Simple Population Control Model
Modeling of Agricultural Systems [AGS721]
LAB 7
Simple Population Control Model
Suppose that you're hired as a modeler to construct a population control model for a small town (present populaiton size is 10,000 in 1996). As a system modeler, you defined the problem, set the objectives and came out with the flow diagram (see handout). Gathering all necessary information then you decide to construct the model using PD Plus. Following are these information.
1. Birth rate = Fractional Birth Rate x Population
where Fractional Birth Rate depends upon the efect of birth control as;
Effect of Birth Control |
Fractional Birth Rate |
0 |
0.1 |
0.1 |
0.09 |
0.2 |
0.08 |
0.3 |
0.078 |
0.4 |
0.075 |
0.5 |
0.05 |
0.6 |
0.048 |
0.7 |
0.045 |
0.8 |
0.03 |
0.9 |
0.02 |
1 |
0.02 |
2. Death rate = Population/Average Life Span
where the average life span of the population is 70 years.
3. The effect of birth control is determined by the ratio of number of birth control officers and population. That is if the ration is get closer to 1 the effect of birth control becomes more effective and vice versa. This indicates that number of birth control officers play significant role in birth control program. More birth control officers would educate more people in terms of family planing program.
4. Number of birth control officers depends upon butget. This butget is part of income tax. TAX money uses for hiring birth control officers is the amount of money left (saving) after the city used certain amount for city development program (eg. contruction of road, education, transportation etc.). Only 5% of the saving is used for hiring birth control officers.
5. Generally, the city plan to hire birth control officers every year. That is the birrh control officers will be hired 5% of the total population (normal hiring fraction). Thus;
Hiring rate = Population x 0.05
x Potential Hiring fraction
where potential hiring fraction is depended on the total butget as follow;
Budget (Dollar) |
Potential Hiring Fraction |
0 |
0 |
100,000 |
0.05 |
200,000 |
0.1 |
300,000 |
0.2 |
400,000 |
0.4 |
500,000 |
0.45 |
600,000 |
0.5 |
700,000 |
0.7 |
800,000 |
0.8 |
900,000 |
0.9 |
1,000,000 or above |
1 |
6. Budget paid for each birth control office is $2,000 per year.
7. Given initial and constants
Initial |
Constant |
| Population = 10E3 | Tax Paying Fraction = 0.10 |
| TAX = 10E4 | Spending Fraction = 0.70 |
| Birth Control Officer = 5 | Normal Hiring Fraction = 0.05 |
| Saving = 10E3 | Job Duration = 10 years |
| Average Life Span = 70 years |
Formulate the model then run the base-run.
Consequently, select your best strategies for controling the population.
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