Could you please help me with the modeling problem attached below?

UCLA. has a population of nerds (N), hipsters (H) and regular folks R. When nerds, hipsters, and regular folks interact with each other socially, there is a chance that some individuals will switch from one group into another. Write down a diEerential equation model of the three populations, by using the following assumptions. All rates are per year rates. I The more hipsters a. nerd meets, the less lilrely she is to turn into a hipster. Thus, the per capita. probability that a nerd turns into a hipster is a. decreasing sigmoid of the hipster population, with a maximum per eapita probability of 111% and half-saturation density of 2m. 0 The more nerds a hipster meets, the euro likely she is to turn into a nerd. Thus, the per capita probability that a hipster turns into a nerd is an increasing sigmoid of the nerd population, with a maximum per capita probability of 15% and half- saturation density of 500. o Hipsters generally like other hipsters, but it only goes so far. When two hipsters meet, there is a probability of 20% that they both will turn into regular folks. :- When a regular person meets a nerd and a hipster at the same time. there is a probability of 10% that she will turn into a nerd and a probability of 5% that she will turn into a hipster. | When a nerd and a hipster meet, there is a probability of 3% that they both will drop out of school to form an internet start-up together. 0 New nerds enroll at UCLA at a constant rate of 3141 per year. c Hipsters like to tell: about their interests with regular folks (preferably without being interrupted by other hipsters}, so new hipsters enroll at a rate proportional to the ratio of regular folks to hipsters, with a proportionality constant of h. a Regular folks like to go to school with a nice mix of dimnt types of people. so new regular folks enroll at a rate propor- tional to the pro-duet of the three populations. with a proportionality constant of k. c Nerds graduate at. a per capita rate of 3.3. regular folks at a per capita rate of (1.25, and hipsters at a per capita rate of [1.2