## Comments on Midterm exam questions

On our midterm exam, there were two questions that were open-ended and asked for creativity and critical thinking. For the most part, there were no wrong answers to these questions, but there were some answers that were better or more interesting than others. This page is here to help you reflect on your own answers to these questions.

### 6c. How might the Ross-MacDonald malaria model be wrong and improved?

The Ross-MacDonald model was a huge advance for Malaria research when it proposed by MacDonald in 1957. It was not so much the equations themselves, but the framework the equations created for discussing the problem of malaria. MacDonald's book on the equations is 200+ pages.

• Any other facts of life would only alter the rates that are already present in this model, so no changes are necessary.

In one sense this is correct. All time-series observations can be exactly fit by a Fourier series (or wavelets or ...) description of time-dependent rates. However, in many cases this is useless nonsense because the model will not have any predictive value without also being coupled to some constraining predictive mechanisms. In cases like MP3's where fourier models ARE used, it is primarily for data compression of a deterministically reproducible pattern. There is no change or randomness like that for which science theories need to account.

• All suscetiples are turned into infecteds eventually.

Be particular about what you are saying. This comment has two different interpretations, one with is wrong and one which is right. In the Ross-MacDonald model, every person will eventually get malaria. This is pretty close to the truth in places where malaria is endemic. BUT, in this model, there will always be people in the susceptible compartment.

• The model does not account for differences in living conditions in different places.

The parameters of the model should be different at different places.

• Shouldn't the model include mosquitoes infected other mosquitoes or people infecting other people, or maybe even other animals?

Ross won the Nobel prize for "figuring out" the life cycle of malaria. Actually, Giovanni Grassi should have gotten the prize. But allong the way, people had discovered that malaria does NOT transmit directly person-to-person OR mosquitoe-to-mosquitoe under normal circumstances. The life cycle actually requires a stage in humans and a stage in mosquitoes.

• Populations change over time, and the model says they don't.

Well, technically, the model does allow populations to change. It just assumes constant birth and death rates, with force the population sizes to converge* to a constant value relatively quickly. But the real questions is whether or not the population sizes change happen fast enough for us to care. The answer is yes, in some places with rainy and dry seasons, numbers of mosquitoes very significantly.*

• What about death vs recovery?

The model does not say the removal rate of people from I actually refers to.

### 11. Essay on the Blind Men and the Elephant

• This poem is basically a story about how we make a Fermi model.

• The blind men should build their model like we build compartmental models with reaction networks.

• The poem is a warning about not collecting enough data.

• Much of mathematical modeling is attempting to approximate a natural process from a set of observations.

• Modelling is finding parallels between the novel and the familiar ("an elephant is like a tree").

• Are the blind men doomed to be dumber than we who can see?

• We are all blind trying to see, and we always only see a part of the reality before us. Others with different perspectives may see different parts.