Assignment week 2

Question 1

dcdt = q*u - q*c -((y*c)/(K+c));

dydt = (y*r*c)/(K+c) - q*y

First I started a simulation with a nutrient concentration of 100, a starting population of 10, q at 0.1, and u,r & K at 10. This resulted in a gradual decline in nutrient which eventually reached 0 and exponential cell growth that leveled off when nutrient levels reached zero. This is illustrated by fig. 1. Next I ran the same simulation but changed starting population to 100 and nutrient concentration to 10, this resulted in the same effects in growth, and is illustrated by fig. 2. Next I ran the same simulation but made initial cell population 100 and initial nutrient concentration 1000, and again the same results occurred in terms of graph shape, and this is illustrated by fig. 3. Next I ran a simulation with a nutrient concentration of 100, a starting population of 10, q at 10, and u,r & K at 10. This resulted in both cell population and nutrient concentration declining, with cell pop. reaching zero and nutrient concentration leveling out. This is illustrated by fig 4.Next I ran a simulation with a nutrient concentration of 100, a starting population of 10, q at 5, and u,r & K at 10. in this case both nutrient concentration and cell pop. reached stable levels where neither approached zero. This is illustrated in fig 5. Overall I would say the system tends to produce high rates of cell growth when nutrients are sparse, cell decline when nutrients are overabundant, and stability of population growth (sustainable) when nutrient concentration is in sufficient.