Prediction of the Epidemic Strength of COVID-19 in the Holy Places of Saudi Arabia during the Forthcoming Hajj Season 2020

The first outbreak of the COVID-19 epidemic in Saudi Arabia was reported on March 2nd, 2020. Every year more than 2 million people come from more than 188 countries to Saudi Arabia to perform pilgrimage (Hajj in Arabic). Therefore, extrapolating the epidemic strength during the Hajj season (end of July) in the holy places has become essential. In this paper, we employ the power of mathematical modeling to infer the epidemic intensity over a 300 days’ time span in Saudi Arabia generally and the Holy places specifically. In particular, we obtain the following epidemiological insights such as the number of infections, the daily infection increase, the expected number of death cases, and the epidemic peak. Results indicate that, the epidemic peak has already been reached in both Makka and Madina. In addition, the number of infections will reach its saturation point by the first week of October 2020 as the daily increase in the number of infections will diminish. This means that, Hajj can be conducted safely only by reducing the number of pilgrims and providing suitable sets of preventive and precautionary measures.


Introduction
The outbreak of novel coronavirus (COVID-19) disease was first reported in Wuhan City, China in December 2019. Since then, more than 2.7 million cases have been confirmed with more than 180,000 confirmed deaths worldwide [1]. Meanwhile, pathologists around the globe are working tirelessly to find a vaccine or treatment for the invading virus. Researchers are also working hard to model the virus spreading dynamics and developing mathematical models to predict the spreading behaviour of the coronavirus. In [2], Toshikazu Kuniya employed the SEIR model to predict the epidemic peak of Coronavirus in Japan. The author found out that, an epidemic peak may reach the early-middle summer. Hiroshi Nishiura [3], studied the infection scenario of the novel coronavirus in on the Diamond Princess. He employed a back-calculation method to estimate the peak time of infection and the estimated number of infections on the ship. Zaho et al., [4] presented

Abstract
The first outbreak of the COVID-19 epidemic in Saudi Arabia was reported on March 2 nd , 2020. Every year more than 2 million people come from more than 188 countries to Saudi Arabia to perform pilgrimage (Hajj in Arabic). Therefore, extrapolating the epidemic strength during the Hajj season (end of July) in the holy places has become essential. In this paper, we employ the power of mathematical modeling to infer the epidemic intensity over a 300 days' time span in Saudi Arabia generally and the Holy places specifically. In particular, we obtain the following epidemiological insights such as the number of infections, the daily infection increase, the expected number of death cases, and the epidemic peak. Results indicate that, the epidemic peak has already been reached in both Makka and Madina. In addition, the number of infections will reach its saturation point by the first week of October 2020 as the daily increase in the number of infections will diminish. This means that, Hajj can be conducted safely only by reducing the number of pilgrims and providing suitable sets of preventive and precautionary measures.
estimates of the basic reproduction number, R0, of 2019-nCoV in the early phase of the outbreak of COVID-19 in Wuhan city, China. In this paper, we study the epidemiological situation in Saudi Arabia.
Every year more than 2 million people from more than 188 counties come to Saudi Arabia to perform pilgrimage (Hajj). Moreover, more than 5 million visitors come to perform Umrah. Saudi government spares no effort in seeking to provide them with all support to perform their worship in peace and tranquillity. Therefore, Originating from its keenness to protect the people's health and ensuring their safety, the Saudi Government has taken a stringent set of proactive measures [5]  • Banning of serving food and beverages in restaurants and cafes • Imposing a 24-hour curfew on major cities.
Based on the Saudi Ministry of Health's statistics [6], even with such stringent precautionary measures adopted by the kingdom, the number of infections in Saudi Arabia is doubling every 6 days as shown in Table-1. However, this exponential growth in the total number of infected cases with COVID-19 has been reported by most of the world.
Pilgrimage is the world's largest annual public gathering that is held this year in the period from 29 th July to 1 st August. Due to the gigantic number of pilgrims assembled in Arafat (an area of approximately 20 km 2 ), the possibility of spreading the virus becomes very high. Therefore, there is an urgent need to forecast the epidemiological situation in the Holy places. This certainly will help decision-makers to determine whether to suspend pilgrimage this year or it can be executed safely.
In this paper, we will extrapolate the epidemiological situation of the novel coronavirus in Saudi Arabia generally and in the Holy places (Makka and Madina cities) specifically. In particular, we use mathematical modeling to forecast the future number of infections, deaths, percentage increase in infection and death, and predict the epidemic peak of the coronavirus in the Holy places of Saudi Arabia. The rest of this paper is organized as follows. Section-2 presents the model employed in our experiment. Section-3 demonstrates our experimental results. Section-4 exhibits an interesting discussion about our results. Section-5 concludes the paper.

COVID-19 Model Used
Available datasets of COVID-19 show interesting behavior. It usually increases slowly at the beginning then, followed by a very fast increase. Finally, it began to show some sort of leveling off.
In order to model this behavior empirically, the functions must have the same behavior mentioned above. One of the functions that support this behavior is the hyperbolic tangent function given by the following equation [8].
Where N is the number of cases, t is the time in days, and a 1 , a 2 , a 3, and a 4 are the fitting parameters.
The initial values of the fitting parameters are set to 1000, 10, 5, and 0 for a 1 , a 2 , a 3, and a 4 , respectively.
Then, the rate of change in the number of cases (Q) can be calculated as: Then, the data are fitted to this equation using the Matlab nonlinear fitting facility. The results are shown in section-3.

Results
In this section, we first validate our model in Saudi Arabia. Then, we focus on investigating the epidemiological situation in the Holy cities (Makka and Madina).

Epidemiological situation in Saudi Arabia:
The first outbreak of the COVID-19 epidemic in Saudi Arabia was reported on March 2 nd , 2020. Then a surge in the number of infections has been announced along the following weeks as indicated in Table-1 that, it is expected to have a saturated number of infections of 350,000 cases by day 250 (7 th November) .   Fig-2 shows that, the used model is very clever in estimating the number of death cases in Saudi Arabia as the fitted data and extrapolated data is very close to the actual data.  Fig-3 presents the actual mortality rate in Saudi Arabia. The results depicted in Fig-3 indicate that, the peak mortality rate has been passed on day 36 (April 7 th ). However, Fig-3 indicates clearly that, there is a second wave of coronavirus infections in Saudi Arabia that started after day 85 (26 th May). It is also notable that, the rate of increase in the mortality rate of the second wave is significantly lower than that of the first wave.

Epidemiological analysis in Makka and Madina:
In this section, we investigate the epidemiological situation in Makka and Madina cities in terms of the total number of infections, daily infection increase, the Number of Death Cases, and the mortality rate. Note that, the first infected case was reported on March 10 th and March 20 th for Makka and Madina, respectively.
The period of our analysis is 300 days since March 2 nd , 2020. Fig-5 show the total number of infections in Makka and Madina, respectively. The result depicted in these figures indicates that, the total number of infections will continue increasing until it levels off after 150 days (from the first outbreak) in Makka (August 7 th ) and (from the first outbreak) in Madina (August 17 th ). It is worth noting that, the expected total number of infections is 28,000 and 16,500 in Makka and Madina, respectively.  Fig-6 and Fig-7 demonstrate the mortality rate in Makka and Madina, respectively. The mortality rate is defined as the number of death cases relative to the number of confirmed cases in a given day [9]. The mortality rate plot shown in Fig-6 indicates that, the mortality rate is made not stable yet and passing through the second wave of coronavirus infection. However, the good news is that, the reported maximum mortality rate in Makka is below 2% which is in a safe margin compared to the global mortality rates (4.3% to 11%) as reported in [10][11][12]. On the other hand, the mortality rate plot shown in Fig-7 confirms that, the situation in Madina is far better than that in Makka as the mortality rate in Madina is converging to zero. Fig-9 show the daily infection increase in Makka and Madina, respectively. The Results in Fig-8 and Fig-9 indicate that, the fitted daily infection increase of coronavirus in Makka and Madina is very similar as they begin with an exponential increase up to a peak point after which the increase in the daily infections starts falling down. Fig-9 indicate also that, the daily infection increase has already passed its epidemic peak value in both Makka after 75 days (24 th May) and Madina after 70 days (29 th May) and it is expected to continue falling down up to zero by day 200 in both Makka (26 th September) and Madina (6 th October). It is also notable that, the value of the daily infection increase in Makka is significantly higher than that in Madina. For example, on day 100, the infection increase rates are 275 and 103 in Makka and Madina, respectively.

Fig-8 and
The result shown in Fig-10 presents that, the number of death cases in Makka starts increasing linearly from day 50 and it is expected to continue up to day 150 (7 th August ) and then it levels off at day 200 (26 th September) with 600 death cases. On the other hand, Fig-11 depicts that, the expected behavior of the number of death cases in Madina is increasing with the increase in time. However, the rate of increase in the number of death cases is sharply higher in Makka than that in Madina. For example, on day 100, the number of death cases in Makka is 330 while in Madina is 100 death cases. Most notable that, the number of death cases will continue increasing in Makka until it levels off after day 200 (26 th September). However, the reason behind the excess of the number of death cases in Makka than that in Madina needs an elaborate study as it requires further investigations and it is behind the scope of this paper.

Discussion
Based on the results depicted in section-3, we can extrapolate the following:

•
The total number of infections will saturate after (August 7 th ) in Makka and after (August Based on our analysis that spans 300 days from the first outbreak of the virus (up to 4 January 2021), we conclude that, the coronavirus epidemic will diminish by the first week of October 2020 in Makka and Madina. However, more than 70% of the epidemic strength has passed. This means that Pilgrimage can be executed safely this year (by the end of July) given that suitable preventive and precautionary measures are applied while reducing the number of pilgrims.

Conclusions
The Holy places of Saudi Arabia are expected to receive more than 2 million people by the end of July 2020 for performing pilgrimage. Such assembly may be catastrophic if the coronavirus is still spreading in the Holy places. Therefore, we are in an urgent need for studies that forecast the epidemiological situation. In this paper, we introduced using a mathematical model that depends on the hyperbolic tangent function for extrapolating the epidemic; results indicate that both Makka and Madina will be free of the epidemic by the first week of October. By now, only 70% of the epidemic strength has passed. Therefore, executing hajj with traditional numbers of pilgrims could be