Team:HZAU-China/Modeling/Gray logistic

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Gray logistic


Aim:

To know the growth curve in the dog’s blood

Steps:

1.Do experiment to measure the number of bacteria;

2.Establish the gray logistic model to simulate the growth of bacteria;

3.Determine the parameter through the experiment;

4.Test the predicted results.

Results:

The gray logistic model gets the good forecasting result.And the model precision is excellent.

Background:

The color of blood is so deep that it is not fit to measure the OD value to determine the growth of bacteria in the blood.Then we choose dilution-plate method to detect the number of total bacteria. So we coated a large number of plates.The logistic model of population can well predict the increase of population.

Establish the logistic model:

In the environment of the blood,the number of bacteria have a maximum value K.And when the number of bacteria approach K,the growth rate is next to nil.Then the population growth equation is as follows:

The solution of the equation is :

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