Transparent famine models III
The full resource scarcity model and visualizations
Before getting into the main discussion, I want to once again underline the importance of the problem of famine in Sudan - Doctors Without Borders announced October 10th that they had to cut back services in the Zamzam camp in Darfur - home to 450,000 displaced people and 2,900 children with acute malnutrition, because they couldn't get deliveries of food and other supplies through.
"We’ve been sounding the alarm about emergency conditions in Zamzam camp since February, but the international community has failed to act." Avril Benoît, CEO of MSF USA
In addition to be a critical situation for the people of that camp, it underlines the broader problem that more international attention needs to be brought to bear to push for an end to the conflict and, regardless of whether that’s possible currently, at a minimum for humanitarian corridors to provide aid.
The resource-scarcity famine model
According to at least one of my readers it's been a bit of a slog to get through the technical details, but today's post will complete the process of laying out the basics of a preliminary model of how famine may impact Sudan in the coming year(s). That is, I began the project with broadly the question, “how can it be that a model would predict millions of deaths from famine in Sudan?” (and also why aren’t more people paying attention, but that’s another story). Today I complete the delivery to anyone who’s interested to understand how that is possible, presenting a model that differs in minor details but comes to broadly similar conclusions and thus provides all the basic calculations and assumptions needed to understand how the Clingendael Institute reports could come up with estimates of millions of deaths from famine in the coming years in Sudan.
To review briefly, the first post explained some basics about calculating the sources of food available and how those are converted to calories. The second post outlined the calculations for caloric deficit for individuals, then how that impacts their change in BMI, and an equation for estimating excess mortality. Today I provide an overview of the initial BMI distribution, how calories are distributed across the population, and then overview the steps involved in calculating month-by-month estimates, and provide some visualizations of the outcomes.
Again, if you prefer walking through the discussion with the code at hand in a Python notebook, you can do so here to see the model elements and here to see a run of the model and plots of the output.
Initial BMI distribution
As before, the model is based on working with percentiles of the population in which higher (“rich”) percentiles have both greater initial body-mass index (BMI) and greater food consumption. We consider a reference BMI distribution and simple models of linear interpolation between BMI of 18 and 30 or a logarithmic function that assumes the majority of the population have similar BMI levels but the poorest have significantly lower BMI. Note that for the calculations focused on excess mortality, the most critical part of the distribution is the first roughly 20 percentiles since those are the most subject to malnutrition (and also note that the Integrated Food Security Phase Classification (IPC) levels are based on this group (i.e. the poorest 1/5th of the population).
Distributing calories across the population
The next critical piece is to determine how calories are distributed among the population. We will investigate this in depth in the future, as for example the sharing of food among the population can have a significant effect, but for now we consider two simple functions. The first is a linear interpolation (with a given slope as a parameter that measures inequality), and the second is a piecewise linear function with both a slope parameter for the first segment and also a percentile above which all consumption is equal. The motivation for the latter is that at some point individuals stop consuming additional calories and shift consumption to non-food items. Also note that, for a given level of overall consumption, the more the rich consume, the less will be consumed by the poor.1
Consumption over time
Even when we know how much grain is produced in each month and available over the year, it is not clear how much grain the population will consume in a given month. For example, we could imagine scenarios such as:
1. (necessary) Everyone consumes the necessary calories to maintain their current BMI, subject to the availability constraint (This is not at all forward looking, but people may not be able to forecast future supplies)
2. (seasonally-adjusted): Because people expect season variation in availability (or because of price signals), people might adjust their consumption over the year in response to harvests and lean times. (This is forward looking (and based on past experience), but could lead to under-consumption if a future harvest is better than expected or aid is delivered in a future period).
3. (famine optimal): Based on the information about available calories over the whole year and the population's BMI, we could define the optimal consumption to minimize excess mortality, based on linear or dynamic programming.
In reality there are likely complex dynamics relating (1) and (2) and other social and human behaviors and response to the conflict environment. So for now we simply rely on a set of fixed month-by-month consumption numbers as inputs in which (a) consumption is reduced roughly linearly over time and (b) almost all available grain is consumed by the end of the lean season (September 2024).
Step-by-Step
Because the calculations of each month depend on previous months outcomes (e.g. remaining food stock, current BMI levels, etc), in each month we calculate a number of updates, as follows:
1. Updating Grain Stock
Add new grain inputs for that month (from harvest and other sources) to the existing stock. This provides a maximum for what can be consumed in that month.
2. Total Caloric Supply
As noted above, the model for now uses pre-defined monthly consumption levels that decrease over time and consume roughly all calories by the end of the lean season.
3. Distributing Calories Across the Population
The model next allocates these available calories from (2) across the population, using the methods described above.
4. Updating BMI for each group and estimating excess mortality
Caloric intake directly affects a group’s health, which the model measures through changes in Body Mass Index (BMI). For each percentile group, the model calculates the energy deficit based on their caloric intake relative to their energy needs (previous BMI). This deficit is then used to adjust each group's BMI, and estimate excess mortality using the methods described in the previous post.
5. Adjusting Population Figures
At the end of each month, the model updates population figures to reflect births, deaths, migration, and the excess mortality impacts calculated earlier. All but the latter population changes are evenly distributed across the percentile groups.
Results
The following results are illustrative, not definitive, as the focus is clarifying the method, and providing a perspective on the outputs that can generate predictions that are roughly similar to those of the Clingendael Report. Roughly speaking BMI levels become critical for the poorest percentiles in June 2024 and spread to 20-25% of the population by the end of September 2024. This appears to be notably higher than what the IPC reported in their 27 June report, that roughly 18% of the population were in “Emergency” (Phase 4) conditions at that time.2 But we will return to the analysis in a future post where we can go into greater depth.
Next steps
Now that the basic foundations of the model have been laid out, we can begin exploring how variations in the model’s inputs affect its predictions. This investigation will help pinpoint where to allocate effort to reduce uncertainty and ensure comprehensive risk mitigation. For each input, we can define a range or distribution of plausible variation, then do uncertainty quantification (how much uncertainty results), and sensitivity analysis (too see which inputs are most responsible for variations in the output). This process will not only deepen our understanding of the model but also provide guidance on where to focus efforts to minimize uncertainty. Finally, future analysis will also situation this model with respect to alternative methodologies for identifying famine based on price and other indicators.
Appropriately constructed, the area under each curve is the same, it is the amount of the total consumption for that period, if population of each percentile is equal.
The IPC documentation that I found that discusses the relationship between the IPC Stages and BMI suggests that the Phase 4 corresponds to 20-39.9% of the population having a BMI of less than 18.5. As I understand it, this means that within certain geographic regions the corresponding percentages are below BMI 18.5. If so, then a very rough estimate of the population with sub-18.5 BMI would be:
(755,000 in stage 5) * (“> 40 %”, so say 0.5) = 377,500
(8.5M in stage 4) * (“20-39.9%”, so say 0.3) = 2.55M
So the total with BMI< 18.5 would be roughly 2,927,500, which is far lower than the model predicts. A maximum estimate would be 755k*1.0 + 8.5M*39.9= 4.7M. Source: IPC Guidance Note on Indicators, p.30.