For example, this is a time series of the number of infected persons confirmed in a day, or daily epidemic count data. The epidemic curve shows how the scale of the infection increases. The development of good mathematical models for predicting prevalence and subsiding is strongly expected. While COVID-19 epidemic has been spreading worldwide, its characteristics are still unclear. Regression analysis articles Logarithmic count data articles Quadratic exponential function articles Bell curve articles Linear regression articles Generalized linear model articles Article Details 1. Regression analysis, Logarithmic count data, Quadratic exponential function, Bell curve, Linear regression, Generalized linear model These estimates can be informative to reveal the transition mechanism from pre-epidemic to epidemic, and to pandemic. By applying the logarithmic quadratic function model to the data of the number of cases in each country of the world, the starting and the subsiding dates of the epidemic and the total number of cases in each country were estimated.Ĭonclusions: Although an epidemic curve in an early period said generally to be exponential, namely linear in the logarithmic space, a quadratic curve regression fits better than the linear and the generalized linear model. Results: It was shown that the statistical properties of the logarithmic quadratic function model were good even in the early stages of the epidemic, which is generally said to increase exponentially and monotonically. Methods: We modeled the initial emerging period of the epidemic curve of COVID-19 in Tokyo with a model that introduces a quadratic polynomial function to the logarithms of the numbers of infected cases, and modeled it with other regression models including the generalized linear model to compare. On the other hand, a regression model with a small number of parameters is more robust against data errors than a highly sensitive nonlinear differential equation model, though, it is not clear what a good regression model is for epidemic data. However, model parameter values of these ordinary differential equation based models are very sensitive for errors of observed data, and it is often difficult to find a reliable model especially when the amount of data is not sufficient. To express this with a mathematical model, the compartment model such as the SIR model is used generally. This is the number of persons found infected daily. The epidemic curve shows how the epidemic increases and subsides. The development of good mathematical models for predicting its prevalence and subsiding is strongly expected. When did the rocket reach its maximum height?Īlthough the rocket was in fact launched from ground level at time0, the graph seems to indicate that the rocket was launched at abouttime -1 seconds.Background: While COVID-19 epidemic has been spreading worldwide, its characteristics are still unclear. Press the TRACEkey and use the arrow keys to predict when the rocket will be atvarious heights (you may need to use the up arrow key to trace theparabola). The graph will show the individualdata points as well as the best fit parabola. You can letthe calculator choose these values for you by pressing the ZOOM key and choosing option number 9: ZOOMSTAT.Ħ. When you do a stat plot, you need to look atyour data and choose values that will include your data. These numbers will tell the graphing calculator what part of thegraph it should display. Press the WINDOW key and enter the following: Press the StatPlot key ( 2nd and Y=).Choose Plot1 and press ENTER. The variables a, b, and c are the coefficients for the quadraticequation that best fits the data you entered.Ĥ. You will see something like: y = ax 2 +bx + c Your homescreen should show: QuadReg L1, L2, Y1 Type "L1, L2" by pressing 2nd and 1, then comma, then 2nd and 2.Type "Y1" by pressing VARS, moving across to Y-VARS,choosing Function, and choosing option number 1. This will bring you back to the homescreen, with QuadReg showing. Press the STAT key, select CALC, and chooseoption number 5: QuadReg. The numbers under the L2 heading are the heightof the rocket in feet.ģ. The numbers under the L1 heading are the seconds since therocket was launched. These data points represent the height of a model rocket atvarious times during its flight after its rocket motor has burnedout. Press the STAT key, use the arrow keys to select EDIT, and enter this data: L1 Press the Y= key and clear any equations.Ģ. Quadratic Regression Quadratic Regression on the TI-83ġ.
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