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Conditions for the occurrence of car accidents are introduced in the Nagel-Schreckenberg model. These conditions are based on the thought that a real accident depends on several parameters: an unexpected action of the car ahead (sudden stop or abrupt deceleration), the gap between the two cars, the velocity of the successor car and its delayed reaction time. We discuss then the effect of this delayed reaction time on the probability of traffic accidents. We find that these conditions for the occurrence of car accidents are necessary for modeling realistic accidents.

Populations of erythrocytes in solution were heated “instantaneously” to and maintained at temperatures in the range of 44 to 60°C on a microscope stage specifically designed for this purpose. Simultaneously, the visually observed hemolysis-time history of these cells was measured. The results were successfully correlated on the basis of two models: 1) a kinetic scheme assuming two sequential, first-order reactions by which the cells are first reversibly altered and then irreversibly damaged; and 2) a statistical model for which the number of cells that are damaged at each instant is assumed to be normally distributed. From the experimental data the rate constants for the two reactions in the kinetic model were determined and were found to have an Arrhenius dependence on temperature. By applying the statistical model to the data, we were able to determine the mean and standard deviation of the distribution curve for this model. The logarithms of these latter two parameters vary with temperature in a linear fashion.

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In this paper, we are interested to forecast and predict the time evolution of the Covid-19 in Morocco based on two different time series forecasting models. We used Auto-Regressive Integrated Moving Average (ARIMA) and Long short-term memory (LSTM) models to predict the outbreak of Covid-19 in the upcoming 2 months in Morocco. In this work, we measured the effective reproduction number using the real data and also the fitted forecasted data produced by the two used approaches, to reveal how effective the measures taken by the Moroccan government have been controlling the Covid-19 outbreak. The prediction results for the next 2 months show a strong evolution in the number of confirmed and death cases in Morocco. According to the measures of the effective reproduction number, the transmissibility of the disease will continue to expand in the next 2 months, but fortunately, the higher value of the effective reproduction number is not considered to be dramatic and, therefore, may give hope for controlling the disease.

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