We describe our modeling approach in three steps: 1) Estimation of new cases and deaths, 2) Calculation of disability weights, and 3) DALY estimation.
To estimate new cases (incidence) and number of death, we used the extended form of the Susceptible-Exposed-Infected/Infectious-Recovered/Removed (SEIR) model (Appendix, Figure A), which is a dynamic compartmental mathematical modeling. The SEIR conceptual model is shown in Figure 1.
The susceptible population (In our model, we assumed the entire population as susceptible) and exposed people (which refers to individuals who are exposed to COVID-19 while they are asymptomatic and not yet infectious), will be become infected (referring to infected cases who demonstrate clinical symptoms after their incubation period and have the potential to transmit the disease to other susceptible individuals). Ultimately, depending on the severity of the disease, the infected cases will have one of the following four states:
- Recovered and assumed to be immune from re-infection and no longer transmit the infection, or
- Mild to moderate clinical symptoms while they follow home-isolation guidelines without requiring hospitalization,
- Severe clinical symptoms and require hospitalization. Two probable outcomes are considered for this group of individuals such that they will be either recovered (and then discharged) or will not respond to the cares received (and then die), and
- Death and removed from the model.
We considered a probable scenario for the percentage of self-isolation of the infected or symptomatic cases in response to the epidemic in Iran. This scenario is one of the most possible intervention of the health system, behavior change of the public, and containment strategies. The mean of the self- isolation rate was considered to be 10% from January 21 to February 17, 20% after the initiation of the epidemic from February 18 to March 18, 30% from March 19 to April 17, 40% from 18 April to 24 September 2020 and finally, 50% from September 25 to January 19, 2021. The parameters of this part analyzed based on a recent established national study (13) and extended for one year instead of four months. The effective contact rate was considered a time-varying state. We extracted the values considered for effective contact rate within 12 months (one year) of the COVID-19 epidemic stratified by different national models. The first model incorporated and maximum value for effective contact rate, assumed to be 13 in the national model in the early weeks of the epidemic and after the announcement of the epidemic by the officials the minimum value of contact rate was considered to 5. The descriptions of time date and calibrations input parameters are presented in recent established study (13). The value of effective contact rate are presented in table 1 in Appendix.
A Monte Carlo method was used to build the 95% uncertainty intervals (UI) around the point estimates of the expected numbers. We used the statistical distribution of a set of parameters obtained from both the literature review and expert opinion. In order to generate more precise and reliable estimation of model parameters, we did a calibration and depicted the number of simulated cases in contrast to reported actual data. Data were analyzed using Vensim DSS 6.4E software.
- Disability weights
A key variable for YLD estimation is disability weight (DW). The amount of DW should be obtained from a national survey of DW (14-16). However, a limitation for this analysis is the lack of morbidity data for COVID-19, which forced us to rely on estimates for relative weights attributed to similar health states. To the best of our knowledge, there has been no study on the DW of coronaviruses, therefore we convened an expert panel and focused on alternative health states (14-16). The expert panel included fifteen clinical experts with relevant experience in infectious and pandemic diseases. We asked participants to rate possible COVID-19 disability weight compared to selected similar diseases for different severity levels and age groups (i.e., mild, moderate, and severe). We considered the statistical distribution for DWs from the existing evidences and expert opinions.
- DALY estimation
This study provides a prediction for burden of COVID-19 by measured in DALY. DALY is the sum of YLL and YLD (Equation 1).
DALYs = YLL + YLD (Eq1.)
We calculated the DALY using an incidence-based approach. The Coale and Demeny model life-table West was used to set the life expectancy table (10). The basic formula for YLLs is in Equation 2:
YLL = N × L (Eq2.)
N is the number of deaths due to the cause for the given age and sex in year; L is a standard loss function specifying years of life lost for death at age for sex (17). The estimation of YLD, which is calculated by multiplying the prevalence of disease by the disability weight, needs several parameters, including the number of deaths, incidence, age at onset, duration, and disability weight (DW) of COVID-19 (Equation 3).
YLD = Prevalence of disease ×DW (Eq3.)
Given the scarcity of evidence on the magnitude of the outbreak and the burden of COVID-19 in Iran, the research team used multiple sources of data to estimate the burden of COVID-19 under a social distancing and isolation scenario. Social distancing control measures are policies that aim to minimize close contacts within communities and include individual-level strategies (e.g., quarantine, self-isolation) and community-level strategies (e.g., prohibitions on public gatherings, closing public facilities, especially schools, and non-essential businesses) (18).
Our prediction is based on all PCR-confirmed COVID-19 cases, in line with WHO recommendations. The age-gender distribution of confirmed cases and deaths up to June 19, 2020 was extracted from the Ministry of Health and Medical Education (MHME) of Iran through a secure line of access.
To assess the impact of methodological choices (model and methodological uncertainty), such as the application of age weighting and the choice of the discount rate, we ran results under different scenarios for comparison. “Scenario analysis” is a type of multi-way sensitivity analysis (19), which can be used to identify the best scenario likely to appeal to decision-makers. From the economy and based on the concept that persons prefer benefits immediately rather than in the future, we can apply time discounting for future lost years of healthy life and age weighting (20, 21). We calculated DALY for COVID-19 based on four different social weighting scenarios. These were no age weighting or time discounting (A), age weighing but no time discounting (B), no age weighting but 3% time discounting (C), and age weighting and 3% time discounting (D). These analyses were done by SPSS and Excel software packages.