3.0 Method of Solution
3.1 Mathematical Model
The team members create the beginning program. The first program outputs the information for one year of data. The birth rate and death rate are entered into the program is from the state of New Mexico. The information first calculated is the number of susceptible people. The susceptible group is the people in the city who can not get the smallpox virus. Then the number of infected people is calculated. The infected is the people who get the smallpox virus when the initial downwind cloud hits the city. This program outputs the number of infected.
In the second program additional variables are incorporated. First it calculates the death due to the smallpox virus. This is calculated by multiplying the infected population by 40%1.The 40% is the number of people who die from the smallpox virus. Next, will be the survivors. Which is the number of people who do not die from the virus. The deaths due to other causes is 6%3. The formula is the number of infected people multiplied by .06 for the percentage.
The recovery rate is 2% (2 infected per 100 exposed.) The formula is 2% multiplied by the population divided by 100. Also taken into account is the birth rate. The formula is population divided by 1000 multiplied by 16. The number 16 are the average number of people born per year in the state of New Mexico3. The output of the program is the number of people infected. The formula is the population minus the infected plus the death due to the disease. Outputted is the percentage of people infected. This is completed by taking the variable used in the formula of the infected people and dividing it by the population, then multiplying it by 100 to get a percentage.
Added to the second program is a For loop. This loop allows the output of the infected population and the percentage for any number of years. The loop has the ability to be changed. If it runs for 3 years there is a significant change, yet if it is run for a period of 15 years then all the numbers are lowered and the change each year is visible. Refer to Appendix 3 and 4. The disease will die out within 20 years of the first infected year. To better this second program, it can be used as a input parameter. This will allow the user to enter the data for any particular place.
3.2 Computational Methods
The first program provides the best results if it is allowed to run for a year. It shows the dramatic percentage of people who get the virus within the first year of the initial contact from the downwind transport. The second program is run for any number of years. This shows the breakdown of the virus as the years move on from the initial downwind contamination. Both serve a representation of the first year and the years thereafter. This can help in finding the time to try and control the initial contamination period.