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KKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAo
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12Serif
SansSerif
METHOD RK4
STARTTIME = 0
STOPTIME=105248
DT = 0.25
DTOUT=1
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Serif SansSerif
d/dt(Sus_to_infn) = -force_of_infection *Sus_to_infn + New_entrants - m_rate*Sus_to_infn
d/dt(Latent_fast_prog_infn) = force_of_infection *Sus_to_infn
- rate_prim_dis_onset*Latent_fast_prog_infn - ave_rate_become_latent*Latent_fast_prog_infn
- m_rate*Latent_fast_prog_infn
d/dt(Latent_slow_prog) = + ave_rate_become_latent*Latent_fast_prog_infn + ave_rate_become_latent*Latent_fast_prog_reinfn
- force_of_infection *Latent_slow_prog
- rate_reactn_dis_onset*Latent_slow_prog
- m_rate*Latent_slow_prog
d/dt(Latent_fast_prog_reinfn) = force_of_infection *Latent_slow_prog + force_of_infection*Recovered
- rate_exog_dis_onset*Latent_fast_prog_reinfn - ave_rate_become_latent*Latent_fast_prog_reinfn
- m_rate*Latent_fast_prog_reinfn
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Serif SansSerif
d/dt(Smneg) = rate_reactn_dis_onset*prop_smneg*Latent_slow_prog + rate_prim_dis_onset*prop_smneg*Latent_fast_prog_infn
+ rate_exog_dis_onset*prop_smneg*Latent_fast_prog_reinfn
+ rate_relapse*prop_smneg*Recovered
- rate_natural_cure*Smneg - used_rate_detect_and_recover_smneg*Smneg
- m_rate*Smneg - m_rate_smneg*Smneg
d/dt(Smpos) = rate_reactn_dis_onset*prop_smpos*Latent_slow_prog + rate_prim_dis_onset*prop_smpos*Latent_fast_prog_infn
+ rate_exog_dis_onset*prop_smpos*Latent_fast_prog_reinfn
+ rate_relapse*prop_smpos*Recovered
- rate_natural_cure*Smpos - rate_detect_and_recover_smpos*Smpos
- m_rate*Smpos - m_rate_smpos*Smpos
d/dt(Recovered) = (used_rate_detect_and_recover_smneg+rate_natural_cure)*Smneg
+ (rate_detect_and_recover_smpos+rate_natural_cure)*Smpos
- rate_relapse*Recovered - force_of_infection*Recovered - m_rate*Recovered
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Serif
SansSerif
INIT Sus_to_infn = total_popn-Latent_fast_prog_infn-Latent_slow_prog-Latent_fast_prog_reinfn - Smneg - Smpos - Recovered
; Number of individuals who have never been infected in the population at the start
INIT Latent_fast_prog_infn = 10 ; Number of individuals who have been recently infected in the population at the start.
; These individuals face a high risk of developing (primary) disease, before
; experiencing the low risk of disease through reactivation, in the absence of reinfection.
; The average time period after infection or reinfection during which the high risk is experienced
; is determined by the value of ave_period_initial_high_dis_risk
INIT Latent_slow_prog = 10 ; Number of individuals with "latent" infection in the population at the start. Individuals with latent
; infection can develop disease either through reactivation or following reinfection and have
; passed through the period of high risk of (primary) disease following initial infection.
INIT Latent_fast_prog_reinfn = 10 ; Number of individuals with "recent" reinfection in the population at the start. These individuals face a
; high risk of developing (exogenous) disease, before experiencing the low risk of disease through
; reactivation
INIT Smneg = 50 ; Number of individuals with undetected smear-negative disease in the population at the start.
INIT Smpos = 50 ; Number of individuals with undetected smear-positive disease in the population at the start.
INIT Recovered = 10 ; Number of individuals who have recovered from TB disease in the population at the start.
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Serif SansSerif
force_of_infection = (ecr*Smneg*rel_infousness_smneg + ecr*Smpos)/sum_pop
; Force of infection, defined as the rate at which uninfected individuals and those in the latent category
; are infected and reinfected respectively.The force of infection is calculated using the numbers
; of smear-positive and smear-negative cases and the average number of individuals
; effectively contacted by each person per week. Smear-positive cases are assumed to be more
;likely to transmit infection than smear-negative cases. The relative infectiousness of smear-negative
; cases, compared to those who are smear-positive is determined by the value of
; rel_infousness_smneg
ann_force_of_infection = force_of_infection*tsteps_pyr ; Annual force of infection
ann_risk_of_infection=ann_force_of_infection*100
ecr_pyr = 15 ; Average number of individuals that would be effectively contacted by each smear-positive person
; during 1 year
ecr = ecr_pyr/tsteps_pyr ; average number of individuals effectively contacted by each person per time step
ave_rate_become_latent = 1/ave_period_initial_high_dis_risk
; average rate at which individuals move from the initial high risk of developing disease after
; infection to the low rate of developing disease (through reactivation)
rel_infousness_smneg = 0.22 ; Infectiousness of smear-negative cases, compared to smear-positive cases
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Serif SansSerif
ave_period_initial_high_dis_risk_yrs = 5 ; average duration (years) during which individuals experience increased disease risk after infection
; or reinfection
ave_period_initial_high_dis_risk = ave_period_initial_high_dis_risk_yrs*tsteps_pyr
; average duration during which individuals experience increased disease risk after infection
; or reinfection
dp_pyr = 0.03 ; annual rate of disease onset following initial infection
prot_init_infn_vs_reinfn = 0.65 ; protection provided by previous infection against disease following reinfection
dx_pyr = dp_pyr*(1-prot_init_infn_vs_reinfn) ; annual rate of disease onset following recent reinfection
dn_pyr = 0.0003 ; annual rate of disease onset through reactivation (only applies to those in the latent catogory who
; have not yet been recently infected or reinfected
rate_prim_dis_onset = dp_pyr/tsteps_pyr ;
rate_exog_dis_onset = dx_pyr/tsteps_pyr
rate_reactn_dis_onset = dn_pyr/tsteps_pyr
prop_smpos = 0.7 ; proportion of incident cases that are smear-positive
prop_smneg = 1-prop_smpos ; proportion of incident cases that are smear-negative
mort_rate_smneg_pyr = 0.19 ; annual disease-related mortality rate for smear-negative cases
mort_rate_smpos_pyr = 0.22 ; annual disease-related mortality rate for smear-positive cases
m_rate_smneg = mort_rate_smneg_pyr /tsteps_pyr
m_rate_smpos = mort_rate_smpos_pyr /tsteps_pyr
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Serif SansSerif
rate_natural_cure_pyr = 0.20 ; rate at which cases cure naturally without treatment per year
rate_natural_cure = rate_natural_cure_pyr/tsteps_pyr ; rate at which cases cure naturally without treatment per time step
rate_relapse_pyr = 0.001 ; annual rate at which individuals who have have recovered after treatment or natural cure relapse
rate_relapse = rate_relapse_pyr/tsteps_pyr ; rate at which individuals who have have recovered after treatment or natural cure relapse
; per time step;
ave_wks_to_health_services_smneg = 52
ave_wks_to_health_services_smpos = 52
ave_wks_HS_visit_to_treatment = 5.4 ; time from visit to sputum submission (30 days) plus time to recieving test result (3 days)
; plus time to starting treatment (5 days)
ave_wks_to_treat_if_Xrayed_smneg = ave_wks_to_health_services_smneg + ave_wks_HS_visit_to_treatment
ave_wks_to_treat_smpos = ave_wks_to_health_services_smpos + ave_wks_HS_visit_to_treatment
prop_access_Xray = 0.3
X_ray_sensitivity = 0.8
prop_default_treatment = 0.15
prop_treated_successfully = 0.75
preinterv_rate_detect_and_recover_smneg = prop_access_Xray*X_ray_sensitivity*(1-prop_default_treatment)*prop_treated_successfully/ave_wks_to_treat_if_Xrayed_smneg
; rate at which smear-negative cases are detected and recover. Takes account of
; the proportion who are provided with a chest X-ray, the sensitivity of chest X-rays
; and the proportion who are treated successfully
rate_detect_and_recover_smpos = (1-prop_default_treatment)*prop_treated_successfully/ave_wks_to_treat_smpos
; rate at which smear-positive cases are detected and recover
; and the proportion who are treated successfully
preinterv_rate_detect_only_smneg = prop_access_Xray*X_ray_sensitivity/ave_wks_to_treat_if_Xrayed_smneg
; rate at which smear-negative cases are detected. Takes account of
; the proportion who are provided with a chest X-ray, the sensitivity of chest X-rays,
rate_detect_only_smpos = 1/ave_wks_to_treat_smpos ; rate at which smear-positive cases are detected
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Serif SansSerif
intervention_on = 1 ; indicates if intervention is on (1) or off (0)
new_diagnostic_sensitivity_for_smneg = 0.7
new_diagnostic_ave_wks_to_treat_smneg = ave_wks_to_treat_if_Xrayed_smneg
interv_rate_detect_and_recover_smneg = new_diagnostic_sensitivity_for_smneg*(1-prop_default_treatment)*prop_treated_successfully/new_diagnostic_ave_wks_to_treat_smneg
; rate at which smear-negative cases are detected and recover after the introduction
; of the new diagnostic test. Takes account of the sensitivity of the new diagnostic test
; and the proportion who are treated successfully
interv_rate_detect_only_smneg = new_diagnostic_sensitivity_for_smneg/new_diagnostic_ave_wks_to_treat_smneg
; rate at which smear-negative cases are detected after the introduction
; of the new diagnostic test. Takes account of the sensitivity of the new diagnostic test.
used_rate_detect_and_recover_smneg = if (yearyear_start_intervention) AND (intervention_on0) THEN interv_rate_detect_and_recover_smneg
ELSE preinterv_rate_detect_and_recover_smneg
used_rate_detect_only_smneg = if (yearyear_start_intervention) AND (intervention_on0) THEN interv_rate_detect_only_smneg
ELSE preinterv_rate_detect_only_smneg
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Serif SansSerif
tsteps_pyr = 52 ; number of time steps per year
year = time/52
year_start_intervention = 2014 ; year in which the intervention starts
num_yrs_impact_evaluated = 10 ; number of years over which the intervention is evaluated
fin_year_impact_evaln = year_start_intervention+num_yrs_impact_evaluated
; final year when the impact is being evaluated
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Serif SansSerif
crude_annual_mort_rate = 0.021;
m_rate = crude_annual_mort_rate/tsteps_pyr ; general population mortality rate per time step
total_popn = 100000 ; total population size
Sum_pop = Sus_to_infn + Latent_fast_prog_infn + Latent_slow_prog + Latent_fast_prog_reinfn + Smneg + Smpos+Recovered
Tot_deaths = (Sus_to_infn + Latent_fast_prog_infn + Latent_slow_prog + Latent_fast_prog_reinfn + Smneg + Smpos+Recovered)*m_rate
+ Smneg*m_rate_smneg + Smpos*m_rate_smpos
New_entrants = Tot_deaths
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Serif SansSerif
Tot_Infous = Smneg+Smpos
tot_new_cases_undet = rate_reactn_dis_onset*Latent_slow_prog + rate_prim_dis_onset*Latent_fast_prog_infn
+ rate_exog_dis_onset*Latent_fast_prog_reinfn
; This sums the total number of new cases per week and excludes cases which have relapsed.
tot_new_deaths = Smneg*m_rate_smneg+Smpos*m_rate_smpos
tot_new_infns = force_of_infection*Sus_to_infn
tot_new_prim = rate_prim_dis_onset*Latent_fast_prog_infn
tot_new_exog = rate_exog_dis_onset*Latent_fast_prog_reinfn
tot_new_reactn = rate_reactn_dis_onset*Latent_slow_prog
prop_prim = tot_new_prim/tot_new_cases_undet
prop_exog = tot_new_exog/tot_new_cases_undet
prop_reactn = tot_new_reactn/tot_new_cases_undet
prop_reactn_and_exog = prop_exog+prop_reactn
New_cases_react_pHK = rate_reactn_dis_onset*Latent_slow_prog*100000*tsteps_pyr/sum_pop
New_cases_prim_pHK = rate_prim_dis_onset*Latent_fast_prog_infn*100000*tsteps_pyr/sum_pop
New_cases_exog_pHK = rate_exog_dis_onset*Latent_fast_prog_reinfn*100000*tsteps_pyr/sum_pop
Ann_TB_incidence_pHK = tot_new_cases_undet*100000*tsteps_pyr/sum_pop
TB_mort_rate_pHK = tot_new_deaths*100000*tsteps_pyr/sum_pop
TB_prevalence = (Smneg+Smpos)/sum_pop
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Serif SansSerif
INIT cum_cases_since_start_intervention = 0
NEXT cum_cases_since_start_intervention
= if (yearyear_start_intervention) AND (yearfin_year_impact_evaln) THEN cum_cases_since_start_intervention+tot_new_cases_undet*DT
ELSE cum_cases_since_start_intervention
INIT cum_deaths_since_start_intervention = 0
NEXT cum_deaths_since_start_intervention
= if (yearyear_start_intervention) AND (yearfin_year_impact_evaln) THEN cum_deaths_since_start_intervention +tot_new_deaths*DT
ELSE cum_deaths_since_start_intervention
INIT cum_infns_since_start_intervention = 0
NEXT cum_infns_since_start_intervention
= if (yearyear_start_intervention) AND (yearfin_year_impact_evaln) THEN cum_infns_since_start_intervention +tot_new_infns*DT
ELSE cum_infns_since_start_intervention
INIT cum_diagnoses_since_start_intervention = 0
NEXT cum_diagnoses_since_start_intervention
= if (yearyear_start_intervention) AND (yearfin_year_impact_evaln) THEN cum_diagnoses_since_start_intervention +tot_new_diagnoses_TBcases*DT
ELSE cum_diagnoses_since_start_intervention
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Serif SansSerif
tot_new_diagnoses_smneg = Smneg*used_rate_detect_only_smneg ; number of smear-positive cases diagnosed per week
tot_new_diagnoses_smpos = Smpos*rate_detect_only_smpos ; number of smear-negative cases diagnosed per week
tot_new_diagnoses_TBcases = tot_new_diagnoses_smneg + tot_new_diagnoses_smpos
rate_ratio_attendance_non_TBcases_vs_TBcases = 0.01 ; rate ratio of clinic attendance for individuals who do not have TB
; compared to those who do have TB. Based on the value used by Menzies et al (2013), derived
; from WHO reports
rate_test_TBcases = 1/ave_wks_to_treat_smpos ; rate at which TB cases are tested (same for smpos and smneg)
rate_test_non_TBcases = rate_ratio_attendance_non_TBcases_vs_TBcases*rate_test_TBcases ; rate at which non TB cases are tested per week
Num_smear_exams_in_smpos = Smpos*rate_test_TBcases ; number of sputum smear examinations in smear-positive cases per week
Num_smear_exams_in_smneg = Smneg*rate_test_TBcases ; number of sputum smear examinations in smear-negative cases
Num_smear_exams_in_non_TBcases = (1-TB_prevalence)*rate_test_non_TBcases*sum_pop ; number of sputum smear examinations for non TB cases
; In the intervetion both smear negatives and non TB cases
; will also recieve the new diagnostic test
Num_Xray_exams_in_smneg = if (yearyear_start_intervention) AND (intervention_on0) THEN 0
ELSE
prop_access_Xray*Num_smear_exams_in_smneg ; number of X-ray examinations for smear negative cases per week
Num_Xray_exams_in_non_TBcases = if (yearyear_start_intervention) AND (intervention_on0) THEN 0
ELSE
prop_access_Xray*Num_smear_exams_in_non_TBcases ; number of X-ray examinations for non TB cases per week
; note that in the intervention no X-rays are used
Num_new_test_in_smneg = if (yearyear_start_intervention) AND (intervention_on0) THEN Num_smear_exams_in_smneg
ELSE
0 ; number of new tests for smear negative cases per week
Num_new_test_in_non_TBcases = if (yearyear_start_intervention) AND (intervention_on0) THEN Num_smear_exams_in_non_TBcases
ELSE
0 ; number of X-ray examinations for non TB cases per week
total_sputum_smear_examinations = Num_smear_exams_in_smpos + Num_smear_exams_in_smneg + Num_smear_exams_in_non_TBcases
total_X_ray_examinations = Num_Xray_exams_in_smneg + Num_Xray_exams_in_non_TBcases
total_new_diagnostic_tests = Num_new_test_in_smneg + Num_new_test_in_non_TBcases ; in the intervention all smear negative and non-TB cases
; will be tested with the new diagnostic
INIT cum_smear_since_start_intervention = 0 ; sum the cumulative number of sputum smear examinations
NEXT cum_smear_since_start_intervention
= if (yearyear_start_intervention) AND (yearfin_year_impact_evaln) THEN cum_smear_since_start_intervention +total_sputum_smear_examinations*DT
ELSE cum_smear_since_start_intervention
INIT cum_X_ray_since_start_intervention = 0 ; sum the cumulative number of X-ray examinations
NEXT cum_X_ray_since_start_intervention
= if (yearyear_start_intervention) AND (yearfin_year_impact_evaln) AND (intervention_on1) THEN
cum_X_ray_since_start_intervention +total_X_ray_examinations*DT
ELSE cum_X_ray_since_start_intervention
INIT cum_new_test_since_start_intervention = 0 ; sum the cumulative number of test using the new diagnostic
NEXT cum_new_test_since_start_intervention
= if (yearyear_start_intervention) AND (yearfin_year_impact_evaln) AND (intervention_on0) THEN cum_new_test_since_start_intervention +total_new_diagnostic_tests*DT
ELSE cum_new_test_since_start_intervention
new_diagnostic_cost = 20 ; Cost of a sputum test using the new diagnostic
smear_cost = 5 ; Cost of a sputum examination using smear microscopy
X_ray_cost = 10 ; Cost of a chest X-ray
total_cum_cost_smear = cum_smear_since_start_intervention*smear_cost ; cumulative cost of sputum smears
total_cum_cost_X_ray = cum_X_ray_since_start_intervention*X_ray_cost ; cumulative cost of X-ray examinations
total_cum_cost_new_test = cum_new_test_since_start_intervention*new_diagnostic_cost ; cumulative cost of new diagnostic tests
total_cum_cost = total_cum_cost_smear + total_cum_cost_X_ray + total_cum_cost_new_test ; total costs of diagnosing TB over the intervention period
cost_per_diagnosed_case = if (cum_diagnoses_since_start_intervention0) THEN total_cum_cost/cum_diagnoses_since_start_intervention ELSE 0
Serif
euler
ecr_pyr
15.0
0.0
20.0
0.5
false
false
intervention_on
1.0
0.0
1.0
1.0
false
false
1.0
-1
0
0
Graph 1
true
Graph
1
3
125 83 148 76
true
255 255 255
true
year
Ann_TB_incidence_pHK
true
false
TB_mort_rate_pHK
true
false
ann_risk_of_infection
true
true
year
true
false
false
false
true
false
false
true
false
true
true
true
false
false
false
0.0 0.0
1
2010.0 2024.0 14
false
0.0 300.0 10
false
false
1
true
false
false
0 0
1 0
2 0
year
Annual_TB_incidence_and_mortality_rate_per_100000
Annual_risk_of_infection
0.30000001192092896 0.5
0.30000001192092896 0.5
Graph 2
true
Graph
1
3
52 91 243 68
true
255 255 255
true
year
cum_cases_since_start_intervention
true
false
cum_infns_since_start_intervention
true
false
cum_deaths_since_start_intervention
true
false
year
false
false
false
false
true
false
false
true
false
true
true
true
false
false
false
0.0 0.0
1
2010.0 2024.0 14
false
0.0 12000.0 6
false
false
1
true
false
false
0 0
1 0
2 0
year
Cumulative_number_of_infections_cases_and_deaths
0.30000001192092896 0.5
0.30000001192092896 0.5
Graph 3
true
Graph
1
3
31 71 264 88
true
255 255 255
true
year
tot_new_diagnoses_smneg
true
false
tot_new_diagnoses_smpos
true
false
tot_new_diagnoses_TBcases
true
false
cum_diagnoses_since_start_intervention
true
true
year
false
false
false
false
true
false
false
true
false
true
true
true
false
false
false
0.0 0.0
1
2010.0 2024.0 14
false
false
false
1
true
false
false
0 0
1 0
2 0
year
New_diagnoses_per_week
cum_diagnoses_since_start_intervention
0.30000001192092896 0.5
0.30000001192092896 0.5
Graph 4
true
Graph
1
3
73 71 213 88
true
255 255 255
true
year
Num_smear_exams_in_smpos
true
false
Num_smear_exams_in_smneg
true
false
Num_Xray_exams_in_smneg
true
false
Num_new_test_in_smneg
true
false
year
false
false
false
false
true
false
false
true
false
true
true
true
false
false
false
0.0 0.0
1
2010.0 2024.0 14
false
false
false
1
true
false
false
0 0
1 0
2 0
year
Weekly_number_of_examinations
0.30000001192092896 0.5
0.30000001192092896 0.5
Graph 5
true
Graph
1
3
165 131 120 28
true
255 255 255
true
year
total_cum_cost
true
false
total_cum_cost_smear
false
false
total_cum_cost_X_ray
false
false
total_cum_cost_new_test
false
false
false
false
true
false
false
true
false
true
true
true
false
false
false
0.0 0.0
1
2010.0 2024.0 14
false
0.0 300000.0 6
false
false
1
true
false
false
0 0
1 0
2 0
year
Cumulative_costs_incurred_since_2014_($)
0.30000001192092896 0.5
0.30000001192092896 0.5
Graph 6
true
Graph
1
3
111 121 184 28
true
255 255 255
true
year
cost_per_diagnosed_case
true
false
false
false
true
false
false
true
false
true
true
true
false
false
false
0.0 0.0
1
2010.0 2024.0 14
false
0.0 200.0 10
false
false
1
true
false
false
0 0
1 0
2 0
year
cost_per_diagnosed_case_($)
0.30000001192092896 0.5
0.30000001192092896 0.5
1
-1
true
true
true
true