# ICM 2013 – Network Model of Earth’s Health

This is my first time joining a mathematical modeling contest. As long as I knew, student’s mathematics contest should be held in a few hour, while the participants are working individually, in a close & silent room, doing some hard problems in several hours. However, this time is totally different. MCM/ICM 2013 := Mathematics/Interdisciplinary Contest in Modeling, 1-4 February 2013. This is my first 4 x 24 hrs nonstop mathematics competition. In these 144 hrs, we’re ‘locked up’ in a mathematics laboraty, just doing research on a problem, which is initially doesnt seem like a mathematics problem.

Well, it started on 2 Feb actually (officially it’s 1st, but in WIB, the time would be 8 am in 2nd feb). Me, with my 2 friends, Kevin and Nita, faced 3 problem, of which we should choose 1 of them to be modeled. We chose the problem C, which is also an ICM problem. It is “Network Model of Earth’s Health”. Sort of environmental and biological global issue. Well, the problem said that our mother earth is being more likely to be unpredictable. Many last biological forecastings fail to predict today’s phenomena. Of course, we all know that we could not anymore say that our earth is in a good condition. Natural disasters, varied global disease, extreme poverty & food scarcity, higher carbondioxyde emission, etc. Well, although most of the phenomena might be forecasted in many years ago, the impact of the phenomena is extremely beyond our expectation. We need to develop a more complex model to get a better forecasting. The important aspect, which everybody didnt care at that time is the presence of local factors. They just considered global factors which can affect the earth’s health. In our present, we can’t just consider those things only. We need to model the whole big picture. Every local factors count! Every detail of local’s properties of earth’s health aspect is directly influencing the global scale state shift! So, why is it so important? Why don’t we just go with flow and enjoy our mother nature? Holy crap! It’s just the same condition as you’re about crossing a very old bridge that you can not determine whether you can accros that safely or not, then you just said that ‘Why should we worry about this? Just go with the flow. Is that a problem if the bridge is going to be down?’. To make a proper follow up to the future possible natural phenomena, we should reduce the variety of biological surprise. That’s the point of global biological and ecological global forecasting!

Next, the ICM problem setters give us many many many many papers to read. 4 days to do research! The first day, we’ve just read, read, read, read, and read. Biology paper, environment paper, ecology paper, economic paper, mathematics paper, etc. The first day was the not-so-exciting part of the research. Well, the ICM asked us to make a dynamic network model on this problem. Dynamic, then the ‘time’ property should be the one of the most important dimention of our model. Network, then we should construct some nodes and assign some links to them in a appropriate type of relation. In day one, at least we found 24 variables involving in the attemp to measure the global earth’s health. TWENTY FOUR VARIABLES. Of course, those variables are absolutely not independent. 24 varibales, then at most, we can find $\binom{24}{2} = 276$ kinds of relation between them. That’s quite insane right? So, in our first attemp, we choose just about 10 variables involving in our model, some of these are: food availability, water availability, wood availability, disaster regulation, cultural site, GDP, carbon emission on atmosphere. Well then, although we’ve made a very complicated relation between one another, we found that our model was not a network at all. All of the country (which act as the nodes) were independent of every other country. The health of a nation was then not determined by other nation’s condition. That’s a big failure. Our first failure. Day 1 was end with no prospective model at all.

Day two. We started the day with our new perspective in our model. Also, we did data mining again in the morning. In the middle of the day, we were end in a conclusion: you can’t model those 24 variables in just 4 days. You may if it were 4 months or 4 years, however that was not possible. Then, instead of stand still in our 10-variables model, we choose another model. 1 variable model. Well, this is embarassing, but this is the only one which we’re could overcome. Well then, we choose that 1 variable: food supply of each country. Of course this variable is the local factors of each nations. Food suply in country A can not be the same as in country B. However, other factors which may be involved in our model are political and economic stability in each country, and also strenghtness of bilateral political relation between 2 arbitrary nations. Ok, in a food flow, each country should have a production factor, consumption factor, export factor, and import factor. These factor varied among country, and moreover the rate of each were also varying extremely. This is our second attempt. Well, we were so excited with this model, at least at that time T__T. Next, we started to gather the data of each country’s food production, consumption, and international trading. This is really not an easy job. Gathering a data of a district may be an easy job, but to gather the data of 20 country, and the existing bilateral relationship between them is a really really exhausting job. In the end of the day, we still didnt get the entire data for each nations. However, the embrio of our model had been existed at that time. A dynamic directed graph. We choose 24 countries around the world to be the vertices, representing our whole mother nature, and we said that country A had a flow to country B if and only if there is a food export deal from country A to country B. That was our Day 2.

Day 3. It’s Sunday. While our other friends were enjoying a relaxing day, we didn’t. Our morning research began with collecting data (again). Gathering data about which country having certain amount of food export to another country is really really hard to do. We just found the complete statistics of United States. We did not find any data about other country’s food trading. That’s suck. Next, we decided to just collect the data of wheat and rice production, consumption, export, and import. Just that. Thus, it would be another simplification of our model. Okay, just forget about the data. That’s the not-so-interesting part of our research, Now, we’re gonna talk about the model. As I’ve mentioned above, our model was a dynamic digraph. We built a weighted adjacency matrix of our graph, let say matrix $K$. Then each component value, $k_{ij}$ means that country i have a $k_{ij}$ amount of wheat and rice commodity to be exported to country j. Next, as I’ve also mentioned, we also have a production and consumption vector, representing each country’s. Then all of those structure is then influenced by the economic and political condition of each country and of every 2 countries (bilateral). Also it is influenced by the scientific research on food production of each country. Each of those conditions are then modeled as stochastic process. We assign some random variables to each of those factors, and also we choose an appropriate distribution to each of them. Determining the proper distribution was also a really hard work. We had to deal with some distribution transformation, regarding to some mode and mean changes; and this stuff is a little bit complicated. Later, we model the consumption of each country is following the population of the country. The higher population, the higher food demand would be. Well then, we model the population growth as a simple differential equation (also known as population growth model / radioactive decay model) introduced in Calculus. The very simple one, the naive one, and the one which later destruct our whole model. In this model, our equation give an unlimited growth of consumption, an exponential rate of human population. This allow our model to give a higher consumption than the production rate. This is our second failure. In our simulation, we projected that most of developed country such as United States, Russia, Japan, China, etc would be down in 2020. The lack of food supply. We thought that our model was absolutely not feasible to be applied in a serious biological fotecasting.

Day 4. It’s monday. Many other friends were having lecture & we’re just staying still on laboratory. Miserable. Okay, in this state, we’re just writing our research report. Making a document, a paper-like document to be submitted to the committee of the contest. Nothing special here. Just several hours spent in front of laptop, typing and typing. At the end of the day, we did not change our failure of the model. We submitted the exponential consumption model. That’s all.

Not a great model. Not an amazing result. No sophisticated solution / conclusion. However, we were happy, enjoying those days. Personally, these events may could affect my whole life ahead. Thanks Lord for the providence You’ve given to us. Thanks for the opportunity. Thanks for the days.