Table 2. Studies on compartmental modeling, stratified by the natural history of the disease and type of modeling, with details referring to the assumptions, stratifications and subpopulations modeled, geographic area studied, time horizon and the main outputs investigated.

Model	Natural History	Model type	Assumptions	Stratification/ subpopulations	Spatial scale	Time Horizon	Purpose	Main outputs
SIR	Do not include exposed/latent compartment; Do not consider reinfections;	Deterministic	Asymptomatic, mild, moderate and severe disease [26]; Asymptomatic and symptomatic [27–31]; Government interventions [30, 32]; Mobility [33]; Healthcare capacity [26, 29, 33]; Natural birth and death rates [34]; Delays in state and control variables [28]; Considered a population response parameter [29, 31]; Underreporting [31];	Age structured [33]; Favelas’ population [26]; School and university population [33];	Country [28–36]; City [37, 38]; State [27, 39]; Assumed [26];	Various [35]; 200 days [36]; 80 days [34, 37] 2 years [26]; 50 days [32] 100 days [28, 33]; 150 days [27]; 10 days [38]; 2000 days [39]; 400 days [29]; 3 months [30]; 360 days [31];	Future projections [30, 35–38] Specific interventions [26–34, 39] Economic analyses [28];	R0 [33, 35, 37, 39]; Prediction of the epidemic [27–38]; Transmission rate [32, 37]; Peak of the epidemics [36]; ICU availability [26, 33] Symptomatic and asymptomatic [27, 28, 30, 31] Isolation effect [29, 39]; Hospitalizations [28]; Economic evaluation [28];
		Stochastic	Government interventions [40]; Mobility [40]; Healthcare capacity [40];	School population [40];	City [40];	720 days [40];	Specific interventions [40];	Prediction of the epidemic [40];
SEIR	Exposed compartment included; Do not consider reinfections;	Deterministic	Asymptomatic and symptomatic [41–50] Mild, moderate and critical disease [46–52] Healthcare capacity [45, 48, 51–57]; Different case-fatality rates [51, 53] Vertical social distance policies [46, 55, 58]; Underreporting [42, 56]; Environmental resevoir [59]; Natural birth and death rates [46, 47, 49, 50, 59, 60]; Mobility [44, 51, 52, 59, 61]; Government interventions [43, 44, 61, 62]; Distinct incubation rates for variants [63]; Distinct asymptomatic/symptomatic rates for variants [47]; Considered limited resources [45]; Considered tested and untested population [50, 64];	Age structured [46, 47, 49, 51, 55, 56, 58, 60, 65–67]; School population [41];	Country [42, 45, 51, 53, 54, 56, 57, 63, 65–69]; State [46–50, 52, 58, 59, 61, 64, 70–72]; City [41, 43, 55, 60]; Regional [44];	120 days [65, 69]; 480 days [71]; 365 days [54] [47]; 150 days [58] [42]; 250 days [55] [45]; 300 days [56] [59]; 500 days [51, 64, 67]; 30 days [41]; 180 days [43, 46]; 60 days [60, 66]; 3 weeks [63]; 5 months [50]; 6 months [48, 49, 72]; 7 months [56, 72]; 2 years [52, 53];	Future projections [42, 43, 46, 51, 54, 56, 60, 62, 65, 71, 72] Specific interventions [41, 42, 44–50, 52–59, 61, 63, 64, 65–67, 69]; Economic analyses [50, 66];	R0 [41–45, 48–52, 59, 62, 65, 71]; Prediction of the epidemic [41–43, 46–55, 57–66, 69, 71, 72]; Hospitalizations [48, 51, 55, 60, 66, 67]; Peak of epidemics [52, 56, 65]; Isolation effect [45, 49, 65, 66]; Symptomatic and asymptomatic [42, 43, 45, 50, 62, 67]; Secondary cases caused by infected children [41]; Transmission rate [44, 45]; Economic evaluation [50, 66]; ICU availability [48, 56, 57]
		Stochastic	Natural birth and death rates [63]; Mild, severe and critical disease [73]; Asymptomatic and symptomatic [74]; Considered a population response parameter [73]; Mobility [73]; Healthcare capacity [73]; Underreporting [74];	Age structured [75];	City [75]; Regional [73]; Assumed [74];	60 days [75]; 365 days [73]; 120 days [74];	Future projections [74]; Specific interventions [73–75];	Prediction of the epidemic [73–75]; Isolation effect [73, 75]; R0 [73] [74]; Peak of epidemics [70]; Hospitalizations [73]; ICU availability [73];
SEIRS	Exposed compartment included; Considers reinfections;	Deterministic	Healthcare capacity [76]; Mobility [76]; Asymptomatic, symptomatic and hospitalized [75]; Considered reinfection by gamma (P1) variant [77]; Distinct transmissibility rates for variants [77];	Age structured [77];	City [77]; State [76];	365 days [76]; 3 months [77];	Future projections [77]; Economic analyses [76];	Prediction of the epidemic [76]; Hospitalizations [76, 77]; ICU availability [76]; Transmission rate [77]; Economic evaluation [76];