key: cord-0856174-64twq6sw authors: NAJI, M. title: Exploring the spread dynamics of COVID-19 inMorocco date: 2020-05-22 journal: nan DOI: 10.1101/2020.05.18.20106013 sha: d8d0fddc14c4b5c36355d80bea092e262415a557 doc_id: 856174 cord_uid: 64twq6sw Despite some similarities of the dynamic of COVID-19 spread in Morocco and other countries, the infection, recovery and death rates remain very variable. In this paper, we analyze the spread dynamics of COVID-19 in Morocco within a standard susceptible-exposed-infected-recovered-death (SEIRD) model. We have combined SEIRD model with a time-dependent infection rate function, to fit the real data of i) infection counts and ii) death rates due to COVID-19, for the period between March 2nd and Mai 15th 2020. By fitting the infection rate, SEIRD model placed the infection peak on 04/24/2020 and could reproduce it to a large extent on the expense of recovery and death rates. Fitting the SEIRD model to death rates gives rather satisfactory predictions with a maximum of infections on 04/06/2020. Regardless of the low peak position, the peak position, confirmed cases and transmission rate were well reproduced. The spread of an epidemic disease depends on the availability of susceptible individuals that can lead the virus to survive. New susceptible persons will keep transmission between individuals and therefore promote the virus to survive. As the severe acute respiratory disease COVID-19 presents a high transmission 5 rate, it will very likely save it from been extinct, at least for several years. To slow-down the transmission of COVID-19 among the population and to avoid a high fatality rate, each country was forced to adopt drastic containment and preventive measures going from social distancing to a complete lock-down of the entire country. 10 Earlier in March 2020, Morocco found itself fighting against COVID-19, which seems to be one of the worst waves of transmissible diseases that hits the country in the past 200 years. Morocco took strict preventive measures to limit the spread of the virus, including the closure of borders, the nationwide 15 lock-down, as well as the compulsory wearing of face-masks. Thanks to these measures, the COVID-19 spread seems to be controlled so far. However, a clear picture regarding the magnitude and the dynamics of the epidemic wave is still not yet drawn. (I), Recovered (R) and Dead (D) . Any individual in the fraction of the population that will get sick belongs to one of the aforementioned compartments. Since COVID-19 has an incubation time, the E compartment (for exposed) is allocated for individuals that have been infected but are not yet infectious themselves. The system of equations in the SEIRD model is given by: where N is the total number of individuals in the considered population. At each time N is equal to the sum of (Eq.1) N = S + E + I + R + D. β represents the infection rate, i.e., an expected amount of people an infected person infects per day, α is the incubation rate and T I is the average infectious period and f is the rate at which people die. The same model has been used elsewhere [7] to describe the widespread of COVID-19 in Italy. The total number of infected people in a population is determined by the R 0 number. This can be expressed as the infection rate multiplied by the mean time of recovery or deaths. It describes the expected number of individuals an infected person infects in a susceptible population. Equivalently, R 0 is computed as: The system of Eq. for some initial time t 0 . To test the model, we have used a set of parameters and initial conditions found in literature for the COVID-19 spread in China and Italy 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 May 22, 2020. . and reintegrated the system of Eq.(1) using the set of parameters shown in table 1. 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 May 22, 2020. . https://doi.org/10.1101/2020.05.18.20106013 doi: medRxiv preprint [8, 9] , solid lines correspond to best-fit of the SEIRD model. . CC-BY-NC-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 May 22, 2020. . https://doi.org/10.1101/2020.05.18.20106013 doi: medRxiv preprint The t 0 value which seems to reproduce best the data was 7 days. Note that a lag-time of t 0 = 30 days has been observed for Italy in order to reproduce the outset of the outbreak [10]. The best-fit parameters as well as those fixed are reported in table 1. Figure 1 (a) represents the best-fit to the daily counts of infections of COVID-19 in Morocco. It is noteworthy to visualize that the 60 inflection point of I(t) was very well reproduced with our model, although it seems to underestimates the reported values around April 20 th and Mai 8 th . As the set of initial conditions were adequately adjusted, we believe that this mismatch is very likely due to the abrupt change in testing rate at this period related to the presence of several hotbeds of contagion throughout the country. One can also note that starting from March 8 th a visible increase of the number of infections is also accompanied by an increasing number of the performed tests. Figure 2 Figure 4 ), this suggests that the decay of the infection rate I(t) is higher than that recorded for the data. This discrepancy will very likely to get reduced when more data on 80 the COVID-19 spread in Morocco will be available. Despite, its reproducibility of the infection dynamics, the analysis of the COVID-19 outbreak in Morocco, using the fit of SEIRD model seems to be very crude. First, the data contain several spikes and looks noisy (though it has 85 been averaged), and second the number of tests that have been performed, is 6 . CC-BY-NC-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 May 22, 2020. . https://doi.org/10.1101/2020.05.18.20106013 doi: medRxiv preprint CC-BY-NC-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 May 22, 2020. . https://doi.org/10.1101/2020.05.18.20106013 doi: medRxiv preprint very low, as compared to those performed in Italy, Germany or China. Note that during the early stage of the epidemic period, Morocco made tests to only those who presented COVID-19 symptoms, so obviously, infected individuals who did not present symptoms, have escaped to the tests. This explains the 90 low estimation of confirmed cases. In order to avoid external factors and get more accurate analysis of the COVID-19 spread in Morocco, SEIRD model has been fitted death cases due to 95 COVID-19 in Morocco, for the period between 03/02/2020 − 05/15/2020. As Morocco, did not have an intensive wave of death cases due to COVID-19, as the one observed in Italy or China for example, the reported COVID-19 death cases should be reliable as it is hard to miss any case. To initialize the system of equations, we have used the same initial parameters 100 [S(t 0 ) = N − 1, E(t 0 ) = 1, 0, 0, 0] with t 0 = 7. The best-fit parameters as well as those fixed are reported in table 1. Figure 1 (b) represents the best-fit to the reported death cases due to COVID-19 in Morocco. The fit gives rather satisfactory reproduction of the expected "S" shape of the death data. Further, it reaches a plateau of about 220 death cases, which looks quite reasonable, if 105 considering the low number of individuals in intensive care and the low fatality rate 0.03 in Morocco. This suggests also that our fixed initial conditions were very well estimated. Figure 2 (b) represents the predicted evolution of COVID-19 outbreak in Morocco, as calculated using the parameters set in table 1. As it is seen from Figure 2 (b) , the position of the epidemic peak, occurs 110 18 days earlier than the one reported in real data and also the number of the infected individuals is ten times higher than that in the real case. Analysis of R 0 = 2.5 at the early stage of the epidemic period seems be rather satisfactory as it agrees very well with that computed from the real reported infection data ( Figure 3 ). This also explains the low infection cases and low fatality rate seen 115 in Morocco. It is important to note that starting from 03/30/2020, R 0 (t) de-8 . CC-BY-NC-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 May 22, 2020. . https://doi.org/10.1101/2020.05.18.20106013 doi: medRxiv preprint . CC-BY-NC-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 May 22, 2020. . https://doi.org/10.1101/2020.05.18.20106013 doi: medRxiv preprint [8, 9] . . CC-BY-NC-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 May 22, 2020. In this paper, we have analyzed the data of COVID-19 epidemic wave that 140 hits the Moroccan territory starting from March 2 nd . Thanks to the aggressiveness of containment measures, the country has recorded one of the low death rates across the Globe. The analysis of COVID-19 data using a standard model composed of five compartments: susceptible, exposed, infected, recovered and dead (SEIRD) during the period 03/02/2020 − 05/15/2020 suggest that the 145 11 . CC-BY-NC-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. fitting the SEIRD model to death rates due to COVID-19, looks more reliable especially as the data did not depend on external factors. Indeed, the death rate depends on several factors, like the health system, the average age of the elderly people, their health conditions, availability of intensive care units, etc. But in the absence of statistics regarding the factors influencing death rates, it is still 160 premature to draw conclusions. Besides that, the fit gives rather satisfactory reproduction of the death data. Further, it reaches a plateau of about 220 death cases, which seems reasonable, with the data reported so far. The drawback of such approach is the down-shift of the position of the epidemic peak and the large number of infections reported on that day. Although, this is rather harsh 165 but it still not very surprising if taking into account the low testing rate. Moreover, the predicted R 0 and the total number of infections C(t) further support the robustness of this approach when fitting the model to data. . CC-BY-NC-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 May 22, 2020. . https://doi.org/10.1101/2020.05.18.20106013 doi: medRxiv preprint A contribution to the mathematical theory of epidemics Global stability of an sir epidemic model with time delays Extending the sir epidemic model Seir epidemic model with delay Early dynamics of transmission and control of covid-19: a mathematical modelling study The effect of travel restrictions on the spread of the 2019 novel coronavirus (covid-19) outbreak Preliminary analysis of covid-19 spread in italy 190 with an adaptive seird model An interactive web-based dashboard to track covid-19 in real time Covid-19 data repository at github