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Year : 2020  |  Volume : 4  |  Issue : 2  |  Page : 79-83

Dynamics of SARS-CoV-2 outbreak in the Kingdom of Saudi Arabia: A predictive model

1 Department of Critical Care, King Saud Medical City, Riyadh, Kingdom of Saudi Arabia
2 Department of Critical Care, King Saud Medical City; Department of Critical Care, Al Imam Abdulrahman Al Feisal Hospital, Riyadh, Kingdom of Saudi Arabia
3 Department of Critical Care, King Saud Medical City, Riyadh, Kingdom of Saudi Arabia; Department of Anesthesia, Faculty of Medicine, Tanta University, Tanta, Egypt
4 Department of Critical Care, King Saud Medical City, Riyadh, Kingdom of Saudi Arabia; Department of Anesthesia, Faculty of Medicine, Ain Shams University, Cairo, Egypt
5 Department of Critical Care, King Saud Medical City, Riyadh, Kingdom of Saudi Arabia; Department of Critical Care, Keck School of Medicine, University of Southern California, Los Angeles, CA, USA

Date of Submission04-May-2020
Date of Decision20-May-2020
Date of Acceptance24-May-2020
Date of Web Publication1-Jul-2020

Correspondence Address:
Waleed Tharwat Aletreby
Department of Critical Care, King Saud Medical City, Riyadh
Kingdom of Saudi Arabia
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/sccj.sccj_19_20

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Background: COVID-19 is a worldwide pandemic that was first reported in China, and has spread to almost all nations. Measures of containment and control practiced by governments and authorities may benefit from prediction of the extent and peaks of spread to properly prepare to face the pandemic. Aim: The aim of the study was to predict the peak numbers of mortality, intensive care unit (ICU) admission, hospitalization, and positive cases and the time of their occurrence. Settings and Design: The study design is of a mathematical prediction model of prediction of spread of infectious disease, based on data from Saudi Arabia. Materials and Methods: We utilized a SEIR predictive model that divides the population into compartments and utilizes mathematical equations to predict the dynamics of the infection and its peak. The model exploited data from reliable sources on the Internet, and is – by design – based on certain assumptions. Statistical Analysis: Predefined mathematical equations that incorporate different parameters and assumptions were used for statistical analysis. Results: We estimated an R 0 value for our model of 2.2, and the model predicted a peak incidence of the pandemic around July 26, 2020. The peak mortality was predicted at 99,749 persons, predicted peak ICU admission of 70,246 patients, and peak hospitalization of 11,997,936 patients; all these predicted values were out of a total of predicted 14,049,104.83 COVID-19-positive cases. Conclusion: The COVID-19 pandemic in Saudi Arabia is predicted to peak by the end of July 2020, and may pose a serious burden on health-care systems already in shortage. Proper crisis management and effective resource utilization is crucial to safely overcome the pandemic, in addition to continuing control measures at least till the predicted peak time is over.

Keywords: COVID-19, dynamics, prediction, SARS-CoV-2

How to cite this article:
Aletreby WT, Alharthy AM, Faqihi F, Mady AF, Ramadan OE, Huwait BM, Alodat MA, Lahmar AB, Mahmood NN, Mumtaz SA, Alzayer W, Karakitsos D. Dynamics of SARS-CoV-2 outbreak in the Kingdom of Saudi Arabia: A predictive model. Saudi Crit Care J 2020;4:79-83

How to cite this URL:
Aletreby WT, Alharthy AM, Faqihi F, Mady AF, Ramadan OE, Huwait BM, Alodat MA, Lahmar AB, Mahmood NN, Mumtaz SA, Alzayer W, Karakitsos D. Dynamics of SARS-CoV-2 outbreak in the Kingdom of Saudi Arabia: A predictive model. Saudi Crit Care J [serial online] 2020 [cited 2023 Mar 26];4:79-83. Available from: https://www.sccj-sa.org/text.asp?2020/4/2/79/288730

  Introduction Top

In the late 2019, the city of Wuhan (Hubei province, China) first reported cases of pneumonia of unknown origin.[1] Since then, a global outbreak of severe acute respiratory syndrome (SARS) was confirmed due to infection by a novel coronavirus that was termed as SARS-CoV-2 (COVID-19).[2] High-throughput sequencing has revealed that COVID-19 is the seventh member of enveloped RNA coronavirus belonging to the Orthocoronavirinae subfamily.[3] Despite the severity of COVID-19 seeming to be lower compared to the previous coronavirus diseases namely severe acute respiratory syndrome (SARS) and Middle East respiratory syndrome (MERS), its incubation period, the droplets/contact transmission, and the relatively low pathogenicity contributed in sustaining the pandemic thus far.[4] COVID-19 is transmissible via contact, the fecal–oral route, and aerosolized particles, but whether the infection might be considered as airborne remains obscure.[5] As of May 1, ≥3 million confirmed cases and ≥200,000 deaths were reported across the globe, while the already-burdened health-care infrastructure is exposed up to an irreparable point.[2] Saudi Arabia confirmed just above 24,000 cases and 169 fatalities so far.[6] The Kingdom applied strict measures to contain the outbreak such as suspension of schools, public/religious gatherings, and international flights, as well as imposing of curfews and lockdowns within its borders.[7] Notwithstanding, during a pandemic, understanding the transmission dynamics of the infection to clarify the changing patterns of spread and evaluate the effectiveness of control measures is essential.[8] In that sense, health-care systems should demonstrate readiness to face the increasing demand of hospitalization and intensive care unit (ICU) admissions.[9] Several predictive models were used to understand the pattern of spread and recovery of infectious outbreaks.[10] A popular model is the Susceptible–Exposed–Infected–Recovered (SEIR), which divides the population into compartments and utilizes numerous mathematical equations based on certain predetermined assumptions to predict peaks of infection spread. Moreover, the SEIR model takes into account various interventions aimed on controlling the infection spread.[8],[11],[12],[13] In this study, we devised a simplified SEIR model that would conveniently help in evaluating the peak rates of COVID-19 cases, ICU/hospital admissions, and deaths within a specific time period in Saudi Arabia.

  Materials and Methods Top

Data collection

Required input to construct the model was gathered from various governmental and other internet sources such as the Weqaya website (https://covid19.cdc.gov.sa/daily-updates/) and the Saudi Arabia COVID-19 dashboard (https://covid19.moh.gov.sa/), which are both affiliated to the Saudi Ministry of Health (MOH).

Susceptible–Exposed–Infected–Recovered model compartments

The model focuses on the basic processes that are directly related to the COVID-19 pandemic. The population was divided into six compartments as follows:

  • Susceptible compartment, S(t): The total number of population susceptible to be infected, which we assumed to be the total population of Saudi Arabia
  • Exposed compartment, E(t): The total number of population who are infected but are yet to show signs and symptoms (still in the incubation period)
  • Infected compartment, I(t): The total number of infected persons showing signs and symptoms
  • Recovered compartment, R(t): The total number of population who recovered from the infection
  • Deaths' compartment D(t): The number of fatalities
  • P(t): The public perception of risk.

The mathematical equations that formulated the SEIR model[8],[11],[12],[13],[14],[15],[16] are briefly presented hereby:

where a is the flow rate constant and N is the total population; β is the probability per unit time of transmitting a disease between two individuals in contact; λ is the contact rate; E is the mean latent period; α is the disease death rate; γ is the mean infectious period; T(t) is the treatment rate function which is the measure of health-care system of a country; u, u+, and u−, respectively, represent the total testing rate, positive testing rate, and negative testing rate; h is the rate constant for elderly population which have been the target of this virus; e is the proportion of severe cases; and f is the public reaction constant; α was calculated as the average value of daily death rate. The reason is that the disease death rate is fluctuating with every day. Here, βλ is the transmission rate C. This C is established in equation (7) as:

The reason for using the factor of 0.3 as coefficient to δ is that before the lockdown, everything was normal and people were free to move in the country. After the lockdown, the constant will be −1, and it will take the form described in equation (8)

where C0 is the transmission rate, δ is the government strength constant, and k is the respond intensity constant. The reason for adopting this transmission rate is that it integrates the lockdown and public responses.

Model assumptions

Our SEIR model is based on several assumptions. The latter remain mostly theoretical and could be indeed wrong as they were not tested; however, they are deemed to be necessary when tailoring a predictive model.[8],[11],[12],[13],[14],[15],[16] Hence, the basic assumptions used were:

  1. Recovered patients were assumed to have immunity and were consequently removed from the susceptible compartment. Although no definitive data existed to support this notion, the latter may be justified at least partially by the fact that the re-infection rates are generally considered to be low in the Kingdom. However, complete recovery might not have been the case, and the former may be related to low viral loads rather than the established immunity[15],[16],[17]
  2. Population mixing is assumed to be homogeneous: When a group of people have the same exposure risk to a positive case, then they are considered to have equal chances of getting the disease[16],[17],[18],[19]
  3. The incubation period is relatively short and the disease is of an acute nature.[16],[17],[18],[19]

A critical parameter integrated in the model is the reproduction number (R0) defined as the number of secondary cases resulting from exposure to a primary one. R0 usually follows an approximated exponential growth rate when integrated in predictive models.[8],[11],[12],[13],[14],[15],[16],[17],[18],[19] Taking into account the control measures imposed by governments to control the infection spread, R0 is reduced by percentages on the dates of imposing the control measures. In addition, the model takes into consideration both the hospitalization and ICU admission rates. No individual patient's data were collected and used in this study as such no ethical approval or consent was applicable.

Statistical analysis

We utilized Microsoft® Excel sheet to construct our simplified prediction model by using mathematical equations that were described in detail elsewhere.[8],[11],[12],[13] Data that were changing daily were used from reports on April 30, 2020, and the model was constructed for 365 days from the onset of the first case in Saudi Arabia. As a sensitivity test of our model, we reported the predicted number of positive cases, number of hospitalized cases, number of cases admitted to ICU, and mortalities on April 30, 2020 and compared them to actual numbers using two-tailed Chi-square test, considered statistically significant with P < 0.05 (two tailed).

  Results Top

Fixed-model variables

The first COVID-19 case in Saudi Arabia was reported on March 2, 2020. The population of Saudi Arabia for 2020 is 34,810,000 constituting the susceptible population. On April 30, 2020, there were a total of 22,753 reported positive cases, out of which 3163 recovered (recovery rate = 13.9% [95% CI = 13.5%–14.4%]), 19,428 cases were hospitalized at a rate of 85.4% (95% CI: 84.9%–85.9%), ICU admission accounted for 123 cases at a rate of 0.5% (95% CI: 0.4%–0.6%), and the mortality rate was 0.71% with 162 reported deaths (95% CI: 0.61%–0.83%). We assumed an incubation period of 5.2 days, which accounted for a R0 value of 2.2 using previously published data from China.[16],[17]

The predicted numbers in our model on April 30, 2020 for positive cases, hospitalized cases, cases admitted to ICU, and mortalities were 22,903.02, 19,559, 115, and 163, respectively. There was no statistically significant difference between any of the actual and predicted values [Table 1].
Table 1: Comparison of actual and predicted numbers on April 30, 2020

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Peak predicted number

Our model showed that the peak values of the pandemic may occur around June 26, 2020. The model estimated 14,049,104.83 positive cases, out of which, 11,997,936 cases required hospitalization. Similarly, the predicted ICU admission and mortality rates were 70,246 and 99,749, respectively [Figure 1], [Figure 2], [Figure 3].
Figure 1: Susceptible–Exposed–Infected–Recovered predictive model

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Figure 2: Predictive model featuring peak hospitalization rates

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Figure 3: Predictive model featuring peak intensive care unit admission and mortality rates

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  Discussion Top

The SEIR model is commonly used to predict the spread, peak, and recovery rates of infectious outbreaks in epidemiological studies.[16],[17],[18],[19] The model offers several advantages including simplicity of its hypothesis, straightforward calculations, and fairly accurate projections that are comparable to those derived by more complex models.[8],[11],[12],[13],[14],[15],[16],[17],[18] However, the model remains mainly within the realm of prediction. All similar models are inherently stochastic, which means that they follow a random probability distribution or pattern that could be statistically analyzed but not precisely predicted.[8],[11],[12],[13],[14],[15],[16],[17],[18],[19] We fitted our model with as few as possible parameters to avoid overfitting, hence our sensitivity test revealed its robustness as the predicted and actual values for April 30, 2020, in Saudi Arabia were almost similar. The present results integrated various predictions regarding the COVID-19 outbreak in the Kingdom. Among the rather optimistic predictions of the model was the prediction that the pandemic would start to decline by the end of July 2020. Moreover, the current mortality rate in the Kingdom remains significantly lower than the 3.4% estimated by the World Health Organization (WHO) and the same applies to ICU admission rates.[2] Nevertheless, the model predicted that around 12 million people would require hospitalization during the peak of the epidemic, which could be merely an overestimation as all theoretical models tend to produce similar results. Therefore, the model should not be interpreted in terms of absolute peak numbers but as a tool in identifying trends and projections.[15],[16] Despite the aforementioned limitations, the high hospitalization rate practiced by Saudi Arabia could be considered as an independent control measure due to the fact that COVID-19 patients are definitely isolated and thus cease to be an active threat of shedding the virus to the community. However, higher hospitalization rates reflect a tremendous burden on the health-care system and increase the exposure risk of health-care workers. This becomes more evident when reviewing the statistics' book issued by the MOH in 2018 that summed available hospital beds in MOH hospitals to 43,680 at a rate of 13.1 hospital beds per capita.[20] MOH collaborators reported that our national health-care system will probably require an additional 2.2–2.7 hospital beds per capita by 2030.[21] However, a comforting statistic regarding the MOH ICUs is that the bed occupancy rates never exceeded 80% (≤30% for ICUs with ≤50 beds), which, in turn, means that when operated at full power, MOH hospitals and ICUs may be able to accommodate a larger number of patients.[20] A critical factor in our model was the R0 which was estimated to be 2.2. The latter is the average number of new infections that result from a single infected person in a wholly susceptible population. Previous studies estimated larger R0 values. Liu et al.[22] reported a mean R0 value of 3.28 and a median of 2.79, with upper limits reaching up to 6.49. Obviously, the lower median value is more realistic than the mean in view of the apparent lack of normality in the distribution. The R0 can vary by factors that influence the contact rate between people, such as physical distancing strategies and lockdowns aimed at driving the R0<1, indicating that that an outbreak is shrinking rather than expanding.[8],[11],[12],[13],[14],[15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25] Our estimated R0 of 2.2 is in accordance with that of previously published studies and data derived by the WHO.[15],[21],[24],[25] Furthermore, we may argue that a value of 2.2 is considered to be more realistic for Saudi Arabia because the first case was reported in early March 2020. By then, the issue of COVID-19 pandemic was well known worldwide and authorities have already implemented precautions and control measures accordingly. Notwithstanding, the Kingdom's government should be praised as Saudi Arabia was one of the first countries to shutdown schools, suspend public gatherings as well as international and domestic flights, and impose curfews and lockdowns on entire regions and districts within its borders. All these measures presumably attributed significantly in reducing the number of secondary cases and partially control the COVID-19 outbreak. However, the R0 for COVID-19 cannot be accurately determined in various countries due to the challenges in identifying and testing infected persons. It was suggested that it could be even higher as it is different for each person and may also change due to the natural variability in viral shedding by infected persons.[26]


Our theoretical SEIR model predicted that the COVID-19 outbreak will reach its peak by the end of July 2020. Peak predicted rates for mortality were 100,000 cases, ICU admissions approximately 70,000 and about 12 million people requiring hospitalization bearing in mind that the aforementioned numbers are subjected to the model's restrictions. The latter integrate several theoretical assumptions and calculations that were deemed necessary to tailor such a model. All epidemiological models when predicting infection spread dynamics tend to overestimate the aforementioned parameters due to the exponential growth rate of the R0 integrated by design.[8],[11],[13],[15],[16],[17],[18],[19],[20],[21],[22],[23],[24],[25] Therefore, the interpretation of our results should be performed with caution as it is not regarding absolute numbers but rather about predictive trends. Moreover, the average value of the R0 used does not reflect accurately the biological quantity as it depends on social behavior and contacts.[20],[21],[22],[23],[24],[25],[26] Despite the aforementioned limitations, the present results clearly showed the heavy burden applied on our national health-care system by the pandemic despite proper crisis resource management. Finally, based on the current predictive model, it is strongly advisable not to relax infection control policies and continue to practice recommended safety measures as the MOH clearly advocates. The Kingdom should be prepared for at least another 18–24 months of COVID-19 activity as virus shedding in the community may continue. Hopefully, the latter could match a seasonal pattern of outbursts with diminished severity over time similar to the traditional viral pandemics.[26],[27] Concluding, our predictive model estimated a reproduction number (R0) of 2.2 and a peak incidence of the pandemic around July 26, 2020, in the Kingdom, while the projected ICU admission and mortality rates were 99,749 and 70,246, respectively.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

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  [Figure 1], [Figure 2], [Figure 3]

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