Figure 1.
Schematics of (a) the neoclassical growth model, and (b) the SIS epidemic model demonstrate basic similarities in their structure.
In the neoclassical growth model (c), the blue line represents capital accumulation and the red line represents capital depreciation. The steady state level of capital occurs where these curves intersect. In the typical epidemic model (d), the green line represents transmission (i.e., the force of infection) and the pink line represents recovery. The steady state prevalence of disease is where these curves intersect.
Figure 2.
(a–c) are examples of nonlinear production functions extracted from the economics literature [2].
The x-axis is the stock of capital. The blue line represents the rate of capital accumulation (i.e., savings) and the red line represents that rate of capital depreciation. Income (generated from capital) will necessarily fall when the red line is above the blue line, and will rise when the reverse is true. (c) is the canonical depiction of a poverty trap, but (a–c) all have stable equilibria in the basin of attraction of a poverty trap, and unstable equilibria that represent a critical threshold of capital necessary for growth. These models are speculative, based on hypothetical scenarios, but are useful for demonstrating a range of theoretical possibilities. The scientific community should contribute to our understanding of how such nonlinearities might emerge from, or be nested within, real world biophysical systems.
Figure 3.
Multiple infections cause the appearance and expansion of the basin of attraction of poverty traps.
For graphs (a) and (b) (dashed blue line) and
(solid dark green line). Graph (b) is a magnified version of the initial portion of graph (a), while graph (c) is a magnified version of the initial portion of graph (b) showing a stable positive poverty trap. The filled circles denote stable equilibria while the open circle denotes an unstable equilibrium. Graph (e) is a magnified version of the initial portion of graph (d), while graph (f) is a magnified version of the initial portion of graph (e). Each curve in graphs (d–f) represents the structure of capital accumulation for different numbers of pathogens.
Figure 4.
Disease and food systems exhibit bistability.
Phase plots of (a) human capital against disease prevalence, (b) capital against plant density, and (c) human capital against nutrition showing two stable equilibria (solid circles), and one unstable equilibrium (open circle) in between. Sample trajectories that converge to the good equilibrium (solid blue circle) are denoted by blue lines, while sample trajectories that converge to the bad equilibrium (solid red circle) are denoted by red lines.