System dynamics models have been used extensively in biological research exploring human physiology, nutrition, and metabolism [19, 20], including the relationship of energy balance to body weight, composition, and mortality [21,22,23,24,25,26,27], blood glucose and insulin kinetics [28,29,30,31], the effect of gut contents on satiety [32], the effect of zinc on body growth in infants [33], the effects of pathogens on digestion [34], and the interactions between malnutrition and hypothermia [35]. In this section we review potentially relevant physiology models and discuss their applicability to predict acute malnutrition and associated mortality outcomes during famines.

While there are abundant systems models related to energy balance for obesity, weight loss, and athletics, there are relatively few models on energy balance in starvation or severe acute malnutrition. We focus here on a small number of systems models explicitly addressing energy balance in long-term starvation [26, 27, 36], alongside several more general systems models of energy balance or metabolic flexibility that may be relevant for famine systems [22,23,24,25, 30, 31].

Although the simplest model for energy balance can be expressed as a single ‘stock’ for the amount of energy stored (Fig. 1a), correctly modeling relevant metabolic processes requires understanding the conversion of energy stores from different chemical forms in the body (sugars, fats, and proteins), the location of those stores (in adipose tissue, muscles, organs, etc.), the multiple demands for energy within the body, and variation in the rate of energy expenditure change over time. Models vary in both detail and conditions considered by the model, as well as their purpose. Caloin’s [36] model simulates depletion of fat and protein energy stores during zero caloric intake as a function of adiposity and daily metabolic demand specified by the user. Song and Thomas [26] model depletion of fat, protein, and ketones to estimate maximum survival time with no caloric input, assuming only basal metabolic requirements. In a model intended to test the ‘thrifty gene’ hypothesis for obesity, Speakman and Westerterp [27] similarly track fat, protein, and glycogen, while defining a generic trajectory for increasing and decreasing physical activity depending on phase of starvation. Hall’s models [21, 22] do not focus specifically on starvation, but are the most physiologically comprehensive that we have seen, accounting not only for partitioning of fuel sources in the body, but also the macronutrient composition of the diet, and some other physiological variables.

Stocks and flows diagrams for basic energy balance and energy conversions within the body. Rectangles represent ‘stocks’ or forms in which the energy may be stored. The arrows annotated with circles and triangles represent the ‘flows’ or rates at which energy moves or is converted between forms. The cloud images indicate sources and destinations outside of the system (details that are not modeled explicitly). a) The most basic model of energy storage in the body states that the change in energy stored over a period of time is equal to the amount of energy consumed minus the energy expended in that time interval. b) The main stocks of energy in the body are blood glucose (rapidly depleted, and therefore not shown), fat, glycogen, and protein (diagram adapted from Hall [23]). The relative importance of flows between these stocks changes as reserves are depleted when the body starves

All of these models are based on well-established scientific understanding of energy stores in the body. The body’s most readily available energy source is glucose circulating in the bloodstream, but this is a relatively small pool of energy at any moment in time. In healthy bodies, glucose is depleted or converted to other chemical forms within hours, after which the body shifts to other energy sources [26, 27]. Because blood sugar levels can fluctuate rapidly and the body seeks to maintain homeostasis through multiple mechanisms, systems models of long-term starvation typically disregard glucose as a stock of energy in the body, focusing instead on energy stored as fat, glycogen, and protein [21,22,23, 26, 27]. Figure 1b—adapted from Hall’s review of models for energy balance and metabolic regulation in humans [23]—diagrams the key stocks and flows used in this framework.

Although these energy storage tissues are central to the mechanisms of energy balance, it is generally not practical to measure them directly outside of a lab setting. Instead, total body weight is measured, and measurements such as upper arm circumference are used as a proxy to estimate body mass [37, 38], and skinfold thickness may be used to estimate fat mass [39]. Mathematical conversions are required to translate energy storage pools into these real-world measurements. The energy density of fat, sugars, and proteins allows conversion between the caloric energy stored and the masses of these molecules. Lean body weight includes both extracellular water (which can vary significantly over short periods) and skeletal mass (which is typically assumed to be constant). Simpler models may assume constant extracellular water, or water as a constant percentage of tissue mass, depending on the type of tissue [26, 27]. A more sophisticated framework, such as Hall’s model for human energy balance, weight gain, and metabolic adaptation can track extracellular water as a separate stock, including the role of sodium concentration in water retention [22]. Hall’s initial 2006 model, which described energy metabolism during semi-starvation and refeeding, did not model changes in extracellular water, but incorporated laboratory data on extracellular water of semi-starved volunteers in a classic starvation experiment conducted in Minnesota in the 1940s to evaluate model predictions against real-world data from that experiment [21, 40]. Unlike the human starvation model by Song and Thomas, the two energy balance models by Hall explicitly include stocks of nitrogen in the body (in the form of amino acids), including the role of physical activity in maintaining lean body mass (preventing muscle wasting), a consideration omitted from many other models [21, 22, 26].

The suitability of models for understanding famine conditions depends on the scenarios they are designed for and simplifying assumptions made. Models of total starvation (zero caloric intake)—which have been used to estimate the maximum survival time as a function of starting body composition when no food is provided [26, 27, 36]—are useful for scientific understanding, but are unlikely to reflect real-world famine conditions, in which some limited food is almost always available. Models of partial starvation, such as Hall presents, may therefore be more suitable [21, 22]. Another factor is the realism of assumptions about energy expenditure. For instance, Song and Thomas focus only on the basal metabolic energy needed to maintain body function, assuming no energy needs for physical activity or thermoregulation, whereas Speakman and Westerterp assume physiologically adaptive changes in activity levels [26, 27].

Finally, it should be noted that almost all models are based on data from lab-based studies on adult volunteers, most of them are healthy or have the same health issues within a model. Few models consider energy balance in growing children. One exception is the human growth model by Rahmandad, which calculates food energy needs from birth to old age and simulates the long-term effects of malnutrition on child height [25].

While system dynamics models can provide unique insights into how changes in one factor affect other factors and pathways to a given outcome, their construction depends on access to large volumes of raw historic data. During a famine, agencies primarily collect data for operational needs, like the design of interventions. Nevertheless, this data has enormous scientific value, including in the development of models, which may change the course of future famines. Unfortunately, raw data are rarely shared outside of the organizations collecting the data. The lack of robust reference data is a major challenge in model development.

Overall, existing models of energy balance tend to focus on caloric or micronutrient deficiency in isolation, whereas causes of death in real-world famines are much more complicated.