The 2019 coronavirus (COVID-19) pandemic is a global outbreak of coronavirus disease. Given the economic and social impacts of this phenomenon, mathematical modeling and prediction are essential to aware people and decision-making managers of the consequences of this epidemic. Accordingly, the present research team has mathematically investigated the COVID-19 growth in Iran using the available statistical data and epidemic curve. Available official long-time data of Iran were used to predict the number of victims (V) of this virus in this country. Different types of mathematical models can be used for predicting an epidemic infection, and many important unknown variables can be achieved by the use of real available data. The first predictions of an epidemic infection exponential growth, that is typical for the initial stages of all epidemics, have been presented in [1] .
More complicated mathematical models were obtained as the susceptible-exposedinfectious-recovered (SEIR) model. SEIR model is engaged upon anticipating the potential domestic and international spread of the COVID-19 outbreak [2] . The intricate models need more attempts for the man parameter identification. Accordingly, Nesteruk [3, 4] developed an appropriate mathematical model of contamination and SIR-model of spreading an infection to predict the time dynamics of the unknown children's disease, which occurred in Chernivtsi (Ukraine), and COVID-19 China epidemic. In this paper, the known SIR model for the dynamics of an epidemic [5] [6] [7] [8] is used to identify Iran (COVID-19) epidemic in Iran. In this respect, an exact solution of the SIR linear equations is considered simultaneously with a statistical approach based on the confirmed and recovered victims as the reliable long-time statistical data of Iran [4] . Main epidemic characteristics such as epidemic victim numbers, infected, and recovered people are estimated over time. Furthermore, Iran's official data [9, 10] are fitted to the China epidemic curve [11] [12] [13] and compared with the results of the SIR model.
The SIR-model linear equations are illustrated for an infectious disease [3, 4] , as below:
The number of infected people is denoted by I, susceptible by S, recovered by R. ), but rather it . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review)
The copyright holder for this preprint this version posted March 31, 2020. Relation (4) is supposed to define the initial conditions for Eqs. (1) (2) (3) .
It follows from Eqs. (1) and (2):
Integration of Eq. (5) with the initial conditions presented in relation (4) results in:
‫ܫ‬ reaches its maximum value at
and approaches zero-value at infinity.
Also, the number of susceptible people at infinity ሺ ܵ ஶ 0 ) can be calculated via Eq. (6).
, corresponding to the number of victims. The corresponding equation integration would be [3] :
Resulting in: and time function (t), subsequently [3] .
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The copyright holder for this preprint this version posted March 31, 2020. . https://doi.org/10.1101/2020.03.29.20046532 doi: medRxiv preprint
The obtained solution of the differential equations (1-3) can be simplified with the use of these different approximations for the function
and ultimately:
According to (11) epidemic starts exponentially and only two parameters (ߛ
describe the process.
If we would like to anticipate more appropriately and accurately, we can assume
And the solution's form will be:
Finally, this approximation (Eq. (12)) reached a limited amount of victims, since ܸ ൌ ‫ܫ‬ ܵ tends to N at infinity.
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The copyright holder for this preprint this version posted March 31, 2020. . The optimal calculated values of parameters are shown in Table. 1. Also, Table 2 lists the values obtained by the SIR model for the COVID-19 epidemic in Iran. As can be observed, the official statistical data of Iran for the susceptible and recovered people were used for the extrapolation process. It has been predicted that the maximum number of infected people would occur on 27.03.2020, and the disease peak would occur on 19.03.2020 (which was obtained based on the calculation of infection rate). Hence, due to a 2-to 3-day difference between death and infection peaks, there is a good agreement between the curves depicted in Figs. 1 and 2 . The infection rate would be zero at the beginning of May 2020, and the number . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint this version posted March 31, 2020. . of susceptible people would converge to its lowest value. According to the articles on epidemics in China and Japan [4, 15] , the proportion of people with the . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint this version posted March 31, 2020. ⁄ ) is as low as 1.89 to 3.58 percent. As this subject, here, we consider 2.14 percent. This means that the total number of people caught in Iran will be approximately 1.8 million. According to Figure 3 , the number of people exposed to the disease will reach beside four hundred thousand but using a suitable diagnosis system and regarding hygiene behavior of susceptible persons and quarantine conditions, it is anticipated that disease spreading will be stopped and most of the victims will be recovered. As can be seen in Figure 4 , the epidemic will continue by mid-June (late spring).
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The copyright holder for this preprint this version posted March 31, 2020. 2  0  2  2  0  2  3  0  0  5  0  2  13  0  2  18  0  4  11  0  2  29  0  6  14  1  2  43  1  8  2020/2/24  18  2  4  61  3  12  34  22  4  95  25  16  44  0  3  139  25  19  106  29  7  245  54  26  143  19  8  388  73  34  2020/2/29  205  50  9  593  123  43  385  52  11  978  175  54  523  116  12  1501  291  66  835  144  11  2336  435  77  586  117  15  2922  552  92  2020/3/5  591  187  15  3513  739  107  1234  174  17  4747  913  124  1076  756  21  5823  1669  145 . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint this version posted March 31, 2020. (1) Daily (2) Total . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint this version posted March 31, 2020. is achieved.
Ultimately, people can prevent from spreading the disease by doing some things such as . CC-BY-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.
The copyright holder for this preprint this version posted March 31, 2020. . https://doi.org/10.1101/2020.03.29.20046532 doi: medRxiv preprint home quarantine and personal hygiene [17, 18] since the infection rate has had low value, expecting a longer time with fewer infected and died people based on forecasting will be occur. Owning to, Coronavirus Incubation Period time to show symptoms is varied. This may appear 2-14 days (known more as 11.5 days) after exposure [19], it's better to determine an interval time for peak time. According to this investigation, this interval is from 2020/3/27 to 2020/4/7. Hence, in this interval time, Covid-19 will be at its peak and the epidemic will disappear by mid-June.
In previous studies, the number of recovered people was not considered, which led to a significant error in the calculations. However, by incorporating the available official statistical values of recovered people along with the number of susceptible people in the present study, the accuracy of results obtained by the SIR model. Furthermore, another desirable feature of the current predictions is the fact that the estimation of susceptible people, who are still present in the population ܵ ஶ ൌ ܰ െ ܸ ஶ , has a suitably lower value compared with the previous works. It means that these people would not couch the infection after the suppression of the epidemic. Also, good agreement has been observed between the predictions obtained by fitting the official number of deaths ( Fig. 1 ) and the results of the SIR model. By using the coefficient of the considered number to the total population, it is anticipated that the total number of infected people will reach four hundred thousand and finally, the epidemic will end in late spring.