Rapid review of COVID-19 epidemic estimation studies for Iran

Pourmalek, Farshad; Rezaei Hemami, Mohsen; Janani, Leila; Moradi-Lakeh, Maziar

doi:10.1186/s12889-021-10183-3

BMC Public Health

Table 1 Reported items of methodology of the reviewed studies

From: Rapid review of COVID-19 epidemic estimation studies for Iran

Study first author	Ahmadi [44]		Al-Qaness [51]	Ayyoubzadeh [52]	DELPHI [10]	Ghaffarzadegan [41]	Gu (YYG) [17]	Haghdoost [27]
Situation of study	Published paper		Published paper	Published paper	Web site	Published paper	Web site	Full report (Farsi)
Epidemic start date	20-02-19		20-01-22	20-02-11	N/M ^a	20-01-02	20-01-26	20-01-21
Inputs: population	N/M ^a		N/M ^a	N/M ^a	Yes	Yes	Yes	Yes
Inputs: cases	Yes		Yes	Yes	Yes	Yes	No	No
Inputs: cases (source)	MOHME ^b official reports		World Health Organization	Worldometers website ^c	Johns Hopkins University ^d	MOHME ^b official reports; unofficial reports	Johns Hopkins University ^d	N/A ^e
Inputs: deaths	Yes		No	No	Yes	Yes	Yes	No
Inputs: deaths (source)	MOHME ^b official reports		N/A ^e	N/A ^e	Johns Hopkins University ^d	MOHME ^b official reports; unofficial reports	Johns Hopkins University ^d	N/A ^e
Other input data	Number of cured [recovered] cases		N/A ^e	N/A ^e	Nonpharmaceutical interventions	Number of tests, Detected infected travelers, Travel data	Case and hospitalization data ^f	Post-infection isolated persons, Hospitalized cases, Infected cases recovered without isolation or hospitalization
Output date range (number of days)	20-02-19 to 20-04-03 (45 days)		20-01-22 to 20-04-07 (77 days)	20-02-11 to 20-03-18 (37 days)	20-06-01 to 20-07-15 (45 days)	19-12-31 to 20-06-30 (183 days)	20-01-26 to 20-11-01 (281 days)	20-01-21 to 20-05-20 (121 days)
Place	Iran		4 countries	Iran	148 countries	Iran	70 countries	Iran and Tehran capital city
Compartmental model ^g	SIR ^g		None	None	SEIR+ ^{g, h}	SEIR+ ^g	SEIR ^g	SEIR+ ^g
Statistical method: name	3 growth models ⁱ		6 time-series models ^j	2 Models ^k	Regression trees	Dynamic simulation model	Machine learning	Dynamic model
R0 estimation results	1.75		None	None	None	2.72 (before starting the interventions)	4 estimates ^k	3 estimates ^l
Scenarios /models: number	3 ^m		1	1	1	6 ⁿ	1	4 ^o
Other factors	No		No	No	Yes. Asymptomatic cases, under-reporting	Yes ^p	Yes. Asymptomatic cases, under-reporting	Yes ^q
Primary outcomes	Cumulative deaths, Cumulative cases		Cumulative cases	Normalized Daily cases	Cumulative and daily deaths and cases	Cumulative deaths, Cumulative cases, Current cases	Cumulative and daily deaths and cases, Daily prevalent cases	Cumulative and daily deaths and cases, Daily prevalent cases
Primary outcomes interval estimates	No		No	No	No	No	Yes	No
Other outcomes	None		None	None	Active, Active hospitalized, Cumulative hospitalized, Active ventilated	None	Reproduction Number	Needed hospital beds, ICU beds
Other outcomes interval estimates	N/A ^e		N/A ^e	N/A ^e	No	N/A ^e	Yes	No
Model validation	No		Yes ^r	Yes ^s	No ^t	Yes ^u	Yes ^v	No
Study limitations mentioned	Yes		Yes	Yes	Yes	Yes	Yes	No
Study limitations described	Yes		No	No	Yes	No	Yes	No
Study first author	Hsiang [45]		IHME [12]	Imperial [13]	LANL [14]	Mashayekhi [28]	Moftakhar [53]	Moghadami [36]
Situation of study	Published paper		Web site [12] and published paper [30]	Web site [13] and published paper [34]	Web site	Summary report (Farsi)	Published paper	medRxiv preprint
Epidemic start date	N/M ^aa		N/M ^aa	20-01-03	N/M ^aa	20-02-19 [?]	20-02-19	20-02-19
Inputs: population	Yes		Yes	Yes	Yes	Yes	No	No
Inputs: cases	Yes		Yes	Yes	Yes	No	Yes	Yes
Inputs: cases (source)	Wikipedia ^bb		Johns Hopkins University ^cc	Johns Hopkins University ^cc	Johns Hopkins University ^cc	N/A ^dd	MOHME ^ee and Johns Hopkins ^cc	MOHME ^ee
Inputs: deaths	Yes		Yes	Yes	Yes	No	No	Yes
Inputs: deaths (source)	Wikipedia ^bb		Johns Hopkins University ^cc	Johns Hopkins University ^cc	Johns Hopkins University ^cc	N/A ^dd	N/A ^dd	MOHME ^ee
Other input data	3 variables ^ff		4 variables ^gg	5 variables ^hh	N/M ^aa	N/M ^aa	N/M ^aa	None
Output date range (number of days)	~ 20-02-28 to 20-04-06 (~ 39 days)		20-02-04 to 21-02-01 (364 days)	20-01-06 to 20-11-24 (324 days)	20-03-14 to 20-11-07 (239 days)	N/M ^aa (360 days)	20-03-21 to 20-04-20 (31 days)	20-03-21 to 20-04-20 (31 days)
Place	6 countries		165 countries	164 countries	157 countries	Iran	Iran	Iran and top 5 provinces
Compartmental model ⁱⁱ	SIR+ ⁱⁱ		SEIR ⁱⁱ	SIR, SEIR, SEIR+ ⁱⁱ	SEIR+ ⁱⁱ	SLIR+ ⁱⁱ	None	None
Statistical method: name	Multiple regression		Curve fitting (backcating) functional analysis (forecasting)	Regression trees	Dynamic growth parameter modeling	Dynamic model	Autoregressive Integrated Moving Average (ARIMA)	Exponential smoothing model
R0 estimation results	Not used		N/M ^aa	N/M ^aa	N/M ^aa	Not used	Not used	Not used
Scenarios /models: number	2 ^jj		3 ^kk	6 ^ll	1	3 ^mm	1	1
Other factors	Yes. Under-reporting.		Yes ⁿⁿ	Yes. Under-reporting.	Yes. Under-reporting.	Yes ^oo	No	No
Primary outcomes	Cumulative cases		Cumulative and daily deaths and cases	Cumulative and daily deaths and cases	Cumulative and daily deaths and cases	Cumulative and daily deaths, Daily symptomatic and asymptomatic cases	Daily cases	Cumulative deaths, cases, recovered cases
Primary outcomes interval estimates	Yes		Yes	Yes	Yes	No	Yes	Yes
Other outcomes	None		Yes ^pp	Yes ^qq	None	None	None	None
Other outcomes interval estimates	N/A ^dd		Yes	Yes	N/A ^dd	N/A ^dd	N/A ^dd	N/A ^dd
Model validation	(?)		Yes ^rr	Yes ^ss	Yes ^tt	No	Yes ^uu	Yes ^vv
Study limitations mentioned	Yes		Yes	No	No	Yes	Yes	No
Study limitations described	Yes		Yes	No	No	No	Yes	No
Study first author	Moradi [42]	Muniz-Rodriguez [37]	Pourghasemi (PLoS ONE) [38]	Pourghasemi (IJID) [39]	Rafieenasab [54]	Rahimi Rise [29]	Saberi (web site) [21]	Saberi (paper) [22]
Situation of study	Published paper	Published paper	Published paper	Published paper	Published paper	Published paper (Farsi)	Web site [21]	Published paper
Epidemic start date	20-02-20	20-02-19	20-02-25 [?]	20-02-25 [?]	20-02-19	20-02-01	20-02-19	20-02-19
Inputs: population	No	N/M ^aaa	Yes	Yes	N/M ^aaa	Yes	N/M ^aaa	Yes
Inputs: cases	No	Yes	Yes	Yes	Yes	Yes	Yes	Yes
Inputs: cases (source)	N/A ^bbb	MOHME ^ccc official reports	MOHME ^ccc official reports	MOHME ^ccc official reports	MOHME ^ccc official reports	Worldometers website ^ddd	MOHME ^ccc official reports, WHO, Worldometers ^ddd	MOHME ^ccc official reports, WHO
Inputs: deaths	Yes	No	Yes	Yes	No	Yes	Yes	Yes
Inputs: deaths (source)	MOHME ^ccc official reports	N/A ^bbb	MOHME ^ccc official reports	MOHME ^ccc official reports	N/A ^bbb	Worldometers website ^ddd	MOHME ^ccc official reports, WHO, Worldometers ^ddd	MOHME ^ccc official reports, WHO, Worldometers ^ddd
Other input data	None	Travel data	Environmental and meteorological conditions	Environmental and meteorological conditions	None	Public transportation variables	None	None
Output date range (number of days)	20-02-20 to 20-03-26 (36 days)	20-02-19 to 20-02-29 (11 days)	~ 20-02-25 to ~ 20-06-10 (~ 107 days) ^eee	~ 20-02-25 to ~ 20-06-20 (~ 117 days) ^fff	20-02-19 to 20-06-07 (110 days)	20-02-01 to 20-08-01 (183 days)	20-02-19 to 21-02-02 (350 days)	~ 20-03-19 to 20-10-26 (~ 222 days)
Place	Iran	Iran and 2 multi-province regions	Iran and Fars Province	Iran, 31 Provinces of Iran, World	Iran	Iran	Iran	Iran
Compartmental model ^ggg	None	None	None	None	SIR+ ^{ggg, hhh}	SEIR ^ggg	SIR ^ggg	SEIR+ ^{ggg, iii}
Statistical method: name	Calculating number of cases based on different assumptions for case fatality rate (CFR)	Generalized growth mode; Based on the calculation of the epidemic doubling times	Autoregressive Integrated Moving Average (ARIMA) and polynomial regression	Fourth-degree polynomial regression	3-steps model based on the SIR model	Dynamic model	Classical SIR^ggg mathematical model with homogenous mixing assumption	Ordinary least squares minimization
R0 estimation results	Not used	Two methods: 3.6 and 3.58	Not used	Not used	2.8–3.3 (range)	Not used	2.37 (for the last 7 days before 20-03-21)	1.73 (20-03-01) and 0.69 (2004-15) ^jjj
Scenarios /models: number	4 ^kkk	2 ^lll	1	1	1	2	12 ^mmm	3 ⁿⁿⁿ
Other factors	No	No	No	No	No	Yes. Asymptomatic cases	Yes ^ooo	Yes ^ppp
Primary outcomes	Cumulative cases	Daily cases	Cumulative and daily deaths and cases ^qqq	Cumulative and daily deaths and cases ^rrr	Cumulative and daily deaths, Daily cases	Daily deaths and cases	Cumulative cases, Daily active cases	Fractions of national population estimated to be confirmed and suspected cases ^sss
Primary outcomes interval estimates	No	Yes	No	No	No	No	No	Yes
Other outcomes	Case Fatality Rate	None	None	None	None	None	None	Intensive Care Unit beds needed
Other outcomes interval estimates	No	N/A ^bbb	N/A ^bbb	N/A ^bbb	N/A ^bbb	N/A ^bbb	N/A ^bbb	Yes
Model validation	No	No	Yes ^ttt	Yes ^uuu	No	Yes ^vvv	No	Yes ^www
Study limitations mentioned	Yes	Yes	No	Yes	No	No	Yes	Yes
Study limitations described	No	Yes	No	No	No	No	No	Yes
Study first author	Shen [43]		Singh [55]	Srivastava [15]	Thu [48]	Tuite [46]	Zhan [40]	Zhuang [47]
Situation of study	Published paper		Published paper	Web site [15] and preprint [35]	Published paper	Published paper	Published paper	Published paper
Epidemic start date	20-02-20		N/M ^aaaa	N/M ^aaaa	N/M ^aaaa	N/M ^aaaa	20-02-19	N/M ^aaaa
Inputs: population	No		No	N/M ^aaaa	No	N/M ^aaaa	N/M ^aaaa	Yes
Inputs: cases	Yes		Yes	Yes	Yes	No	Yes	No
Inputs: cases (source)	“WIND DATA” ^bbbb		Worldometers ^cccc	Johns Hopkins University ^dddd	WHO	N/A ^bbbb	MOHME ^eeee official reports	N/A ^ffff
Inputs: Deaths	No		No	Yes	Yes	No	Yes	No
Inputs: Deaths (source)	N/M ^aaaa		N/M ^aaaa	Johns Hopkins University ^dddd	WHO	N/A ^ffff	WHO	N/A ^ffff
Other input data	None		None	None	Social distancing	Exported cases from Iran to other countries; Travel data	COVID-19 spreading profiles of 367 cities in China	Exported cases from Iran to other countries, Travel data
Output date range (number of days)	20-02-20 to 20-04-20 (61 days)		20-04-24 to 20-07-07 (75 days)	20-09-19 to 20-12-19 (every 7th day, 14 dates, 92 days duration)	20-03-30 to 20-05-02 (34 days)	20-01-01 to N/M ^aaaa	20-02-22 to 20-06-24 (124 days)	20-02-01 to 20-02-24 (24 days)
Place	9 countries and 11 provinces / municipalities in China		15 countries	184 countries	10 countries	Iran	Iran and 12 provinces	Iran
Compartmental model ^gggg	None		None	SIR+ ^{gggg, hhhh}	None	None	SEIR+ ^gggg	None
Statistical method: name	Logistic growth		Autoregressive Integrated Moving Average (ARIMA)	Hyper-parametric learning	Linear growth rates ⁱⁱⁱⁱ	N/M ^aaaa	Data-driven prediction algorithm ^kkkk	Binomial distributed likelihood framework
R0 estimation results	Not used		Not used	1.44 (20-03-21), 1.46 (20-03-28)	Not used	Not used	Not used	Not used
Scenarios /models: number	1		1	3 ^llll	1	6 ^mmmm	1	5 ⁿⁿⁿⁿ
Other factors	No		No	Asymptomatic cases, under-reporting	No	No	No	No
Primary outcomes	Cumulative cases		Cumulative cases	Cumulative deaths and cases	Daily cases	Cumulative cases	Cumulative and daily cases	Cumulative cases
Primary outcomes interval estimates	No		Yes	No	No	Yes	Yes	Yes
Other outcomes	None		None	None	None	None	None	None
Other outcomes interval estimates	N/A ^ffff		N/A ^ffff	N/A ^ffff	N/A ^ffff	N/A ^ffff	N/A ^ffff	N/A ^ffff
Model validation	Yes ^oooo		Yes ^pppp	Yes ^qqqq	No	No	Yes ^jjjj	No
Study limitations mentioned	Yes		Yes	Yes	Yes	No	Yes	Yes
Study limitations described	No		Yes	Yes	Yes	No	Yes	No

^a N/M: Not Mentioned
^b MOHME: Ministry of Health and Medical Education, Iran
^c Worldometers Coronavirus [49]
^d Johns Hopkins University, Coronavirus Resource Center ([4, 5])
^e N/A: Not applicable
^f “We do not use case-related data in our modeling. We do look at case and hospitalization data to help determine the bounds for our search grid, as changes in cases lead changes in deaths.” Gu (YYG) [17]
^g Compartmental models: S: Susceptible, E: Exposed, I: Infected, R: Removed or Recovered, L: Latent. In any model with a + sign, there are other components for augmentation of model
^h DELPHI model: The model underlying the predictions is DELPHI (Differential Equations Leads to Predictions of Hospitalizations and Infections), that is based on SEIR with augmentations for under-detection and governmental response. DELPHI [10]
ⁱ Three growth models: M1: Gompertz Differential Equation, M2: Von Bertalanffy differential growth equation, and M3: Cubic polynomial least squared errors
^j Six time-series models: (1) Adaptive Neuro-Fuzzy Inference System (ANFIS) enhanced with Genetic Algorithm (GA), (2) Original Adaptive Neuro-Fuzzy Inference System (ANFIS), (3) Particle Swarm Optimizer (PSO), (4) Artificial Bee Colony (ABC), (5) hybridized of Flower Pollination Algorithm and SALP Swarm Algorithm (SSAFPA), (6) Sine-Cosine Algorithm (SCA)
^h Two Models: Linear Regression, Long Short-Term Memory (LSTM)
^k Four estimates: Initial R0 = 2.65. Reopen R = 1.17. Current R = 1.2. Post-mitigation R = 0.90
^l Three estimates: 7.24 (at the beginning). 2.58 (after interventions). 1.82 (conditional to isolation of 50% within 3 days)
^m Three scenarios based on 3 growth models: S1: Gompertz Differential Equation, S2: Von Bertalanffy differential growth equation, and S3: Cubic polynomial least squared errors
ⁿ Six scenarios based on combination of two factors: Seasonality (S), and Policy interventions (P). (1) S1P1: Seasonality conditions 1 (no effect or status quo) and Policy effect 1 (status quo contact rate). Estimates for 2020-03-19, the end of first month after the epidemic start date, are equal across the six scenarios. (2) S1P2: Seasonality conditions 1 (no effect or status quo) and Policy effect 2 (aggressive efforts to decrease contact rate by half of what it would be otherwise). (3) S2P1: Seasonality conditions 2 (moderate effect; infectivity of the virus decreases linearly from April 1st and halves by June 1st, then stays the same for the rest of the simulation) and Policy effect 1 (status quo contact rate). (4) S2P2: Seasonality conditions 2 (moderate effect; infectivity of the virus decreases linearly from April 1st and halves by June 1st, then stays the same for the rest of the simulation) and Policy effect 2 (aggressive efforts to decrease contact rate by half of what it would be otherwise). (5) S3P1: Seasonality conditions 3 (very strong mitigating effect; infectivity of the virus decreases from April 1st to a quarter of its base value by June 1st, then stays the same for the rest of the simulation) and Policy effect 1 (status quo contact rate). (6) S3P2: Seasonality conditions 3 (very strong mitigating effect; infectivity of the virus decreases from April 1st to a quarter of its base value by June 1st, then stays the same for the rest of the simulation) and Policy effect 2 (aggressive efforts to decrease contact rate by half of what it would be otherwise)
^o Four scenarios: S0: Basic scenario (no intervention), only 10% isolation. S1: Worst scenario, minimum (25%) isolation. S2: Medium scenario, medium (32%) isolation. S3: Best scenario, maximum (40%) isolation
^p Seven other factors included: Asymptomatic cases, Under-reporting / Completeness of reporting cases and deaths to MOHME, Delays in reporting cases and deaths to MOHME, Testing availability, Number of tests performed, Social distancing / Quarantine interventions, Seasonality
^q Two other factors included: Seasonality, Social distancing / Quarantine interventions
^r Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Squared Relative Error (RMSRE), and Coefficient of Determination (R square)
^s Root Mean Squared Error (RMSE)
^t Friedman [31] assessed predictive performance of international COVID-19 mortality forecasting models, using median absolute percent error (MAPE) and Median absolute errors (MAE)
^u Root Mean Squared Error (RMSE)
^v Mean Square Error (MSE), Mean Absolute Error (MAE), and Ratio Error (RE). Did not mention the results
^aa N/M: Not Mentioned
^bb Wikipedia. COVID-19 pandemic in Iran [56]
^cc Johns Hopkins University, Coronavirus Resource Center ([4, 5])
^dd N/A: Not Applicable
^ee MOHME: Ministry of Health and Medical Education, Iran
^ff Four variables: Cumulative recoveries, Active cases, Any changes to domestic COVID-19-testing regimes, such as case definitions or testing methodology, and Non-pharmaceutical interventions
^gg Three variables: Mobility, Testing, and Seroprevalence (the latter for 41 locations)
^hh Five variables: Interventions, Social contacts, Comorbidities, Hospital bed capacity, Intensive Care Unit bed capacity
ⁱⁱ Compartmental models: S: Susceptible, E: Exposed, I: Infected, R: Removed or Recovered, L: Latent. In any model with a + sign, there are other components for augmentation of model
^jj Two scenarios: ‘No-policy scenario’ and ‘Actual policies’
^kk Three scenarios: S1 Best (Masks): ‘Universal Masks’ scenario reflects 95% mask usage in public in every location. S2 Reference (Current): ‘Current projection’ scenario assumes social distancing mandates are re-imposed for 6 weeks whenever daily deaths reach 8 per million (0.8 per 100,000). S3 Worse (Easing): ‘Mandates easing’ scenario reflects continued easing of social distancing mandates, and mandates are not re-imposed
^ll Six scenarios: S1: Additional 50% Reduction. S2: Maintain Status Quo. S3: Relax Interventions 50%. S4: Surged Additional 50% Reduction. S5: Surged Maintain Status Quo. S6: Surged Relax Interventions 50%
^mm S1: Ideal scenario, serious distancing. People reduce their social [physical] contacts to 20% of regular level, voluntarily or on a forced basis, after number of cases and deaths have increased, plus close observation of sanitation cautions, so that transmission rate reduces by 65%. S2: Medium scenario, not serious distancing. People reduce their social [physical] contacts only to 20% of regular level, voluntarily, after number of cases and deaths have increased, and other settings are like scenario 1. S3: Worst scenario. People reduce their social [physical] contacts only to 50% of regular level, voluntarily, after number of cases and deaths have increased, plus inadequate observation of sanitation cautions, so that transmission rate reduces only by 40% (instead of 55%), and 60% of people do not observe the sanitation cautions
ⁿⁿ Five other factors included: Asymptomatic cases, Mobility, Testing, Seroprevalence, Seasonality
^oo Two other factors included: Asymptomatic cases, Social distancing / Quarantine interventions
^pp Six other outcomes: All beds needed, Intensive Care Unit beds needed, Invasive ventilators needed, Tests, Mobility, Seroprevalence
^qq Five other outcomes: Hospital demand, Hospital incidence, Intensive Care Unit demand, Intensive Care Unit incidence, Rt (Effective Reproduction Number)
^rr IHME web site [12] refers to Friedman [31], who assessed predictive performance of international COVID-19 mortality forecasting models, using median absolute percent error (MAPE) and Median absolute errors (MAE)
^ss Mean Absolute Percentage Error (MAPE)
^tt They validated the model “by looking at the coverage of the forecasts, i.e. the proportion of times that the number of confirmed cases/deaths fell within a specified lower and upper bound, X min and X max. Coverage plots can help visualize how well the model is doing”
^uu Graphical residual assessment of the model
^vv Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MEA), Mean Absolute Percentage Error (MAPE), Akaike Information Criterion (AIC)
^aaa N/M: Not Mentioned
^bbb N/A: Not Applicable
^ccc MOHME: Ministry of Health and Medical Education, Iran
^ddd Worldometers Coronavirus [49]
^eee Start and end dates mentioned in manuscript text, mentioned in title of their Fig. 14, and shown within their Fig. 14 do not seem to be congruent
^fff Start and end dates mentioned in manuscript text, mentioned in title of their Fig. 15, and shown within their Fig. 15 do not seem to be congruent
^ggg Compartmental models: S: Susceptible, E: Exposed, I: Infected, R: Removed or Recovered, L: Latent. In any model with a + sign, there are other components for augmentation of model
^hhh SIR with exact and approximated solutions, extrapolation based on least squares model with three functions
ⁱⁱⁱ SEIR+ Distinguishing between fatal and recovered cases combined with an estimate of the percentage of symptomatic cases using delay-adjusted Case Fatality Rate
^jjj Estimated effective reproduction number that ranged from 0.66 to 1.73 between February and April 2020, with a median of 1.16. Estimated a reduction in the effective reproduction number during this period, from 1.73 (95% CI 1.60–1.87) on 1 March 2020 to 0.69 (95% CI 0.68–0.70) on 15 April 2020, due to various non-pharmaceutical interventions
^kkk Four scenarios based on different values of Case Fatality Rate. S1: 0.3%, S2: 0.5%, S3: 1%, and S4: 2%
^lll Based on two different methods to estimate R0
^mmm (1) S1P10: Scenario 1 (Best scenario, based on official reports with correction factor of 1) with 10 million susceptible population. (2) 12 scenarios based on combination of three options for number of cases and deaths to start with, and four options for the susceptible population size. (1) S1P10: Scenario 1 (Best scenario, based on official reports with correction factor of 1) with 10 million susceptible population. (2) S1P30:Scenario 1 (Best scenario, based on official reports with correction factor of 1) with 30 million susceptible population. (3) S1P50: Scenario 1 (Best scenario, based on official reports with correction factor of 1) with 50 million susceptible population. (4) S1P80: Scenario 1 (Best scenario, based on official reports with correction factor of 1) with 80 million susceptible population. (5) S2P10: Scenario 2 (Medium scenario, based on official reports with correction factor of 5 (after Dr. Rick Brennan, Director of Emergency Operations, World Health Organization [57]) with 10 million susceptible population. (6) S2P30: Scenario 2 (Medium scenario, based on official reports with correction factor of 5 (after Dr. Rick Brennan, Director of Emergency Operations, World Health Organization [57]) with 30 million susceptible population. (7) S2P50: Scenario 2 (Medium scenario, based on official reports with correction factor of 5 (after Dr. Rick Brennan, Director of Emergency Operations, World Health Organization [57]) with 50 million susceptible population. (8) S2P80: Scenario 2 (Medium scenario, based on official reports with correction factor of 5 (after Dr. Rick Brennan, Director of Emergency Operations, World Health Organization [57]) with 80 million susceptible population. (9) S3P10: Scenario 3 (Worst scenario, based on official reports with correction factor of 10 (after Russell [58]) with 80 million susceptible population. (10) S3P30: Scenario 3 (Worst scenario, based on official reports with correction factor of 10 (after Russell [58]) with 30 million susceptible population. (11) S3P50: Scenario 3 (Worst scenario, based on official reports with correction factor of 10 (after Russell [58]) with 50 million susceptible population. (12) S3P80: Scenario 3 (Worst scenario, based on official reports with correction factor of 10 (after Russell [58]) with 10 million susceptible population
ⁿⁿⁿ Three scenarios: (1) maintaining the same level of control measures as of 12 April 2020, (2) reinforcing the control measures to increase physical distancing by a 20% increase in the reproduction number, and (3) partial lifting the restrictions to ease physical distancing by a 20% decrease in the reproduction number
^ooo Completeness of reporting cases and deaths to MOHME
^ppp Accounted for the under-reporting of the number of infected cases using delay-adjusted case fatality ratio (CFR) approach
^qqq Cumulative deaths and cases (for Iran and Fars Province), Daily deaths and cases (for Fars Province)
^rrr Cumulative deaths and cases (for Iran and World), Daily or cumulative cases in 30 days after the first day of infected cases in the 31 Iranian provinces)
^sss We transformed their reported fractions of national population estimated to be confirmed and suspected cases to numbers of people estimated to be confirmed and suspected cases, using a total national population of 84,297,880 (used by IHME [12])
^ttt Area Under Curve (AUC)
^uuu Area Under Curve (AUC)
^vvv Root Mean Squared Error (RMSE)
^www Root Mean Squared Error (RMSE)
^aaaa N/M: Not mentioned
^bbbb Mentioned: “WIND DATA, a leading financial data services provider in China”
^cccc Worldometers Coronavirus [49].
^dddd Johns Hopkins University, Coronavirus Resource Center ([4, 5])
^eeee MOHME: Ministry of Health and Medical Education, Iran
^ffff N/A: Not Applicable
^gggg SEIR+ Distinguishing between fatal and recovered cases combined with an estimate of the percentage of symptomatic cases using delay-adjusted Case Fatality Rate
^hhhh SI-kJ alpha model: S: Susceptible. I: Infected. k: k sub-states of infection. J: J is a hyperparameter introduced for a smoothing effect to deal with noisy data. Alpha: an additional hyperparameter to minimizes the Root Mean Squared Error
ⁱⁱⁱⁱ They have not named their method. It could be names as linear growth rates, according to their Eq. (1) and Eq. (2)
j Another study by Zhan and colleagues was cited for validity of their models
^kkkk A data-driven prediction algorithm to find the most resembling growth curve from the historical profiles in China
^llll Three scenarios: Current, Released, Restricted, each with 6 levels of putative under-ascertainment parameter
^mmmm Six scenarios based on six sets of international travel destinations
ⁿⁿⁿⁿ Five scenarios based on selected combinations of (1) Effective catchment population, (2) Detection window 10 or 8 days, and (3) 90% or 70% load factors
^oooo R Square
^pppp Akaike Information Criterion (AIC)
^qqqq Root Mean Squared Error (RMSE)

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