Better before Worse

Sometimes, focusing on solving one set of problems causes another set to pop up. Call it ‘firefighting’. By treating the worst-off patients, the slightly better off become neglected. By only taking care of the most severe issues, we draw time and resources away from issues that are becoming severe. Things tend to get better in the short run, but worse in the long run.

Here is a visual representation of a mathematical model of this issue. Each box (or ‘bathtub’) represents the number of issues in each category: some are Non-issues, some are Mild Issues and some are Severe Issues.

An issue moves from one category to the next by way of one of the pipes that connect the bathtubs. Each of these pipes contains a mathematical equation that governs how quickly issues pass through it from one bathtub to the next. In each of the green-colored pipes, the rate that issues move is simply a fraction of the number of issues upstream. So, we say for example that 5% of Mild Issues become Severe Issues each month and, say, 10% of Severe Issues become Mild Issues.

The only pipeline that works differently from this is the orange one – the rate at which Nonissues become Mild Issues. In that case, let us say that rate is some fraction (again, 10% works) of the number of Nonissues (just like the other flow rates, so far), but multiplied by the number of Mild Issues squared. So, instead of ‘10% x Nonissues’, the equation is ‘10% x Nonissues x MildIssues^2’. Some diseases and health problems work this way. If you are a nonsmoker who lives with a smoker, you might have a 10% chance of becoming a smoker each year, but if you live with two smokers, your chance goes up to 40% each year and if you live with three smokers, it goes up to 90%. The idea is that mild problems recruit new mild problems. Neglecting that slow oil leak in your car’s engine might mean a 10% chance of an engine problem this month, but neglecting both the oil leak and the dirty filter might make that chance go up to 40%.

We can choose these percentages so that the number of issues in each category is constant – one Non-issue becomes a Mild Issue for each Mild Issue that becomes a Non-issue. What happens to the number of Severe Issues as we increase the rate at which Severe Issues are moved into the Mild Issue category?

The graph above show what happens to the number of Severe Issues when we increase the fraction of Severe Issues that are turned into Mild Issues each month from 10% to 15% (starting midway through the first time period). In the short run, the number of Severe Issues drops, since we are treating 15% of them, rather than 10%. But in the long run, this causes the number of Severe Issues to increase.

What is happening here is that, by moving Severe Issues into the Mild Issue category, we are increasing the rate at which Non-issues become Mild Issues. For example, by treating someone’s acute respiratory infection, we get them back on the street sooner to infect more people.

I am not saying that we should neglect Severe Issues or not treat them at all. One lesson from this model is that by increasing the acute care without following through and also increasing the rate of Mild Issues becoming Nonissues makes the problem worse in the long run than it would have been by not increasing acute care at all. It would be especially perverse if things played out slowly enough that the person who made the decision to focus more on treating Severe Issues had gotten all the credit for the short-term improvement and then moved on, or retired, before the next person stepped into the position to take the blame just as the negative consequences of that decision just started to appear.

It is interesting to see this ‘better-before-worse’ behavior in such a simple model. I might spend some time whenever I can trying to find even simpler structures that show similar behavior.