After organizing the data from the BRFSS, our next step was to construct the A-matrix for our sysem


Used logistic regression analysis to identify state variables:

The Odds Ratios in the table  reflect the weighted significance of each of these variables on the likelihood a person receives a vaccine in a given year. The higher the odds ratio, the more likely a respondent is to get the vaccine if their recorded response was a 1 for said variable. For example, having some form of health care coverage makes one three times more likely to receive a flu shot. Being a daily or frequent smoker decreases the likelihood of getting a vaccine by nearly 39%.

Constructing the A-matrix

Our preliminary model consists of only an A-matrix (the system dynamics) and no input (B = 0). The state variables correspond to the variables listed above, as well as our X1 state variable being Flu-shot. These state variables are proportions of the population for whom the description of the variable applies. For example, Smokeday represents the proportion of the population who smokes daily.

The equation that each row of the A-matrix represents is shown below (m = n = 6):

We needed to determine this a coefficients. To do that we would run a least-squares regression with x_dot as the dependent variable and the state variables as the independent variables. We had collected data for each year for each state variable, so we needed to form an approximation for x_dot:

In a discrete system with delta_T = 1 (year), our approximation is now:

Regression yielded row of a coefficients for each x_dot, which we compiled to form the A-matrix for New York: