key: cord-296285-qiez6adj authors: Boudrioua, M. S.; Boudrioua, A. title: Predicting the COVID-19 epidemic in Algeria using the SIR model date: 2020-04-29 journal: nan DOI: 10.1101/2020.04.25.20079467 sha: doc_id: 296285 cord_uid: qiez6adj The aim of this study is to predict the daily infected cases with Coronavirus (COVID-19) in Algeria. We apply the SIR model on data from 25 February 2020 to 29 April 2020 for the prediction. We estimate the parameters of our model by minimizing the negative log likelihood function using the Nelder- Mead method. We found that the epidemic peak reach July month and the COVID-19 disease will disappear in the month of October. We suggest that Algerian authorities need to implement a strict containment strategy over a long period to effectively reduce the epidemic size. 2 Algeria has reported the first case of COVID-19 on 25 February 2020, in Ouargla region and he was an Italian national (HAMIDOUCHE, 2020; Algerian Ministry of Health 2020). Two other cases were reported on 01 march 2020 in Blida region in the North of Algeria (HAMIDOUCHE, 2020; Algerian Ministry of Health 2020).The epidemic continues to spread in other regions of the country. On 03 April 2020, the Algerian authorities have declared 1171 confirmed cases with 105 deaths cases (Algerian Ministry of Health, 2020). Various earlier studies have predicted the confirmed cases of COVID-19 infection in different countries. (Kuniya, 2020) applied the well-known SEIR compartmental model to predict the epidemic peak of COVID-19 disease in Japan. He used data of daily reported cases of COVID-19, from15 January to 29 February 2020. He founds that the epidemic peak in Japan could possibly reach the early-middle summer. (Roosa et al. b, 2020) forecast the covid-19 epidemic in China over a short-term period using generalized logistic growth model, the Richards growth model, and a sub-epidemic wave model. They employed data of cumulative confirmed cases between January 22, 2020 and February 9, 2020. They found that the epidemic has reached saturation in Hubei and other provinces of China.. ( Hamidouche, 2020) introduce the Alg-COVID-19 Model to predict cumulative cases of COVID-19 in Algeria..This model allows predicting the incidence and the reproduction number R0 in the coming months. ( Hamidouche, 2020) . According to his results, the number of infected cases in Algeria will exceed 5000 on April 7 th , 2020 and it will double to 10000 on April 11 th , 2020. (Hamidouche, 2020) . This study applies the Susceptible-Infected-Recovered (SIR) model without demographics (no births, deaths, or migration) (Kermack and McKendrick, 1927; Dietz 1967; Keeling and Rohani, 2008) to predict the daily confirmed cases of COVID-19 infection in Algeria. We use data of reported cases between February 25, 2020 and April 17, 2020. We predict the epidemic peak and the end-date of this disease. These results could be helpful for decision makers in Algeria to implement their strategies. 1) 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. (which was not certified by peer review) The copyright holder for this preprint this version posted April 29, 2020. . The SIR model without demographics is given by the following non linear system of ordinary differential equation (Kermack and McKendrick 1927 , Keeling and Rohani, 2008 , Harko, 2014 : The function (t) S represents the number of susceptible cases at time t .The function (t) I represents the number of infected cases at time t, and the function (t) R is the compartment of recovered cases from the disease. The parameters  and γ are called the contact rate and the recovery rate, respectively. The initial condition of this The model can be written also as follows: The basic reproductive ratio 0 0 R  is'' the average number of secondary cases arising from an average primary case in an entirely susceptible population, and it's given by β/γ'' (Keeling and Rohani, 2008) . We integrate numerically our non-linear system using the Livermore Solver for Ordinary Differential Equations (LSODA) algorithm (Hindmarsh, 1983; Petzold, ,1983 ).This algorithm handle stiff and non stiff systems of size . It has an automatic method selection where it uses Adams methods with . 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 April 29, 2020. . the non stiff problems and Backward Differentiation Formula (BDF) methods with the stiff problems ( Hindmarsh, 1983) . Python software version 3.6.4 was used to implement the SIR model and solve it. After resolving the SIR system we obtain the approximate functions Where the parameter p is a constant reflects a combination of sampling efficiency and the detectability of infections (King, 2017) .We ignore the constant p in this study. Thus the likelihood function is defined as follows: 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 April 29, 2020. . https://doi.org/10.1101/2020.04.25.20079467 doi: medRxiv preprint 5 function, and therefore maximize the log likelihood function. This algorithm is used for solving the unconstrained optimization problem based on the iterative update of a simplex: Where The procedure of estimation can be resumed in the following three steps ( Nsoesie et al, 2013): Step 1: Select the initial parameters  , γ and initialize the SIR model and the Nelder-Mead method, Step 2: Run the Nelder-Mead algorithm to get new parameters which will be used in the simulation and the prediction of the COVID-19 epidemic. All the calculations were conducted as previously stated by Python software version 3.6.4 Empirical results and discussion: The data were obtained from Johns Hopkins University, Center for systems science and engineering (Johns Hopkins University, 2020). We used the number of daily reported confirmed cases for the COVID-19 epidemic in Algeria, from 25 February 2020 to 17 April 2020. We used equation ( 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 April 29, 2020. . We substitute the new parameters in our SIR model to simulate and predict the COVID-19 epidemic in Algeria. . 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 April 29, 2020. In this study we predict the COVID-19 epidemic outbreak in Algeria using the number of daily infected cases, from 25 February 2020 to 17 April 2020. We have applied the SIR compartmental model without demographics in this task. We find that the COVID-19 epidemic peak reach the month of July and the end of this epidemic will be in the month of October. . 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 April 29, 2020. . https://doi.org/10.1101/2020.04.25.20079467 doi: medRxiv preprint 8 Our findings agree with the results of (Kuniya, 2020) in the case of COVID-19 outbreak in Japan, and with the WHO's statement that COVID-19 will maybe disappear in the summer (Kuniya, 2020) . Following (Kuniya, 2020) we suggest that a strict containment strategy is needed in Algeria, over a relatively long period, to reduce the epidemic size. 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