Impact of containment type on Covid-19 propagation in Morocco using the SIR model

Objective and mehtods: Our objective is to determine the containment effect on the spread of Covid 19 in Morocco. The methodology is based on an epidemiological study whose objective is to take stock of the current situation and to estimate the future spread of Covid-19 over time in Morocco. Several conditions were considered using the SIR epidemiological model for a better reliability of the results. During the study period from the appearance of the first case until 19 June 2020, Morocco reported 9074 cases of infections, 213 deaths with a lethality of 2.35% and a mortality of 6.04 per million inhabitants. Results and Conclusion: The results of the SIR model show a sudden increase in infections. The peak would be 4.4 million inhabitants or 12% of the total population under confined conditions. Selon ces résultats,Containment is one of the most effective methods of reducing the risk of infection.


Introduction
Containment remains one of the most effective methods to curb the spread of viruses today. Since the detection of the first real case of coronavirus (Covid-19) on March 2, 2020, the Moroccan authorities have taken a large number of decisions to limit the spread of the pandemic and preserve the health and safety of citizens. They therefore decided to declare a «state of health emergency» and took a series of swift and strict measures against the Covid-19. All Moroccan cities have been closed and the majority of industrial and commercial activities have been forced to cease their activities until further notice. Likewise, the populations were invited to stay at home and only go out in the event of authorized specific needs (purchase of basic necessities, medical consultations, etc.). In addition to these security measures, the authorities have also decided to close transport and travel inside and outside the country, to close schools, universities, restaurants and mosques, and to ban mass gatherings throughout Morocco 1 . On June 20, 2020, it was decided to extend the containment status, first until June 11, 2020 and then until July 10, 2020 with regional relief from the restrictions. At the time when Morocco is preparing for deconfinement, it seemed necessary to us to estimate the spread of the virus over time in Morocco according to several conditions according to the states of strict confinement to the states of deconfinement and to model projections according to various parameters related to the spread of the virus. In order to reach these objectives, we will therefore draw the real curves of the evolution of the number of infections and remissions during the study period, as well as the number of screenings carried out since the appearance of the first case until '' as of June 19, 2020. We will also draw up forecasts of the evolution of covid-19 according to several deconfinement situations based on the SIR epidemiological model. This model makes it possible to better understand the epidemic and to foresee the period and the means of lifting the restrictions imposed by the state of health emergency.

Methods
The data we used is that which is published daily by the WHO website 2 . These data relate in particular to the number of infected cases, the number of deaths and the number of remissions since the appearance of the first imported case on March 2, 2020 until June 19, 2020 2 . The methodology is based on an epidemiological study whose objective is to take stock of the current situation and to estimate the future spread of Covid-19 over time in Morocco. Several conditions were considered using the SIR epidemiological model 3  The principle of this model is based on the fact that at every instant t, the population is subdivided into three compartments S, I and R defined by the functions S (t), I (t) and R (t) so that : -S is the number of Susceptibles: It is made up of individuals who have never had the disease but who can contract it; -I is the number of infected cases: It is made up of individuals who have contracted the virus, and are therefore contagious; -R is the number of Recovered: It is made up of individuals who have already contracted the disease and are now immunized following their recovery, and deceased individuals who can no longer transmit the virus to those around them. Let us consider S (t), I (t) and R (t) the respective proportions of individuals in each of the categories composed respectively of healthy individuals, infected individuals and individuals recovered or deceased at time t. The size of each group constitutes a random variable, which can be modeled according to a function of the independent variable «time» expressed by t so that we will have S (t), I (t) and R (t). During the spread of the virus and the evolution of the epidemic, the size P of the total population can be considered constant at time t, we write then 4 : S(t) + I(t) + R(t) = P 5-6-7 .
The choice of this model is based on the fact that it is the most classic epidemic method for analyzing infectious diseases. It is performed at a defined latency period, and has proven to be predictive for several varieties of acute infectious diseases in the past such as Ebola and SARS 8-9-10-11-12-13-14 . This model has also been used for the estimation of Coronavirus 2019 cases in Wuhan 15 . Thus, and in order to model the dynamics of COVID-19, we will use three differential equations each characterizing the change in each of the three groups of the SIR system previously raised and which model the spread of an infectious disease. An equation characterizing the population dynamics from one group to another, where β is the parameter that controls the transition between S and I and ɣ the one that controls the transition between I and R: It should be noted that, according to this model, the recovered individuals are considered to be immune and cannot be infected again.

Results
During the study period from the appearance of the 1st case until June 19, 2020, Morocco reported 9074 cases of infections, 213 deaths with a lethality of 2.35% and a mortality of 6.04 for a million inhabitants. The high recovery rate of 88.62% is observed following the use of the therapeutic protocol of chloroquine and azithromycin. Similarly, we noted a significant lethality in the period from March 30 to April 05, 2020. We have reported in Table I, the results concerning the spread of the epidemic virus during the study period week by week. These results allowed us to draw the curves of the evolution of the parameters S which represents the general population, I which represents the number of infected individuals and R which represents the total of remissions composed by the sum of deaths added to the cure rate(figure 1). We have shown in Figure 1 the 3 parameters of the SIR system during the 111 days of the epidemic. Thus, there is a parallel evolution between the number of cases (I) and the number of remission (D + G). This rate was 90.48% on June 19, 2020. Screening for the virus is an important factor in limiting its spread and successful containment strategies. In this regard, Morocco has decided to gradually increase the number of screening. Figure  2 shows the evolution of the number of screenings carried out since the start of the epidemic to date.   In this first scenario, the results of our projection show a rapid decrease for the two durations of infection D = 7 d and D = 14 d. This model shows that the epidemic will be completely eradicated during the second week of July for the first case and two to three months later for the second infection rate. We believe that Morocco, which has planned deconfinement on July 10, 2020, is in the conditions of D = 7 days following the therapeutic protocol using chloroquine (or hydrochloroquine) associated with azithromycin generalized to all positive cases screened whether symptomatic or asymptomatic.
-Scenario 2: The contact rate = 5 In this second scenario, we consider a deconfinement from July 10 but a very strict application of the measures of distancing, hygiene and wearing of masks. We estimated in this scenario that the contact rate would be 5 since gatherings exceeding 50 people are prohibited and schools and universities remain closed until September. The results of this scenario, which we have recorded in the figure, show a rapid decrease in the number of cases for a duration of infection D equal to 7 days and an eradication of the epidemic at the beginning of September. We think it is this scenario that is most likely to happen in Morocco. The case of D14 shows an increase in the rate of infection which will reach a peak of 25,000 cumulative cases of Covid-19 disease at the end of September 2020. Under these conditions, the epidemic will last until the beginning of l year 2021 in case there is not a second wave of virus virulence.    16 . In addition, at the international level, the WHO Regional Director for Europe said that the number of cases should increase further. He urged countries to continue implementing a containment strategy while accelerating their efforts to fight the disease. It is essential to act quickly and every day can make a difference 18 . As for the National situation, the Moroccan Ministry of Health has reported 9,074 cases since the first imported case from March 2, 2020 until June 18, 2020, with a higher concentration in large cities. Thus, and according to data from the Ministry of Health, the Casablanca-Settat region represents approximately 32.66% of the covid-19 cases observed, followed by the Marrakech-Safi region with a rate of 18.26%. The high number of positive COVID-19 cases in these two regions could be explained by the high density of the urban population. This high density constitutes a risk factor for the spread of this pandemic both in Morocco and in Africa 17 . In addition, these regions have the distinction of hosting a strong industrial activity, which is the source of professional homes. Conversely, regions with low population density and low industrial activity have experienced only very low contamination rates. This finding is supported by the epidemiological situation in the 4 regions of southern Morocco did not exceed the rate of 1% of infections. As for lethality, it only represents 2.2%, this could be influenced by several factors such as gender and age.
Previous studies have suggested that an increased age is associated with death in patients with SARS-CoV-1, MERS and COVID-19 19-20-21 . Regarding gender, one study found that COVID-19 was more likely to affect men than women, and symptoms appeared to be more severe in men 22 . This could be explained by the reduced susceptibility of females to SARS-CoV-2 infections, due to the protection of X chromosomes and sex hormones including the presumed role of innate and adaptive immunity 23 . Indeed, previous studies have found higher percentages of SARS-CoV-1 infection in male mice compared to female mice and have provided mechanistic information related to estrogens 24 . In order to measure the propagation of COVID-19 as a function of time, we used the SIR model. Two scenarios are assumed, the first with a high contact rate (without containment) and the second with a low contact rate (with containment). According to this model, Morocco is assumed to be situated in the scenario where the pandemic is minor. Indeed, the results of this study show that strict containment is one of the effective methods of reducing the numbers of newly infected cases and controlling the pandemic situation of COVID-19.
Estimates of the risk of transmission and the epidemiological peak of COVID-19 are of great interest since they make it possible to reinforce the vigilance of political decision-makers and give a preventive vision, the objective of which is to protect the public population against the spread of this epidemic. To estimate the number of propagation of cases affected by the coronavirus, several parameters were calculated such as the number of reproduction «R». Indeed, the number of reproduction "R" which measures the transmissibility of a virus, represents the average number of new infections generated by each infected person, whose initial constant is called the basic number of reproduction "R0" 25 . According to studies by Read 26  Finally, pharmacologically, Morocco was one of the first countries to establish a therapeutic protocol for the treatment of Covid-19 disease. Indeed, the Ministry of Health consulted with a technical and scientific medical committee which recommended the treatment of people infected with the combination of chloroquine and azithromycin, a macrolide antibiotic, according to the ministerial note. Chloroquine and its hydroxylated derivative hydroxychloroquine are old drugs with antimalarial properties, the use of which has gradually been restricted with the appearance of strains of Plasmodium falciparumchloroquinoresistant. They also have anti-inflammatory and immunomodulatory activity by regulating the production of TNFα, interferon and certain cytokines. These properties mean that hydroxychloroquine is indicated in certain autoimmune diseases, such as lupus or rheumatoid arthritis [28][29] .

Conclusion :
In conclusion, our results based on the epidemiological situation in Morocco are in harmony with the WHO strategy which recommends the following recommendations `` it is always possible to stop the spread of the virus, provided that the countries put in place measures energetic to detect the disease early, isolate and treat cases, find contacts and promote social distancing measures commensurate with the risk '' 30 .

The added value of the study
The added value of our study is the determination of the effect of containment on the reduction of the spread of COVID-19, thus giving a general idea of the epidemiological situation of this pamdemic in Morocco with the objective of providing health strategies for the Ministry of Health.

Source of fund:
This study is funded by the project PPR-B-Mokhtari-FS-UIT

Conflict of interest:
No conflict of interest Ethical clearence: Our study respects the ethical aspects declared by the University Ibn Tofail of Kenitra, so we kept the anonymity of the patients. Authors's contribution NL was involved in the study design and data collection. contributed to the design, analysisand interpretation of the study and then critically reviewed the manuscript. ZA primarilyanalyzed the data and verified the methods of analysis. researched related documentation,wrote the literature review and finalized the manuscript. SJ contributed to the design of thestudy, interpreted the data and reviewed the manuscript. AM and AS contributed to the studydesign and oversaw the entire study process. All authors read and approved the finalmanuscript.