Population-based Simulation of COVID-19 Outbreak in Iran: Comparison of Different Policy Options

Over the last few decades, mathematical models of disease transmission have been helpful to gain insights into the transmission dynamics of infectious diseases and the potential role of different intervention strategies (Chowell et al., 2016; Jenner et al., 2020). Currently, there is a global pandemic of COVID-19. To assess its prevalence, it is necessary to have adequate models that allow real-time modeling of the impact of various quarantine measures by the state. It is advisable to simulate and assess organizing or planning any epidemic prevention measures before their implementation. In other words, all the possible ways of spreading a viral infection should be simulated in real time without the involvement of real people (Vyklyuk et al., 2021). Simulation and modeling of the COVID-19 outbreak can prognosticate behavior of the disease and simultaneously provide planners with a picture of what to expect. Furthermore, simulation allows the planner to test different scenarios and programs in a hypothetical setting beforehand and choose the suitable option.

When reformulating the conceptual population model into an operative simulation model, one can choose between a micro-model approach describing every individual or a macro-model approach aggregating the individuals into classes/states of individuals where only the number of individuals in each state is described. These types of models are needed for different perspectives (Gustafsson and Sternad, 2007). It was stated that micro-simulation and macro-simulation are essentially two alternative methods for making similar statements about the future. However, despite this essential similarity, for practical purposes one will virtually never be indifferent between micro-simulation and macro-simulation (Van Imhoff and Post, 1998). Macro models can provide useful projections at the aggregate level, but their analyses are usually insufficient to reveal the individual impact (Li, 2011).

In fact, microsimulation models differ from the more traditional cohort-based models since they simulate the impact of interventions or policies on individual trajectories rather than the deterministic mean response of homogeneous cohorts. Cohort models investigate a hypothetical homogeneous cohort of individuals as they transition across health states (Krijkamp et al., 2018; Marois and Aktas, 2021). Microsimulation is a technique used to model complex real-life events by simulating the actions of, and/or the impact of, policy change on the individual micro unit (Harding, 2007; Spielauer, 2011; Marois and Aktas, 2021). In a standard situation, each individual in the simulation is an observation in a rectangular data file, which contains records of demographic characteristics and other key variables of interest. The simulator takes as input population files and demographic/epidemiological rates, and updates the population accordingly (Zagheni, 2015).

Microsimulation is the preferred modeling choice if individuals are different, if differences matter, and if there are too many possible combinations of considered characteristics to split the population into a manageable number of groups (Spielauer, 2011). Microsimulation can be used to create static or dynamic models. A static model is a way of synthesising data to produce an entire population estimate of individuals. It is dynamic microsimulation which is used in population projections and to perform ‘what if’ scenario testing of policy interventions (Lomax and Smith, 2017). When heterogeneous populations are used in simulation, one can not only predict the future behavior of the model, but it’s also possible to test different scenarios and policy options on different population groups and compare the results. In this paper we pursue the latter goal to assess the effect of different policy options on COVID-19 outbreak in Iran.

There are a few simulation studies on the outbreak in Iran. The COVID-19 International Modeling Consortium (CoMo Consortium) was created by researchers at the University of Oxford and Cornell University, is partnering with infectious disease modelers and public health experts from over 40 countries in Africa, Asia and America. Iran is part of this Consortium and uses its results in planning. The CoMo consortium has developed an age-structured, compartmental Susceptible-Exposed-Infectious-Recovery (SEIR) model to estimate the trajectory of COVID-19 based on different scenarios, and assess the potential impact of the various behavioral change strategies as well as treatment and vaccines, when they become available.

In Iran, on the other hand, the study conducted by Ghaffarzadegan and Rahmandad (2020), draws a modeling-in-real-time of the emerging outbreak of COVID-19 for understanding the state of the disease. They developed a simple dynamic model of the epidemic to provide a more reliable picture of the state of the disease based on time series data for official reports of death, recovered patients, and cumulative number of infections over time and unofficial data points including four observations about the number of Iranian passengers diagnosed with COVID-19 upon arrival in international airports, and three estimates aggregated by healthcare providers in Iran and reports by some news agencies about total cases of death from COVID-19. They estimated about 493,000 infected cases (90% CI: 271K-810K) as of March 20th, 2020. Their estimate for cumulative cases of infection until that date is 916,000 (90% CI: 508K, 1.5M), and for total death is 15,485 (90% CI: 8.4K, 25.8K). These numbers are significantly higher than official statistics. In an another study, Zareie et al. (2020) predicted the number of patients until April 15, 2020 through estimating the three parameters of time-dependent transmission rate, time-dependent recovery rate, and time-dependent death rate from COVID-19 outbreak in China and using the number of COVID-19 infections in Iran. Based on their predictions of Iran about 29,000 people were supposed to be infected from March 25 to April 15, 2020. On average, 1,292 people with COVID-19 were expected to be infected daily in Iran. The epidemic peaks within 3 days (March 25 to March 27, 2020) and reaches its highest point on March 25, 2020 with 1715 infected cases.

The Como Model as a representative of macro-models uses UN aggregate data based on age and sex. However, this model defects in assuming the population to be homogeneous. Some of individual based models are suffering from this presumption as well. For example, in the Cellular Automata (CA) model, population movement (in order to be at risk of disease) is assumed to be random and stochastic while a population is heterogonous in terms of demographic, economic and social characteristic.

Indeed, an important feature of a CA is that the automata’s location does not move; they can only change their state. The position of the cells and their neighbourhood relations remain fixed over time. CAs cannot have more than one attribute; for example, a cell could be occupied or unoccupied, but the cell could not contain multiple attributes (Crooks and Heppenstall, 2012).

Simulations considering only final outcomes, e.g. infections/deaths, that use time series data, fall into another problem. In other words, number of infections or deaths is function of age structure, geographical distribution of the population and other socio-economic characteristics. Due to the fact that the population of Iran is scattered in different districts with different population densities, and also this population is heterogeneous in terms of age and sex, our study provides a better understanding of the mechanism of disease prevalence and policy scenarios.

Recent modeling papers on COVID-19 focus principally on the epidemiology, attempting to both estimate the basic reproductive number of the disease and to provide estimates of the effectiveness of different interventions in flattening the growth curve of the epidemic in order to reduce the burden on the healthcare system (Currie et al., 2020). The theoretical framework most commonly used is based on the division of the human host population into categories containing susceptible, infected but not yet infectious (exposed), infectious, and recovered individuals (Lekone and Finkenstädt, 2006). The (SEIR) model provides a mathematical framework to explain the spread of infectious diseases and has been previously used for estimating the epidemiological parameters of several infectious diseases such as measles, Ebola, and influenza (Sharifi et al., 2020).

Iran’s Epidemiological Committee of National Corona Virus Taskforce used an extended form of the susceptible-exposed-infected/infectious-recovered/removed (SEIR) model, which is a dynamic modelling approach. Such epidemiological models are assumed to be compartmental; the target population will be divided into different sections or compartments (To see mathematical formulas and relationships, please refer to the Supplementary file 1 of the study conducted by Sharifi et al., 2020). In brief, they considered the following compartments: (a) susceptible, referring to the total number of individuals (ie, hosts) who have been susceptible to COVID-19. They assumed the entire population as susceptible in their model; (b) exposed, referring to individuals who are exposed to COVID-19 while they are asymptomatic and not yet infectious; (c) infected, referring to infected people who demonstrate clinical symptoms after their incubation period and have the potential to transmit the disease to other susceptible individuals; and (d) recovered/ removed, depending on the severity of the disease. they assumed that the infected people will (i) be recovered and immune from re-infection and therefore, no longer transmit the infection, (ii) have mild to moderate clinical symptoms and follow home-isolation guidelines without the need to be hospitalized, or (iii) have severe clinical symptoms and require hospitalization. These individuals would either be recovered or die and therefore, removed from the model (Sharifi et al., 2020).

In our study, we expanded the conceptual framework of Iran’s Epidemiological Committee of the National Coronavirus Taskforce by incorporating socioeconomic, demographic, and geographical variables into the model.

The aforementioned model assumes that individuals in the society are homogeneous. For example, the probability of infection is calculated by dividing the number of infected individuals by total population and this probability is presumed to be equal for all individuals of the society.

On the other hand, in our study the probability of infection is calculated separately for each district and in case of no infected individual in the district, the probability will be zero. Furthermore, in the households with an infected person, the probability is calculated by dividing the number of infected individuals by the number of the household members. For these households, the model uses the maximum of household or district probabilities of infection. In the expanded model (Figure 1), the variables of district, household, population movement, population density, urban and rural status, economic and social status, age, gender, occupation, and education have been added to the original framework. As a matter of fact, early onset of the disease occurs from a few districts, hence as long as an infected individual has not moved to another district, the probability of infection in the latter district is zero which causes no prevalence. Moreover, the probability of infection within households with an infected individual may be more than other individuals in the same district. Population movement causes the spread and dissemination of the disease in different districts. Population density affects an individual’s number of daily contacts. It is expected that districts with low population density, have lower number of daily contacts. In rural areas, population density is lower than in the urban areas. Employed individuals have more contacts than others and if infected, they are less likely to be effectively isolated. Educated individuals, due to their job type and health literacy level, mostly have fewer contacts (in epidemic conditions) and if infected, they are more likely to isolate. The socioeconomic status of individuals can affect the probabilities of exposure, isolation, recovery, hospitalization, and death. Age and sex can also affect the probabilities of hospitalization and death. The newly added variables are marked with green boxes and red lines in Figure 1.

Figure 1

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The statistical population of this study includes 78,921,893 individuals of population in Iran based on the 2016 census. However, a 2% sample of this census which has been published by the Statistical Center of Iran (SCI) as raw data is used in simulation. The SCI selects a 2% sample of census and publishes for public use.¹ The sampling method is considered as stratified random sampling. After determining the 2% sample size for each urban/rural area of each district, households are selected. To have enough samples from less populated districts, they may contribute more than 2% to the sampling framework. Weights are used at both household and individual level to offset any over or under representation. On the basis of this process, the household weight is calculated equal to the inverse- probability- of- selection and by adjusting this weight based on the population of each sex in the urban/rural area of each district, the individual weight is defined. As a result, there are representative samples from all 429 districts of Iran in this data. For example, more samples are selected from districts with low population, but they will also be given less weight. Therefore, the 2% sample data represents the total population of Iran and its districts at the time of census (SCI, 2016a). The sample size used in this simulation is 1,579,435 individuals. Considering the variable of weight in the data and applying this variable in statistical calculations, we may show indicators for the whole statistical population. Due to the 5.67% growth of the country’s population since the 2016 census, all indicators related to the number of events must be multiplied by 1.0567 to calculate the value of the indicator for the current time. However, one should beware of the fact that not all population groups grow at similar rate.

This simulation uses R Software. R is a programming language that has gained recognition within the field of decision modeling and simulation. It has the capacity to perform microsimulations more efficiently than software commonly used for decision modeling, incorporate statistical analyses, produce more transparent models and reproducible results. However, no clear guidance of implementation of microsimulation models in R exists (Krijkamp et al., 2018). So, all R codes are written by researchers and no specific package was utilized for simulation. However, multiple packages were used in the process of data management and simulation.²

Based on the country’s official reports and available epidemiological data, January 21, 2020 was considered as the initial day of the COVID-19 outbreak in Iran. National Epidemiological Committee used several parameters as model inputs and obtained their values from a comprehensive literature review and published articles in relation to COVID-19, as well as relevant parameters derived from estimates in similar epidemics, in particular, H1N1 influenza (Haghdoost et al., 2009). They first shared the initial values of the parameters with Iran’s national and scientific committees and experts, and made the necessary adjustments, accordingly. They compared the revised values of these parameters with the literature as well as the epidemic pattern in Iran. They then made the final revisions for the values of the parameters used as the extended SEIR model inputs (Sharifi et al., 2020). The model variables and their parameters are presented at Table 1.

As mentioned earlier, in this study, the simulation is using micro and real demographic data. Accordingly, individuals are located in different districts of Iran, a total of 429, and in each district they are clustered within households. The population of the districts is not closed, and a number of individuals move inter-districts daily. On the day of the study, the entire population is in a susceptible to disease state. On the first day (January 21, 2020), in three districts of Tehran, Qom, and Rasht, approximately 1150 individuals (with a probability of 105 individuals per one million individual) are exposed to the disease. Due to population movement, these individuals or new patients who were in contact with the initial cases, may travel to other districts and expose the individuals of these districts to disease. Individuals in the household are exposed to the disease by the maximum of probabilities of infection at the district or household level. The population density of the districts affects the number of daily contacts. In this study, the correlation coefficient between the population density of the districts and the number of daily contacts of individuals is considered in average to be 0.4. To determine daily population movement pattern between districts, the migration matrix of the 2016 census which shows permanent inter-district migration for a five-year period (2011-16), has been used.⁵ As daily movements are not recorded, the migration matrix is used as a proxy for daily movements. In the model which runs by daily increments, single-day movements are assumed which means travelers return to their permanent place of residence at the end of the day. Age and sex distribution of hospitalized patients as well as the deceased patients reported for Tehran University of Medical Sciences, used to determine the probability of hospitalization and death by age and sex (Table 2).

In order to take into account, the stochastic and uncertainty nature of the model, two steps are taken. In the first step, all parameters are randomly determined by a specific distribution for individuals. For example, if it takes an average of 4.9 days for an exposed person to become ill, a random number is assigned to each exposed individual. These random numbers follow a normal distribution with a mean of 4.9, and a standard deviation of 1. However, no one can have a number less than 2. The details of all parameters are presented at Table 1, which are either based on available literature or agreed upon by a group of national experts. In the second step, to consider the randomness of the phenomenon, the whole process must be iterated several times. This allows not only calculation of the average parameter values as the best estimate, but also calculation of the confidence interval of the estimates (for example, with 95% and/or 80% probabilities).

As mentioned earlier the simulation is done in a series of iterations, the procedure to run iterations is as follows. The iteration starts with a rectangular data of 1,579,435 cases and a set of necessary variables including a state variable which is set to susceptible state for all at day 0. At start of iteration, the R code randomly assigns the model parameters for each individual based on information provided in Table 1. At day 1 some cases are exposed to the infection as mentioned above. Once someone becomes exposed to the infection, s/he should pass through the conceptual framework and experience new status values determined by parameters assigned. As the model progresses to next days, it updates the status of each individual by calculating new probabilities of exposure for susceptible cases and assigning new status for exposed cases. The probabilities of exposure are calculated at both household and district levels. The maximum of the two is used in the model, however. At the end of iteration and also at each time increment, cases have different status (i.e. susceptible, exposed, infected, isolated, hospitalized, deceased, & recovered). The weighted frequency of status variable by time provides daily statistics at population level. Once an iteration ends, the program starts the whole process again in a new iteration where new values of parameters for each case are set randomly.

Probabilities of inter-district travel, calculated from migration matrix, are also used to calculate the daily location of each individual. Random number generators with binomial distribution are used to determine daily status and location for each individual utilizing the related probabilities.

The socio-economic and demographic variables added to the conceptual framework could affect the model in two ways. They either act on transition from susceptible to exposure state, by affecting number of daily contacts (e.g. the higher the population density, the higher the number of daily contacts) and population size (e.g. population movement spreads exposed and infected cases across different districts for new districts to be affected). Or they can affect the probabilities of isolation, hospitalization, and death (e.g. age-sex distribution of death). Not all socio-economic and demographic variables of the expanded conceptual framework are used in this simulation. For list of variables and their parameter values see Table 1. It’s worth noting that this study is not aiming to predict number of population at each state for the purpose of predicting the course of the pandemic in Iran. Instead, this study’s main goal is to use the model to examine different policy and health options and their effect on population. If the goal was to predict the course of disease in Iran, one needed to update the parameters regularly as new information becomes available. However, for comparing different policy scenarios, the important point is to run all scenarios using similar parameter values. This study compares the effect of eight different policy options on the spread of COVID-19 pandemic.

The results presented in this research are based on several times iteration of every policy scenario.⁷ The reported results for each scenario include the calculation of the median line, where 50% of the iterations are below the line and 50% above it. The first quarter (Q1) shows the line where 25% of the iterations are below it, and 75% are above the line. The third quarter (Q3) shows the line where 75% of the iterations are below it and 25% above the line. The median line of all scenarios is brought together in Figures 2–4, which compare different policy scenarios. Figures 2–4 show the median line of iterations for population at risk (susceptible state), hospitalized patients, and the total number of deaths at different scenarios. Figures 5–7 show all iterations for each policy scenario. The area between the first and third quarters, in these figures, is marked in light blue color. In these figures, the red line represents the median, and the gray lines are single iterations.

Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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According to Figure 2, the scenario with no intervention on all days of simulation (Scenario 1) has the lowest number of population at risk almost all the times. The most successful disease control policy seems to be the jobless quarantine scenario which has the largest number of healthy individuals at all times after starting of interventions. Based on this figure, of 78,921,893 healthy and susceptible individuals to disease on day zero of study across country, in no-intervention scenario 26,145,683 individuals are still healthy and exposed to disease on the last day of the simulation (day 200). In case of quarantining the students, this number increases to 38,467,580. Providing weekend lockdown, 67,574,552 individuals, with inter-province travel ban 26,334,141 individuals, with jobless quarantining 67,574,552 individuals; with elderly quarantine 31,722,408 individuals; with inter-district travel ban 26,334,142 individuals and with school policy which bears a resemblance to the policy of Iranian schools, 32,739,349 individuals do not get infected during the course of simulation. Therefore, quarantining of jobless individuals, and consequently keeping most people healthy is the most effective scenario among different scenarios. After the scenario without intervention, the least effective scenarios are the inter-district and inter-province travel ban from the 61^st day onwards. It seems day 61^st is too late for travel ban as districts could have their own outbreak once they have enough of infected population. Figure 2 also confirms this conclusion for all simulation days.

In terms of the hospitalized patients, as Figure 3 shows, no intervention and elderly quarantine policy scenarios have the highest number of hospitalized patients on the most days of the simulation. The lowest number of hospitalized patients is related to the policy option of jobless quarantine, which from the day of implementation of this policy, the 61^st day, the number of hospitalized patients shows a decreasing trend. Policy options of students quarantine, weekend lockdown and school closure policy in Iran after the jobless quarantine policy, show the lowest number of hospitalized patients on different days. It should be mentioned that in the school policy of Iran (scenario 8), due to the reopening of the schools after a temporary closure, the number of hospitalized has an increasing trend after the 121^st day. The implementation of two policy options of inter-district and inter-province travel ban from the 61^st day shows the least effect in reducing the number of hospitalized patients.

In terms of the total number of deaths due to COVID-19 disease, as Figure 4 shows, no intervention scenario or Herd Immunity has the highest number of deaths. The lowest number of death is related to the most effective policy option of jobless quarantine. Closuring policy of Iranian schools and universities due to its early start compared to other policies is the second effective policy in reducing the number of deaths up to day 120 of simulation. With reopening of schools and universities, the number of deaths in this scenario also increases. Like the previous indicators, in terms of the number of deaths as well, inter-district and inter-province travel ban due to late start, are the least effective policies after policy without intervention. Based on this figure, on day 200^th of study the median number of deaths in no intervention scenario is 89,839. If the jobless quarantine policy is implemented, this number declines to 19,109 with the highest decrease. Inter-Province Travel Ban with 84,732 deaths and Inter-District Travel Ban with 81,501 deaths are the least effective policy scenarios to reduce deaths from COVID-19 disease. Quarantining of students after the 60^th day of study until the last day of simulation is the second most effective policy.

The purpose of this study is to compare different policy options in Iran to prevent the spread of COVID-19 cycle and achieve the best policy scenarios. To reach this goal, the conceptual framework of the model proposed by the Iran’s National Corona Virus Taskforce has been developed and expanded in this study to include socioeconomic, demographic, and geographical variables. The simulation results of the Coronavirus Taskforce demonstrated that in the absence of new treatments, vaccines and stability of the contagious and infectivity rate of coronaviruses, the natural course of disease will continue in Iran in the coming years and is expected to affect up to 63% of population. This value is similar to the values predicted in other countries of the world. From their point of view, the most effective tool available is patient isolation to delay the severe wave of disease, so that suspected and infected patients have the least contact with healthy population and thus break the transmission chain.

In terms of comparison with other statistical models suggesting policy interventions, Pourmalek et al. (2021) conducted a rapid review to inform researchers about the methodology and results of epidemic estimation studies performed for COVID-19 epidemic in Iran. They believe that COVID-19 models which consider scenarios for policy options include key influencing factors such as role of asymptomatic cases in spread of the disease, under-reporting of deaths and cases, testing availability, and delayed diagnosis, and providing estimates for sub-national regions are more useful for epidemic control. This study has shown that most studies about COVID-19 intended to predict the upcoming situation. However, most of them were unsuccessful in evaluating and presenting policy interventions. This failure was rooted in two distinct reasons. First, using inappropriate data which did not represent heterogeneous population structure of Iran and second, making a model that considered the same probability of infection and death for all population assuming homogeneity of the entire population of Iran.

Contrary to the model proposed by the Coronavirus Taskforce, which uses the macro method and assumes that the entire population of Iran is homogeneous, the main innovation of our study was to use real micro and demographic data in order to simulate the COVID-19 outbreak in Iran. This data allowed us not only to be able to simulate COVID-19, but also to examine various policy scenarios. After defining and investigating eight scenarios including no Intervention, student quarantine, weekend lockdown, inter-province travel ban, jobless quarantine, elderly quarantine, inter-district travel ban, and Iranian school policy, we came to the conclusion that in terms of the number of population at risk, hospitalized patients and total number of deaths, Jobless quarantine is by far the most effective policy option in preventing the rapid spread of the COVID-19 in Iran. In all scenarios, the results are compared with the first scenario i.e. no intervention. In jobless quarantine scenario, all of these people must stay at home and the probability of infection for these people will only be at the household level. This seems to be true because of some demographic characteristics of Iran such as the low employment rate for women, high unemployment rate and the high proportion of student population. On the other hand, regarding restrictions on mobility and population movement, inter-province travel ban and inter-district travel ban scenarios are effective in the early stages of the disease, but if the infected population are scattered in all provinces/districts, these policies will play little role.

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Author details

1. Hassan Eini-Zinab

   Department of Community Nutrition, Tehran, Iran

   For correspondence

   Hassan.eini@gmail.com

   "This ORCID iD identifies the author of this article:" 0000-0002-6895-034X

2. Hananeh Sadat Sadeghi

   Department of Demography, Tehran, Iran

   For correspondence

   sadeghihananeh@gmail.com

   "This ORCID iD identifies the author of this article:" 0000-0002-5115-4312