Modelling a social-ecological poverty trap due to infectious disease

In an interesting article Poverty trap formed by the ecology of infectious diseases (Proc Royal Soc B 2009) Mathew Bonds and others, describes how they couple a simple infectious disease model with an simple economic development model to produce model of a infectious disease induced poverty trap.  They write:

The combined causal effects of health on poverty and poverty on health implies a positive feedback system. Despite the importance of understanding such critical and systematic ecological interactions between humans and their most important natural enemies, and the anecdotal evidence that such poverty traps may indeed exist, we lack mechanistic frameworks of poverty traps that are rooted in the dynamics of disease. Here, we propose such a model. We find that a prototypical host–pathogen system, coupled with simple economic models, induces a poverty trap. More broadly, this model serves to illustrate how feedbacks between people and their environment can potentially give rise to major differences in human survival and economic welfare (Diamond 1997).

… we illustrate our underlying concept using a general one-disease SIS (susceptible–infected–susceptible) model, where individuals can be serially reinfected over the course of their lifetime. This model is meant to serve as the simplest general way of representing the kind of repeated threats of infection faced by poor tropical communities. More specifically, the general model also resembles a typical malaria system (Gandon et al. 2001), which has high prevalence rates among the poor and has been especially implicated in hindering economic growth (Gallup & Sachs 2001).

Their model produces two alternative regimes, a high productivity/low disease regime and a low productivity/high disease regime.

Feedback between economics and the ecology of infectious diseases forms a poverty trap. The prevalence of infectious diseases, I*(M) (black line), falls as per capita income rises, while per capita income, M*(I) (grey line), falls as disease prevalence, I, rises. The disease and income functions are in equilibrium where these two curves intersect at (I*(M*), M*(I*)). Two of these equilibria (I*(M*1), M*(I*1) and I*(M*3), M*(I*3)) are stable, and one (I*(M*2), M*(I*2)) is unstable. The poverty trap is the basin of attraction around (I*(M*3), M*(I*3)). α = 0.06; β̄ = 40; μ̄ = 0.01; ν = 0.02; h̄ = 90; δ = 5; ϱ = 0.003; τ = 0.15; ϕ = 15; κ = 30.

Feedback between economics and the ecology of infectious diseases forms a poverty trap. The prevalence of infectious diseases, I*(M) (black line), falls as per capita income rises, while per capita income, M*(I) (grey line), falls as disease prevalence, I, rises. The disease and income functions are in equilibrium where these two curves intersect at (I*(M*), M*(I*)). Two of these equilibria (I*(M*1), M*(I*1) and I*(M*3), M*(I*3)) are stable, and one (I*(M*2), M*(I*2)) is unstable. The poverty trap is the basin of attraction around (I*(M*3), M*(I*3)). α = 0.06; β̄ = 40; μ̄ = 0.01; ν = 0.02; h̄ = 90; δ = 5; ϱ = 0.003; τ = 0.15; ϕ = 15; κ = 30.

In this model, a social-ecological system can be pushed into or out of the poverty trap by changes that effect labour productivity, such as changes in the level of education or infrastructure, or changes in disease prevalence due to the expansion or contraction of public health.

In the paper the authors show that empirical patterns of disease burden and income suggest the existence of disease poverty traps.

They conclude:

While we hope that our model framework can serve as a useful point of departure for exploring more complex relationships, the theoretical analysis we present here has significant implications: simply coupling economics with a well-established model of the ecology of infectious diseases can imply radically different levels of health and economic welfare (i.e. poverty traps) depending on initial conditions. The practical implications are also significant. Because the world’s leading killers of the poor—malaria, HIV/AIDS, tuberculosis, diarrhoea and respiratory infections—are highly preventable and treatable, current global efforts to improve public health in areas of extreme poverty could theoretically pay long-term economic dividends. Furthermore, this analysis underscores that there are dramatic implications if economic activity is coupled with ecological processes that are well-known to behave in nonlinear ways.

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