SEIR-DIT

SEIR-DIT is a mathematical compartmental model aimed to study the effect of detection of symptoms, isolation and contacts tracing as an alternative to COVID-19 control.

The model is composed of two main ODE systems. A SEIR-like model (see Figure 1) that describes the epidemic dynamics and contains the main epidemiological states, and a secondary compartmental model (see Figures 2,3 and 4), fed by the main SEIR-like model, that allows to calculate the testing requirements and the amount of isolated cases and contacts at every time.

Main SEIR-like model

• S: Susceptible
• Q_S1: Quarantine for suspected index cases and contacts
• Q_S2: Quarantine for non-exposed traced contacts of detected mild infections
• E: Exposed
• E^T: Exposed traced contacts of detected mild infections
• I_M: Mild infections
• I_M^D: Detected mild infections
• I_M^T: Traced mild infections (coming from exposed traced contacts)
• I_C: Infections requiring hospitalization
• I_C^SI: Self-isolated infections requiring hospitalization
• I_C^T: Traced infections requiring hospitalization (coming from exposed traced contacts)
• I_HR: Hospitalized infections that require a general hospital bed and recover
• I_UR: Hospitalized infections that require an ICU bed and recover
• I_HD: Hospitalized infections that require a general hospital bed and die
• I_UD: Hospitalized infections that requiring an ICU bed and die
• I_R: Hospitalized infections requiring a general hospital bed after recovering from ICU stay
• R: Recovered
• D: Dead

Fig. 1. SEIR-like model

Secondary compartmental model for testing and isolation

• Q_IM^D1: Detected mild infections with positive antigen test
• Q_S1: Quarantine for suspected index cases and contacts
• Q_S2: Quarantine for non-exposed traced contacts of detected mild infections
• Q_E^T: Exposed traced contacts (isolated after tracing)
• Q_IM^T: Isolated mild infections (coming from traced exposed contacts)
• Q_IM^T1: Traced mild infections with positive RT-PCR test
• Q_IC^T: Isolated infections requiring hospitalization (coming from traced exposed contacts)

Fig. 2. Isolation and testing of probable index cases	Fig. 3. Isolation and testing of suspected index cases and their contacts

Fig. 4. Isolation and testing of exposed contacts

Fig. 5. Isolation and testing of non-exposed contacts

Parameters

Epidemiological parameters for transitions between infectious states

The parameters of the main SEIR-like model were adapted from https://mrc-ide.github.io/global-lmic-reports/parameters.html, assuming that the probability of death for critical cases is 0.35

Parameter	Value	Definition
R0	3.0	Reproduction number
β0	1.3743	Transmission rate in absence of social distancing
β1	0.0199	Transmission rate within households
b	-	Probability of transmitting the disease b=βM/n
n	15.721	Average number of contacts per individual
βH	0.001	Hospital transmission rate
ω-1	4.6 days	Mean incubation period
σC-1	3 days	Mean time upon self-isolation for severe infections
σCSI-1	4.1 days	Mean duration of isolation for severe infections prior hospitalization
σCT-1	7.1 days	Mean duration of isolation for traced contacts with severe infection prior hospitalization
γM-1	2.1 days	Mean duration of mild infection
γHR-1	9 days	Mean duration of hospitalization for non-critical cases if survive
ν-1	14.8 days	Mean duration in ICU if survive
γR-1	3 days	Mean duration of stepdown post ICU
σHD-1	9 days	Mean duration of hospitalization for non-critical cases if die
σUD-1	11.1 days	Mean duration in ICU if die
δM	0.97902	Probability of mild infection
δHR	0.67959	Probability of recovery for hospitalized infections requiring a general hospital bed
δUR	0.13883	Probability of recovery for hospitalized infections requiring an ICU bed
δHD	0.10682	Probability of dying for hospitalized infections requiring a general hospital bed
δUD	0.07476	Probability of dying for hospitalized infections requiring an ICU bed

DIT parameters

A. Contact tracing

Group	Contacts per group	SAR	Proportion of traced contacts	Traced contacts of suspected index cases (nT)
Index case	0	-	-	0	0	0
Household	2.039	25%	100%	2.039	0.26	0.11
Work / school	5.931	15%	80%	6.784	0.61	0.41
Other	7.751	5%	50%	10.659	0.71	0.67

B. Testing and isolation

Parameter	Value	Definition
α-1	1 day	Mean time between onset of symptoms and detection
ρ-1	12 days	Mean duration of isolation period
TPCR	2 days	Mean time to results of RT-PCR test
ξPCR	0.85	Sensitivity of RT-PCR test
TAG	1 days	Mean time to results of AG test
ξAG	0.75	Sensitivity of AG test