A new model for epidemic prediction: COVID-19 in kingdom saudi arabia case study.

Coronavirus disease-2019 (COVID-19) is a viral infection that rose in a city in the Chinese province of Hubei, Wuhan. The world did not wait too long until the virus spread to reach Europe, Africa, and America to be a global pandemic. Due to the lack of information about the behaviour of the virus, several prediction models are in use all over around the world for decision making and taking precautionary actions. Therefor, in this paper, a new model named MSIR based on SIR model is proposed. The model is used to predict the spread of the disease in three cities Riyadh, Hufof and Jeddah in the kingdom of Saudi Arabia. Also the estimation of disease propagation with and without containment measure is carried out. We think that the results could be used to enhance the predictability of the pandemic outbreaks in other cities and to build long term artificial intelligence prediction model.

Introduction

In 2019 of December, a city in the Chinese province of Hubei, Wuhan got reported on a number of pneumonia cases of an unknown aetiology [1]. It has been investigated for a week and found that the source of this disease in initial cases depends on the sea-food market selling wild animals and poultry [2]. This was the start of COVID-19 a humanitarian crisis on a global scale. Since the vaccine for this disease was not found on those days and the due to the temperament of the virus, it spreads very fast to be a global pandemic. While the situation in Asia and the Middle East evolves rapidly, the impact of the virus was significant not only to healthcare services but, also to education, sport and economy. The human scale of this tragedy is set to worsen as the virus spreads to more developing countries with a dilapidated health system like African countries [3]. According to a survey in America, 43% small businesses temporarily stopped and employment aslo falls by 40% because of COVID-19 pandemic [4]. On the 2nd of March 2020, the Ministry of Health confirmed the first infected case in the kingdom of Saudi Arabia [5]. Also, on the 5th of July, Saudi Arabia has 209,509 confirmed cases; it's the highest registered cases among the Arabian Gulf Countries, with 145,236 recoveries and 1,916 deaths [6]. The fast spread of the disease will make the government and legislative bodies to depend on prediction models to obtain insights about the spread of the virus and to assess the effectiveness of the enforced countermeasures [7]. Also, this outbreak is different from other recent outbreaks, that questions about the capability to adapt a pandemic model that can deliver accurate results. SIR is a model used in predicting the behaviour of the pandemic, particularly the number of susceptible, infected, and recovered people [8]. The core of this study is to predict the number of newly infected people in Saudi Arabia in three states Riyadh, Hufof and Jeddah by developing the SIR model. Also, we want to measure the effect of countermeasure applied on reducing the spread of COVID-19. To do that First, we describe COVID-19 Statistically then, collected the data needed for the calculation. After that, the developed model will be applied to the data and analyse the result. Finally, a conclusion is presented to summaries the primary outcomes.

Related works

This section introduces some important research that applies compartmental models to predict the spread of diseases and pandemics. The models use ordinary differential equations, and in some case stochastic can be used, which is more realistic but complicated to analyse.

SIR model

SIR (Susceptible, Infectious, and Recovered) model is a mathematical model used in disease spread prediction. Saulo B.Bastos and Daniel O.cajueiro utilised two variations of the SIR model to predict the progression of COVID-19 pandemic in Brazil. The effect of social distancing policies applied by the Brazilian government to reduce the COVID-19 spread in the short and long term has been studied. According to the result, the government imposed social distancing policy is managed to reduce the number of infections slightly. Still, it will not affect the spread of the disease in the long term [9].

Markov chain model

In [10], Reza Yaesoubi and Ted Cohen proposed a class of models to predict the disease that spreads over a large population. The proposed models based on a Markov decision process. It can be used efficiently with massive populations. The two advantages of this model in predicting dangerous diseases compared with existing ones are:

Used by dynamic optimisation to maintain health policies.

Prediction of disease spread over large population with limited size of state-space and considerable accuracy and time consumption.

The spreading of disease and information are two connected processes that has been under research for a long time. Guilherme Ferraz de Arruda et al., proposed a common information spreading model using discrete time Markov chains. It describes the relationship between disease spread and rumours propagation. It covers the traditional spreading schemes and features of social dynamics like forgetting, apathy and lost/recover interest. As a result, their model can be used to develop new fast and accurate algorithms for viral information spreading [11].

SIR and Markov chain combined

In [12], Alfonso Vivanco and Lira used Markov chain with SIR model to predict COVID-19 spread in Mexico state. A stochastic model is presented, characterising the probability of distribution of cases in Mexico by states. Although the study result can help the government and other legislative bodies to apply quarantine and fight against this pandemic, they did not compute the effect of medical countermeasures on the spread of the virus.

SEIR model

SEIR model stands for (Susceptible, Exposed, Infectious, and Recovered). It’s an epidemiological model used to predict disease infection. In [13], Cosimo Distante et al., used two approaches to study COVID-19 outbreak progress in Italy, especially in Lombardy, which has the highest count of infections in Italy. At first, the basic number of reproduction is estimated by calculating the exponential growth rate of infection for a month and also by daily calculation of single observations. Second, the SEIR model is used to predict the spread of the disease in Italian Regions. According to their result, they manage to predict daily cases peak and gave an estimation of active cases peak in the Italian region.

SIRD model

SEIR model stands for (Susceptible, Infectious, Recovered, and dead). This model describes the dispersal of an epidemic in specific population. Saptarshi Chatterjee et al., used SIRD model to analyze the COVID-19 pandemic in India and in some other countries and found that the current infection rate in India would be the maximum in the beginning of July at the end of June. They also study the effect of the containment measure on the spread of the disease and conclude that social distance is mandatory even if lookdown and curfew are removed due to the nature of the virus. The prediction result in India is compared with other countries like USA, Spain, South Korea and Germany. However, the final result will not be accurate because their will be many folks infected by the virus without any symptoms and the different nature of each of the society [14]. Also, Luisa Ferrari et al., have used the SIRD for predicting the COVID-19 spread over the regions in Italy [15].

ARIMA model

Zeynep Ceylan developed ARIMA model, which is Auto-Regressive Integrated Moving Average, to foresee the epidemiological trend of COVID-19 occurrence in Italy, France and Spain. It is one of the simplest model based on the time series analysis that uses the data from previous values of time series to predict the future value. In this study, the current state of COVID-19 in the three countries is presented with the help of the data provided by World Health Organization in the range of 21, February to 15, April 2020. Thus a time-series database was built for ARIMA model. The results assists the politicians and health advisors in these three countries to plan and manage their resources like beds and intensive care facilities [16].

Internet of things and artificial intelligence

New technology, like Artificial Intelligence (AI) and Internet of Things (IoT) has significant impact on diagnosis and fight against new disease and pandemic. Raju Vaishya et al., discussed the role of AI in combating COVID-19 by comparing the non-artificial intelligence treatment versus artificial intelligence-based treatment. They also classified some applications of AI for COVID-19 into five categories, early detection/diagnosis, monitoring the treatment, tracking contacts of individuals, projection of cases, and development of drugs [17].

IoT is a recent technology that connects various objects to internet. Since the coining of the term in 1999, IoT has become one of the most important technologies of the 21 century [18]. There are many IoT system that focuses in e-healthcare. In [19], C. R. Srinivasan et al., designed an Arduino based IoT Health Monitoring system to record patients pulse rate as will sending SMA message and email to alert doctors. Also, Norlezah Hashim et al., Design and develop IoT system by Raspberry Pi to monitor patients blood pressure remotely [20].

Mwaffaq Otoom et al., proposed a real-time framework to collect data from patients of COVID-19 and to monitor the treatment given to the recovered. The system is base on IoT and consist of five main components as follow: collecting and uploading symptom data using sensors, quarantine/Isolation Center that collects data from patients quarantined or isolated, data analysis and machine learning centre that apply the data to an algorithm to build a model for COVID-19, health physicians system to monitor the data in real-time and finally cloud infrastructure that joins all the previous component through the internet. Most of the algorithms achieved accuracies more than 90%. The system could also follow up recovered patients to have a better understanding about the disease [21].

SIR model vs SEIR model

In [22] Weston C. Roda et al., compared the SIR model with the SEIR model to determine which is the best model to use with COVID-19 pandemic. To do so, they used COVID-19 data that have been taken from Wuhan City after the lockdown and quarantine. By applying Akaike Information Criterion (AIC) method which can estimate prediction error to both models and established that the SIR model out-performs the SEIR model on behalf of the data provided in the confirmed case.

The spread of covid -19 in asian countries

COVID-19 is an infection that happens to the Respiratory system, which then spreads in the body at high speed and causes death. The Symptoms can range from the common cold to more serious diseases. WHO confirmed COVID-19 as a pandemic on March. 11, 2020. The disease was originted in Wuhan, Hubei, China in late 2019 and develops rapidly to be a worldwide pandemic. The total of infected people reported in China was 85,320, while the deaths reached 4,648. Soon after China, many Asian countries like Iran, Saudi Arabia, Kuwait, Japan, UAE and others started to register the increase in the count of confirmed cases in their cities. Though, the above mentioned countries have various experiences in controlling the outbreak of a disease spread. Moreover, in Japan, the number confirmed cases increases to 19.775, in Kuwait, there exists only 4.971. The thought is to find out whether these countries are also experiencing a convergence to a stable number of confirmed cases [23], [24]. Table 1 shows the current infection rates and the risks in a sample of Asian countries from the start of the pandemic until the last of June 2020 [25].

Table 1

Infection rates and risks in some Asian countries from the start of the pandemic until the last of June 2020.

Country	Population	Confirmed cases	Infection rate %	Risk per 1 inhabitant
Japan	126,469,044	19,775	0.015%	6,395
Kuwait	4,271,809	4,971	0.11%	859
Iran	84,014,016	342,051	0.40%	245
South Korea	51,270,036	13,181	0.025%	3,889
Saudi Arabia	34,824,508	209,509	0.60%	166
UAE	9,892,736	51,540	0.52%	191

Data

The datasets used in this paper are available for public use through the King Abdullah Petroleum Studies and Research Center (KAPSARC) website [26]. Data accuracy has been checked with the daily official reports published by the government of Saudi Arabia. The time series recorded for this study starts from 3, March 2020 until 30, June 2020, with a total observation of 120 days to three states in Saudi Arabia Riyadh, Hufof and Jeddah. Currently, to contain the outbreak, governments have implemented various measures to reduce transmission through inhibiting people movements and social activities. From 21, March 2020, flights have suspended, and on 6, April 2020, a curfew applied to Riyadh. There are other countermeasures used by the government like advice people to stay at home, waring mask, keep washing hands and social distance. These measures may help limit the spread of the disease, but studying their impact will be difficult because it depends on individuals to adhere to it.

The proposed model

To build a prediction model for COVID-19 analysis, SIR classic model is used in this paper and developed it to meet the disease characters. The new model (MSIR), is an epidemiological model which is used to theoretically calculate the number of infected individuals with the communicable disease over time in a closed population. MSIR stands for Immunity, Susceptible, Infected and Recovered. By adding immunity (M) to the SIR model, the result of our prediction will be more accurate. The phases of the model can be defined as follows:

M: Group of people who will not be affected by the disease.

S: Group of people susceptible to be ill. When they comes in contact with an infectious person and got sick, then they are moved from susceptible category to infectious category.

I: Group of infected people those who can spread the disease to the vulnerable and can recover or decease within a specified period.

R: Number of people removed. Those who are infected and either recovered or deceased due to the disease are moved to this category [27]. Fig. 1 . shows the MSIR model.

Fig. 1

MSIR model.

The MSIR model consists of different stage, S (t), I (t), R (t) and M (t). Constant, N = S + I + R + M is the total closed population. The coefficients {β, γ, α}, represents the infection rate, recovery rate, and the number of people that will not be affected by the disease respectively [28]. This study will focus on three regions, Riyadh, Hufof and Jeddah. Riyadh is the capital of Saudi Arabia, and it is considered the worst affected area in the country. Also, Hufof and Jeddah show a significant increase in the count of people infected. The most important aspect of this prediction is the number of people infected by the disease and to estimate the end date of the pandemic. The infectiousness increases to reach its peak before symptoms begin and remain for approximately 4–7 days after the peak infection. A sick person could remain in infected state for an average of 14 days and then be recovered. In the proposed model, the population size is fixed and also assumes a completely homogeneous population. The model consists of four coupled nonlinear ordinary differential equations, as shown in (1), (2),(3), (4).

Eqs. (1) to (4) describe compartmentalisation of the population in the face of the Coronavirus. The right side of Eq. (1) is negative, and the right side of Eq. (3) is positive while β > 0. That means dS/dt ≤ 0, dR/dt ≥ 0, and S(0) ≤ N, while N represents the whole population in each region. The right side of Eq. (4) denotes the number of individuals who will not be affected by the pandemic, because of many reasons, for example, people that gain immunity by following healthcare procedure. The fitting accuracy of the prediction with the real data depends on the coefficients {β, α, γ}. Eq. (3) calculates the number of recovered or deceased people infected by the disease, and its result will keep increasing until the end of the pandemic [29]. Table 2 provides a summary of various models employed in COVID-19 researches compared with MSIR. Most of the models focus on the number of death, cured and quarantined people, which is very important when facing fast spread decease like COVID-19. In [30] the SEIR and regression models are combined and executed with John Hopkins University dataset to analysis the spread of the disease in India. In [31] SIQR (Susceptible –Infected - Quarantined - Recovered) model analysed COVID-19 in Brazil by focusing on the quarantined factor. They predict that the number of isolated individuals will grow until it reaches 20% of the Brazilian population. In [32] SIR (Susceptible-Infectious-Recovered) model is used to predict COVID-19 in different Indian states. Comparing with the other models, the MSIR model can be more accurate in prediction by adding the immunity factor to the SIR classic model.

Table 2

Summary of various mathematical models employed in COVID-19 researches.

No	Model	COVID-19 studies	References
1	Susceptible - Exposed - Infected Removed (SEIR)	Analyse and prediction	[30]
2	Susceptible - Infected - Quarantined - Recovered (SIQR)	Quarantine, management strategies	[31]
3	Susceptible - Infected - Recovered (SIR)	Analyse and prediction	[32]

The MSIR model has several deficiencies. This is due to the fact that, many important factors like population migration, intervention of public health and capacity of diagnosis are ignored in the MSIR model. Hence, this model could be used as a natural transmission model under ideal conditions. The real data employed of this model is collected from 3, March to 30, June 2020. Basic Replacement number or Reproduction number (R) represents the mean of new infections over the entire duration of the condition, which used to determine the transmission speed of the pandemic [33]. Often R0 refers to the average infections caused when an infected individual is placed into a susceptible population. R0 is calculated from the earlier stage of illness when a contagious person contacts the susceptible individual. In the MSIR model, R0 can be represented as β/γ. If R0 ≥ 1, the disease spreads over a community, infecting many people, but the speard will not happen, if R0 < 1. In our prediction, the initial value for the susceptible will be the population of the area under study subtracted from the number of immunity people (5). The initial value of the infected individuals will be determined according to the data taken from each area as in Eq. (6). At the beginning of the pandemic, the recovered individual will be zero as in Eq. (7), and the immunity factor calculated by Eq. (8).

Results and discussion

To prove the contribution of the proposed model « MSIR », we will apply it in a real case study of three cities Riyadh, Hufof and Jeddah.

Riyadh

Riyadh registered the first case of COVID-19 on the 9, March 2020. It is found that from the real data, the reproduction number (R0) approximately is equal to 1.9 until March 2020 end, then the number of infected individuals started to decrease. To make our forecast consistent with the recorded data, we must consider the health measures that have been implemented by the government to minimize the disease spread. On the 21, March 2020, a new countermeasure is implemented like Domestics fights suspension and a curfew for 11 h. Also, on the 26, March 2020, a complete lookdown was applied [26]. These containment protocols help to reduce the infection rate as expected. Therefore, depending on the data, the reproduction number (R1) should reevaluate approximately 1.2 from the 10, April 2020. As showing in Fig. 2 , the maximum peak of infection without the countermeasure is 125,197 while after the lockdown and curfew are 24426. According to the result obtained, there is a significant decline in the infection rate, which will lead to the end of the pandemic approximately at the end of October.

Fig. 2

COVID-19 infection prediction in Riyadh.

Hufof

The first case of COVID-19 in Hufof was registered on 13, March 2020. The government applied curfew on the 6th of April [26]. By following the pattern of data, R0 is estimated at 1.5. Then the number of infected individuals started to decrease after 25, April 2020, so another reproduction number (R1) will be approximately 1.14 from 25, April 2020. As showing in Fig. 3 , the maximum peak of infection without the countermeasure is 47,966 while after the curfew is 9188, and the pandemic will end in Hofof approximate at the end of September.

Fig. 3

COVID-19 infection prediction in Hufof.

Jeddah

Jeddah registered the first case of COVID-19 on 11 March 2020 [26]. The same health countermeasure that used in Riyadh is applied to Jeddah. Following the same concept, at the beginning of the pandemic, R0 equal to 1.3. Then the number of infected individual started to decrease after 3, May 2020, so another reproduction number (R1) will be approximately 1.1 from the 13th of May. As showing in Fig. 4 , the maximum peak of infection without the countermeasure is 89,711 while after the curfew is 15,274 and the pandemic will end at the end of September. The number of infected people has reduced between (20%–17%) as in Table 3 . According to the result, containment measures have a massive effect on the spread of the disease. Many factors can affect the spread of the disease, such as the commitment of individuals to health procedures and social distance. Still, the best method for controlling the COVID-19 spread is to put on a full lockdown in big cities and curfew to small town and villages.

Fig. 4

COVID-19 infection prediction in Jaddah.

Table 3

Compare the result of each city.

Region	R0	R1	Infection rate after applying the contaminant procedure
Riyadh	1.9	1.2	19.5%
Hufof	1.5	1.14	19.15%
Jaddah	1.3	1.1	17.02%

Although there are differences between the three cities in the distribution of population and the degree of adherence to health measures which could affect the result, we managed to find a mathematical relationship that combines the results from the three cities. By using MSIR, we model the number of daily infected with COVID-19 and time-dependent by drawing a curve in a Gaussian function denoted by i(t) and d(t). The model characterised with a bell-shaped curve and 3 independent parameters such as width, maximum height and time at which the Gaussian curve reaches its maximum height.

The functionfits the model result in the Fig. 5, Fig. 6, Fig. 7 by 95%.where A - Height of curve's peak,

Fig. 5

COVID-19 prediction in Riyadh with the Gaussian function.

Fig. 6

COVID-19 infection prediction in Hufof with the Gaussian function.

Fig. 7

COVID-19 infection prediction in Jaddah with the Gaussian function.

xc - Center of the peak position,

w - Gaussian RMS width that can control the bell width.

The Gaussian functions are frequently employed to denote the Probability Density Function (PDF) of normal distribution of random variable with expected value μ = xc and variance σ2 = w2 as in Eq. (9).

This equation summarised the result in the three cities and can be applied to other regions. We also think that our result can be suitable for a more complex simulation or build a long term artificial intelligence prediction model.

Conclusion

In this paper, an SIR model based generalised prediction model (MSIR) is proposed to analyse the epidemic of COVID-19 in three cities in kingdom Saudi Arabia. We measure the infection spread with and without the government countermeasure like curfew and lockdown for predicting the number of infections in both cases. Moreover, estimation of maximum number of infected patients is employed by using real data taken from three cities. Due to the obtained result, a complete lockdown for the big cities and curfew for small cities must apply to end the spread of COVID-19 as a pandemic. The infection rates without these measures will be very high, which will make it difficult to control it in society. For future research, we will integrate the MSIR model using machine learning algorithm to enhance the result for long time prediction.

CRediT authorship contribution statement

Islam Abdalla Mohamed: Methodology, Formal analysis, Supervision, Validation. Anis Ben Aissa: Writing - original draft. Loay F. Hussein: Formal analysis, Writing - review & editing. Ahmed I. Taloba: Formal analysis, Writing - review & editing. Tarak kallel: Formal analysis, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.