Let's give it a go anyway

All these things make epidemics impossible to predict and modelling is all about predictions. Though the obstacles seem huge, we still try. The law of the many gives us some hope. If thing so and so many goes to work everyday, and so and so many children meet at school everyday then with a computer we can generate (or simulate) a large number of possible scenarios, 1000 or so. Even though we know that the probability of one of those scenarios actually occuring is frighteningly low, the general picture gained from this large collection of scenarios can give us important knowledge. Even more information is gained if we repeat the simulation with control measure, vaccination or travel restrictions. Then we might claim that we know the simulations are wrong BUT the control measure works. This is called a comparative result and can be extremely valuable.

Building a model

Coming down to the actual modeling now. Some carefull considerations must be taken. What type of model do you want to make? The first aspect to think about is to which school do you want to lend your support, complex vs. simple. There is no right or wrong. It depends on what results you need and, not on a small part, to personal taste.

Here are a few other things to consider.

The disease

The disease is usually modelled as a condition of the would-be carrier. If you have the disease you a assigned the state "infectious". if you meet somebody else who is in the state "susceptible" with a certain probability he/she will catch the disease. Eventually you will recover or in the case of severe diseases, die. These are also states. In most cases, when you recover you will have period during which you are immune and won't be susceptible. This is important to model since if there aren't enough susceptibles around, above a critical value, the disease will die out no matter how contagious.
This type of disease representation is usually called the SIR-model. It can be made very complicated. One of the first things you can do is add a latent state. That's when you're infected but not yet infectious. Further more you can add different stages of infectiousness, or vary the probability individualy.

People

This is the hard part. No matter what you do, there's always some aspect that you will have overlooked or something deemed insignifcant that the next man regards as crucial. The line must be drawn somewhere. Precisely because of the complexity of human behavior some modelist take the opposing stance and make models as simple as possible. With simple models you need to do less guessing work but uncertainty arises because of everything you leave out. Complicated models, besides being harder to program, are based on more guesses and fuzzy knowledge. It's a matter of taste and the uncertainty in the result is vast either way.

In the simplest models people run around like particles in a gas. There's equal chance of you meeting that guy as the next. The next level is to start introducing some type of structure, like families, schools and workplaces. You have a higher chance of meeting that guy if he works in the same building or floor. Random meetings may still occur at the supermarket but less likely if he lives in another community.

Some models take a stab at the the number of children at each school, in each class. Some rely on more accurate knowledge from survey data or even real data from censuses. The size of the population is also important but comes at the price of time consumption on the computer.
Another direction to head into is time. What difference will time of day, day of the week, winter or summer make?

Any computer simulation is doomed to succeed.

Networks

Contacts is why epidemiolgists are so interested in networks. Social contacts between people can be described as networks. Peoples are nodes and everybody the know or perhaps have had sex with will be linked to them. The probability to meat may be described by placing weights on the links. Other types of nodes can be entered like workplaces and families. Cities can be linked together by flight routes.

All this is important to gain knowledge about. Epidemiologist, like a growing number of scientists in other fields, pay close attention to, and indeed often contribute to, the progress made in complex networks.

Travelling

A disease would spread very slowly or not emerge at all if people didn't move about. In the days of the plague, disease spread like waves on a pond. Towns were hit roughly in the order of their distance from the original source. Today you can make across the globe in a day. The more people travel, the more quickly the disease will spread. Travelling can in fact it self be the tipping point which converts a minor outbreak which less travel would die out on it's own, into a global epidemic. Large scale models will need to adress this in some way, either by randomly dispersing the disease across an area or taking into account the full network of different types of transport.

Control measures

The main result of a simulation will almost invariably be some recomendation on how to stop the disease. What will the effects be if everybody was vaccinated in advance? What would it cost? Sometimes it is possible to reduce the ecenomic costs and adverse effects by employing another strategy like ring vaccination. This means that the contacts of an infected is traced and vaccinated. Hopefully this will break enough links in the network so that the epidemic will hinge back into extinction. Will it work? Epidemic models may hold the key, if you deem them reliable enough.
Other control measure are possible. Like mentioned above, a disease can only spread if people stay at home. Restricting travel, saying only travel if absolutely necessary, may be all it takes to quench an outbreak.

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