repeat([cL[m]],nL[a,m])
cPIL[a,m] = vcat(cEnew, cPnew, cInew, cLnew)
end
end
R0new = zeros(M)
for m = 1:M
# Total number of states for variant m
nstat = nE[:,m]+nP[:,m]+nI[:,m]+nL[:,m]
nstat2 = accumulate(+, nstat)
nstat1 = accumulate(+, vcat(0,nstat)).+1
numstates = sum(nstat)
dimV = numstates*r
# Matrix V (transition rates)
dV = zeros((dimV,dimV))
# Matrix F (new infections)
dF = zeros((dimV,dimV))
for l = 1:r
for a = 1:s
ind1 = (l-1)*numstates + nstat1[a]
ind2 = (l-1)*numstates + nstat2[a]
ra = length(rates[a,m])
dV[ind1:ind2,ind1:ind2] = fill(0.,(ra,ra))+ Bidiagonal(-rates[a,m],rates[a,m][1:(ra-1)],:L)
for lt = 1:r
for at = 1:s
ind1t = (lt-1)*numstates + nstat1[at]
ind2t = (lt-1)*numstates + nstat2[at]
dF[ind1,ind1t:ind2t] = X[(l-1)*s+a,(lt-1)*s+at] .* cPIL[at,m]* PopSize[l,a] ./N
end
end
end
end
R0new[m] = R0[m]/maximum(map.(abs,eigvals(-dF*inv(dV))))*(1+Amp*cos(-2*pi*tR0max/365))
end
# Rates for vaccine effects to manifest
alpha = 1 ./DA
# Look up table for vaccination rates
vaxtime1 = unique(sort(collect(Iterators.flatten(tvax))))
vaxtime =unique(sort(collect(vcat(vaxtime1,tvaxchange))))
T = length(vaxtime)
vaxrates = Array{Union{Missing, Any}}(missing, T+1)
for t = 1:(T)
global tmp3
global tmp4
tmp1 = map(x -> x .< vaxtime[t], tvax)
idx_Dvax = sum(tvaxchange .< vaxtime[t])+1
Dvax = Dvaxlist[idx_Dvax]
tmp2 = map( y -> 1 ./y, Dvax)
tmp3 = map( (x,y) -> x.*y, tmp1,tmp2)
tmp4 = zeros((s,r,V))
for v= 1:V
tmp4[:,:,v] = tmp3[v]'
end
vaxrates[t] = tmp4
end
tmp4 = zeros((s,r,V))
tmp3 = map( x -> 1 ./x, Dvaxlist[length(Dvaxlist)])
for v= 1:V
tmp4[:,:,v] = tmp3[v]'
end
vaxrates[T+1] = tmp4
fratesS = Array{Float32}(undef, (V,3)) # Here, 3 because Im, PI, NI
frates = Array{Union{Missing, Any}}(missing, V)
IndE1 = Array{Union{Missing, Any}}(missing, r)
IndLnL = Array{Union{Missing, Any}}(missing, r)
IndRInf = Array{Int32}(undef, (s, M, r))
INDvec = Array{Union{Missing, Any}}(missing, r)
# Vector of indices for the prodromal, fully infectious, and late infectious indivisuals, respectively
INDvecP = Array{Union{Missing, Any}}(missing, r)
INDvecI = Array{Union{Missing, Any}}(missing, r)
INDvecL = Array{Union{Missing, Any}}(missing, r)
for l = 1:r
indage = Array{Union{Missing, Any}}(missing, s)
indP = Array{Union{Missing, Any}}(missing, s) # Indices for Prodromals per location r, all age groups a, and all strains M.
indI = Array{Union{Missing, Any}}(missing, s) # Indices for I per location
indL = Array{Union{Missing, Any}}(missing, s) # Indices for L per location
indE1l = Array{Union{Missing, Any}}(missing, s) # Indices for E1 per location
indLnLl = Array{Union{Missing, Any}}(missing, s) # Indices for LnL per location
for a = 1:s
indm = Array{Union{Missing, Any}}(missing, M)
indPm = Array{Union{Missing, Any}}(missing, M)
indIm = Array{Union{Missing, Any}}(missing, M)
indLm = Array{Union{Missing, Any}}(missing, M)
indE1la = Array{Union{Missing, Any}}(missing, M)
indLnLla = Array{Union{Missing, Any}}(missing, M)
for m = 1:M
indcomp = Array{Union{Missing, Any}}(missing, 2*V+2) # Number of compartments at a given disease state
indcompP = Array{Union{Missing, Any}}(missing, 2*V+2)
indcompI = Array{Union{Missing, Any}}(missing, 2*V+2)
indcompL = Array{Union{Missing, Any}}(missing, 2*V+2)
pick0 = IndE1Uam[a,m,l]:(IndE1Uam[a,m,l] + nEPIL[a,m]-1) ## Indices of all infected states
pick = (IndE1Uam[a,m,l]+1):(IndE1Uam[a,m,l] + nEPIL[a,m]-1) ## Indices of infected states starting from E2
pick1 = (IndE1Uam[a,m,l]):(IndE1Uam[a,m,l] + nEPIL[a,m]-2) ## Indices of infected states until L_nL
indcompabc = Array{Union{Missing, Any}}(missing, 5)
indcompabc[1] = pick0 .+ 0 .* (nEPIL[a,m])
indcompabc[2] = pick .+ 0 .* (nEPIL[a,m])
indcompabc[3] = pick1 .+ 0 .* (nEPIL[a,m])
indcompabc[4] = 1:(nEPIL[a,m]-1) .*1+.+ 0 .* (nEPIL[a,m]-1)
indcompabc[5] = 2:nEPIL[a,m] .+ 0 .* (nEPIL[a,m]-1)
indcomp[1] = indcompabc
indE1lam = Array{Union{Missing, Any}}(missing, 2*V+2)
indLnLlam = Array{Union{Missing, Any}}(missing, V+2)
indLnLlamPI = Array{Union{Missing, Any}}(missing, V)
indE1lam[1] = IndE1Uam[a,m,l]
indLnLlam[1] = IndE1Uam[a,m,l] + nEPIL[a,m]-1
pickP = (IndE1Uam[a,m,l] + nE[a,m]):(IndE1Uam[a,m,l] + nEP[a,m]-1) # Indices of the unvaccinated prodromals PU.
pickI = (IndE1Uam[a,m,l] + nEP[a,m]):(IndE1Uam[a,m,l] + nEPI[a,m]-1) # Indices of the unvaccinated fully infectious IU.
pickL = (IndE1Uam[a,m,l] + nEPI[a,m]):(IndE1Uam[a,m,l] + nEPIL[a,m]-1) # Indices of the the unvaccinated late infectious LU.
indcompP[1] = pickP # Indices of the unvaccinated prodromals PU.
indcompI[1] = pickI # Indices of the unvaccinated fully infectious IU.
indcompL[1] = pickL # Indices of the the unvaccinated late infectious LU.
for v in 2:(2*V+2)
indcompabc = Array{Union{Missing, Any}}(missing, 3)
indcompabc[1] = pick0 .+ (v-1) .* (nEPIL[a,m])
indcompabc[2] = pick .+ (v-1) .* (nEPIL[a,m])
indcompabc[3] = pick1 .+ (v-1) .* (nEPIL[a,m])
indcomp[v] = indcompabc
indE1lam[v] = IndE1Uam[a,m,l] .+ (v-1) .* (nEPIL[a,m])
indcompP[v] = pickP .+ (v-1) .* (nEPIL[a,m]) # Indices of the vaccinated prodromals PV.
indcompI[v] = pickI .+ (v-1) .* (nEPIL[a,m]) # Indices of the vaccinated fully infectious IV.
indcompL[v] = pickL .+ (v-1) .* (nEPIL[a,m]) # Indices of the vaccinated late infectious LV per vaccine
end
for v in 2:(V+1)
indLnLlam[v] = indE1lam[v] + nEPIL[a,m] -1
end
indLnLlam[V+2] = IndE1Uam[a,m,l] .+ (2*V+2) .* (nEPIL[a,m]) - 1
for v in 1:V
indLnLlamPI[v] = indE1lam[v+V+1] + nEPIL[a,m] -1
end
IndRInf[a,m,l] = IndE1Uam[a,m,l] + (2*V+2) * nEPIL[a,m]
indm[m] = indcomp
indE1la[m] = indE1lam
indLnLla[m] = [indLnLlam, indLnLlamPI]
indPm[m] = indcompP
indIm[m] = indcompI
indLm[m] = indcompL
end
indage[a] = indm # Indices per age group
indE1l[a] = indE1la
indLnLl[a] = indLnLla
indP[a] = indPm # Indices of prodromals per age
indI[a] = indIm # Indices of fully infectious per age
indL[a] = indLm # Indices of late infectious per age
end
INDvec[l] = indage
IndE1[l] = indE1l
IndLnL[l] = indLnLl
INDvecP[l] = indP
INDvecI[l] = indI
INDvecL[l] = indL
end
for v = 1:V
fratesS[v,:] = f[v][1,:]
rates1 = Array{Union{Missing, Any}}(missing, s, M)
for a = 1:s
for m = 1:M
# Transtition rates for latent, prodromal, fully infectious, and late infectious individuals respectively.
afE = repeat(transpose(f[v][2,:] ./DA[a,v]),outer=(nE[a,m],1))
afP = repeat(transpose(f[v][3,:] ./DA[a,v]),outer=(nP[a,m],1))
afI = repeat(transpose(f[v][4,:] ./DA[a,v]),outer=(nI[a,m],1))
afL = repeat(transpose(f[v][5,:] ./DA[a,v]),outer=(nL[a,m],1))
rates1[a,m] = vcat(afE, afP, afI, afL)
end
end
frates[v] = rates1
end
## Build matrix with values f for E1 compartments
fE1 = Array{Float32}(undef, (M,V)) # f3 = Im, PI, NI
for m = 1:M
for v = 1:V
fE1[m,v] = f[v][2,2]
end
end
# Death rates
global delta = nL ./DL
## Store model parameters
IND = [IndSU, IndE1Uam, IndE1, nEPIL, INDvec, IndLnL, IndRInf] # Indices for unvaccinated Susceptibles, Latents...
INDInf = [INDvecP, INDvecI, INDvecL] # Indices for infective individuals
RATES = [rates, alpha, vaxrates, vaxtime, fratesS, frates, fE1, fsickdead, delta, betaP, betaI, betaL] # rates
tspan=(0.,tmax)
thres = 1:1.:tmax # Callback incidence time points
pars = [N, g, h, R0new, Amp, tR0max]
plam = [INDInf] # Parameters for the force of infection
Idx_Incd = IndRInf[s,M,r]+1
ciso = [fiso,tiso1,tiso2] # Parameters for case isolation
p = [IND, RATES, pars, [Xmat, XmatEB, XmatNoSch, conttime, tEB, tEBstop, tEB2, tEBstop2], INDInf, lamexmat, thres, Idx_Incd, r, X, N, Incid_Trig, tschool, mutint,[pPmv,pImv,pLmv], PopSize,ciso]
##########################################################################
###### Main functions force of infection + implementation of ODE system
##########################################################################
## The force of infection
function lambda(u,INDInf,Qmax,ciso,betaP,betaI,betaL,R0new,Amp,X,tR0max,lamexmat,t,mutint,pPmv,pImv,pLmv, mutinttimes)
fiso, tiso1, tiso2 = ciso
EffInf=Array{Float32}(undef, (r*s,M)) # Effective number of infectious individuals per location age group and mutation
PsumU=Array{Float32}(undef, (r,s,M)) # Sum of the infective prodromal individuals
IsumU=Array{Float32}(undef, (r,s,M)) # Sum of the infective fully infectious individuals
LsumU=Array{Float32}(undef, (r,s,M)) # Sum of the infective late infectious individuals
PsumPIv=Array{Float32}(undef, (r,s,M,V)) # Sum of the infective prodromal individuals, Partially imunized inds stratified by vaccine
IsumPIv=Array{Float32}(undef, (r,s,M,V)) # Sum of the infective fully infectious individuals, Partially imunized inds stratified by vaccine
LsumPIv=Array{Float32}(undef, (r,s,M,V)) # Sum of the infective fully infectious individuals, Partially imunized inds stratified by vaccine
PsickU=Array{Float32}(undef, (r,s,M)) # Sum of the infective prodromal individuals
IsickU=Array{Float32}(undef, (r,s,M)) # Sum of the infective fully infectious individuals
LsickU=Array{Float32}(undef, (r,s,M))
PsickPIv=Array{Float32}(undef, (r,s,M,V)) # Sum of the infective prodromal individuals, Partially imunized inds stratified by vaccine
IsickPIv=Array{Float32}(undef, (r,s,M,V)) # Sum of the infective fully infectious individuals, Partially imunized inds stratified by vaccine
LsickPIv=Array{Float32}(undef, (r,s,M,V)) # Sum of the infective fully infectious individuals, Partially imunized inds stratified by vaccine
Ql = Array{Float32}(undef, (r)) # symptomatic individuals supposed to be isolated
for l = 1:r
Q = 0
for a = 1:s
for m = 1:M
Psum = 0
Isum = 0
Lsum = 0
Isick = 0
IsickPI = 0
Lsick = 0
LsickPI = 0
for v=1:(V+1) # Individuals waiting to be vaccinated (U) and vaccinated with pending outcome (V)
Psum = Psum + sum(u[INDvecP[l][a][m][v]])
Isum = Isum + sum(u[INDvecI[l][a][m][v]])
Lsum = Lsum + sum(u[INDvecL[l][a][m][v]])
end
# Not immunized (NI)
Psum = Psum + sum(u[INDvecP[l][a][m][2*V+2]])
Isum = Isum + sum(u[INDvecI[l][a][m][2*V+2]])
Lsum = Lsum + sum(u[INDvecL[l][a][m][2*V+2]])
Isick = Isum * fsick[a,m]
Lsick = Lsum * fsick[a,m]
for v=1:V # Partially immunized (PI)
v1 = v + V+1
PErl=sum(u[INDvecP[l][a][m][v1]]) # sum over Erlang states of P
PsumPIv[l,a,m,v] = PErl
IErl = sum(u[INDvecI[l][a][m][v1]]) # sum over the Erlang states of I
IsumPIv[l,a,m,v] = IErl
IsickPI = IsickPI + IErl * fsickPI[a][m,v]
IsickPIv[l,a,m,v] = IErl * fsickPI[a][m,v]
LErl = sum(u[INDvecL[l][a][m][v1]]) # sum over the Erlang states of L
LsumPIv[l,a,m,v] = LErl
LsickPI = LsickPI + LErl * fsickPI[a][m,v]
LsickPIv[l,a,m,v] = LErl * fsickPI[a][m,v]
end
PsumU[l,a,m] = Psum
IsumU[l,a,m] = Isum
LsumU[l,a,m] = Lsum
IsickU[l,a,m] = Isick # Symptomatic fully infectious individuals I
LsickU[l,a,m] = Lsick # Symptomatic late infectious individuals L
Q = Q + Isick + IsickPI + Lsick + LsickPI # sum of symptomatic individuals going to islolation
end
end
if tiso1[l] < t < tiso2[l]
caseiso = fiso[l]
Q = Q * fiso[l]
is = min(Qmax[l]/Q,1)
for a = 1:s
for m = 1 : M
tmp = (phome + is * (1-phome))* fiso[l]
a1 = sum(pPmv[m,:] .* PsumPIv[l,a,m,:])
a1 = betaP[a,m] * (PsumU[l,a,m] + a1)
a2 = sum((1 .- fsickPI[a][m,:] .* tmp) .* pImv[m,:] .* IsumPIv[l,a,m,:])
a2 = betaI[a,m] * (IsumU[l,a,m] - tmp * IsickU[l,a,m] + a2)
a3 = sum((1 .- fsickPI[a][m,:] .* tmp).* pLmv[m,:] .* LsumPIv[l,a,m,:])
a3 = betaL[a,m] * (LsumU[l,a,m] - tmp * LsickU[l,a,m] + a3)
EffInf[(l-1)*s+a,m] = a1 + a2 + a3
end
end
else
for a = 1:s
for m = 1 : M
a1 = sum(pPmv[m,:] .* PsumPIv[l,a,m,:])
a1 = betaP[a,m] * (PsumU[l,a,m] + a1)
a2 = sum( pImv[m,:] .* IsumPIv[l,a,m,:])
a2 = betaI[a,m] * (IsumU[l,a,m] + a2)
a3 = sum(pLmv[m,:] .* LsumPIv[l,a,m,:])
a3 = betaL[a,m] * (LsumU[l,a,m] + a3)
EffInf[(l-1)*s+a,m] = a1 + a2 + a3
end
end
end
end
lamex = lamexmat[sum(mutinttimes .<t)]
lam = zeros(r,s,M)
for m = 1:M
lam[:,:,m] = reshape(X * EffInf[:,m],s,r)' * R0new[m]
end
if tw1<t<tw2
t1=t-w_adj[1]
elseif tw3<t<tw4
t1=t-w_adj[2]
else
t1=t
end
lam = lam .* (1+Amp*cos(2*pi*(t1-tR0max)/365)) .+ (lamex)
lam
end
## Model - differential equations
function spatialmodel(du,u,p,t)
local delta
IndSU, IndE1Uam, IndE1U, nEPIL, INDvec, IndLnL, IndRInf = p[1]
rates, alpha, vaxrates, vaxtime, fratesS, frates, fE1, fsickdead, delta, betaP, betaI, betaL = p[2]
N, g, h, R0new, Amp, tR0max = p[3]
Xmat, XmatEB, XmatNoSch, conttime, tEB, tEBstop,tEB2, tEBstop2 = p[4]
INDInf = p[5]
X = p[10]
mutint = p[14]
pPmv,pImv,pLmv = p[15]
vrates = vaxrates[sum(vaxtime .< t)+1]
lamex = p[6]
ciso = p[17]
lam = lambda(u,INDInf,Qmax,ciso,betaP,betaI,betaL,R0new,Amp,X,tR0max,lamex,t,mutint,pPmv,pImv,pLmv, mutinttimes)/N
for l = 1:r
u[IndRInf[s,M,r]+1+l] = 0
for a = 1:s
# Susceptibles
du[IndSU[a,l]] = - u[IndSU[a,l]] * sum(lam[l,a,:]) - u[IndSU[a,l]] * sum(vrates[a,l,:])
# Incidence unvaccinated (U)
u[IndRInf[s,M,r]+1+l] += u[IndSU[a,l]]*sum(lam[l,a,:])
for v = 1:V
# Sa,l(V,v)
du[IndSU[a,l]+v] = u[IndSU[a,l]] * vrates[a,l,v] - u[IndSU[a,l]+v] * (alpha[a,v] + sum(lam[l,a,:]))
# Sa,l(PI,v)
du[IndSU[a,l]+v+V] = u[IndSU[a,l]+v] * fratesS[v,2] * alpha[a,v]- u[IndSU[a,l]+v+V] * (lam[l,a,:]'g[:,v])
# Sa,l(Im,v)
du[IndSU[a,l]+v+2*V] = u[IndSU[a,l]+v] * fratesS[v,1] * alpha[a,v]- u[IndSU[a,l]+v+2*V] * (lam[l,a,:]'h[:,v])
# Incidence vaccinated (V)
u[IndRInf[s,M,r]+1+l] += u[IndSU[a,l]+v]*sum(lam[l,a,:]) + u[IndSU[a,l]+v+V]*(lam[l,a,:]'g[:,v]) + u[IndSU[a,l]+v+2*V]*(lam[l,a,:]'h[:,v])
end
## Sa,l(NI)
du[IndSU[a,l]+3*V+1] = transpose(alpha[a,:] .*fratesS[:,3]) * u[(IndSU[a,l]+1) : (IndSU[a,l]+V)] - sum(lam[l,a,:]) * u[IndSU[a,l]+3*V+1]
# Incidence NI
u[IndRInf[s,M,r]+1+l] += sum(lam[l,a,:]) * u[IndSU[a,l]+3*V+1]
for m = 1:M
## E1uam
nusum = sum(vrates[a,l,:])
du[IndE1[l][a][m][1]] = lam[l,a, m] * u[IndSU[a,l]] - (rates[a,m][1] + nusum) * u[IndE1[l][a][m][1]]
#E1_a,l(m,V)
du[IndE1[l][a][m][2:(V+1)]] = lam[l,a, m] .* u[(IndSU[a,l]+1):(IndSU[a,l]+V)] .+ vrates[a,l,:] .*u[IndE1[l][a][m][1]] - (rates[a,m][1] .+ alpha[a,:]) .* u[IndE1[l][a][m][2:(V+1)]]
# ##E1_a,l(m,PI,v)
du[IndE1[l][a][m][(V+2):(2*V+1)]] = lam[l,a, m]* g[m,:] .* u[(IndSU[a,l]+1+V):(IndSU[a,l]+2*V)] + lam[l,a,m] * h[m,:] .* u[(IndSU[a,l]+1+2*V):(IndSU[a,l]+3*V)] .+ u[IndE1[l][a][m][2:(V+1)]] .* alpha[a,:] .* fE1[m,:] - rates[a,m][1] * u[IndE1[l][a][m][V+2:(2*V+1)]]
# ##E1_a,l(m,NI,v)
du[IndE1[l][a][m][2*V+2]] = lam[l,a, m] .* u[IndSU[a,l]+3*V+1] - u[IndE1[l][a][m][2*V+2]] * rates[a,m][1] + sum(alpha[a,:] .* fE1[m,:] .* u[IndE1[l][a][m][2:(V+1)]])
# Infected states
pick = INDvec[l][a][m]
ru = rates[a,m] .* u[pick[1][1]]
du[pick[1][2]] = ru[pick[1][4]] .- ru[pick[1][5]] .- nusum .* u[pick[1][2]] # E2(U) .. L_nL(U)
ru = rates[a,m] .* u[pick[2*V+2][1]]
du[pick[2*V+2][2]] = ru[pick[1][4]] - ru[pick[1][5]] # E2(NI) .. L_nL(NI)
RIm = zeros(nEPIL[a,m])
for v in 2:(V+1)
ru = rates[a,m] .* u[pick[v][1]]
du[pick[v][2]] = ru[pick[1][4]] - ru[pick[1][5]] + vrates[a,l,v-1] .* u[pick[v][2]] - alpha[a,v-1] .* u[pick[v][2]] # E2(V) .. L_nL(V)
fIm = frates[v-1][a,m][:,1] .* u[pick[v][1]]
fPI = frates[v-1][a,m][:,2] .* u[pick[v][1]]
fNI = frates[v-1][a,m][:,3] .* u[pick[v][1]]
ru = rates[a,m] .* u[pick[V+v][1]]
du[pick[V+v][2]] = ru[pick[1][4]] - ru[pick[1][5]] + fPI[pick[1][5]] # E2(PI) .. L_nL(PI)
du[pick[2*V+2][2]] = du[pick[2*V+2][2]] + fNI[pick[1][5]] # E2(NI) .. L_nL(NI)
RIm = RIm .+ fIm
end
# R_al (Im,m)
tmp = 1 .-fsickdeadPI[a][m,:]
du[IndRInf[a,m,l]] = sum(RIm) + (sum(u[IndLnL[l][a][m][1]]) * (1-fsickdead[a,m]) + u[IndLnL[l][a][m][2]]'tmp) .* delta[a,m]
# D_al (m)
du[IndRInf[a,m,l]+1] = ((sum(u[IndLnL[l][a][m][1]]) * fsickdead[a,m]) + u[IndLnL[l][a][m][2]]'fsickdeadPI[a][m,:]) .* delta[a,m]
end
end
end
du
end
# Callback/event at integer time points for triggered contact reductions
function integer_time_values_condition(u,t,integrator)
t in integrator.p[7]
end
function contact_reduction_affect!(integrator)
Sol_t = integrator.sol.t
Cur_t = integrator.t
Sol_u = integrator.sol.u
idx_orig = integrator.p[8]
xmatr = integrator.p[4]
tschool = integrator.p[13]
tEB = integrator.p[4][5]
tEBstop = integrator.p[4][6]
tEBstop2 = integrator.p[4][7]
tEBstop2 = integrator.p[4][8]
totPopSize = sum(integrator.p[16], dims=2)
if !(tEB <= Cur_t <= tEBstop || tEB2 <= Cur_t <= tEBstop2)