Ecosocial consequences and policy implications of disease management in East African agropastoral systems

An East African Grassland System

The flow of energy in an East African grassland/wild herbivore/predator system including the biological analog of consumption in each trophic level is illustrated in Fig. 1 A. These grasslands have largely been converted to agropastoral systems with cattle becoming the dominant herbivore and pastoralists assuming the top position in the food chain with animal trypanosomiasis (tryp) being a major constraint in many areas (Fig. 1 B) (20). An example of such an agropastoral system is the Gurage ethnic agropastoral community at Luke in the sparsely fertile and semimountain region of southwest Ethiopia (21, 22). In 1995, the Luke villagers initiated a program to reduce the prevalence of trypanosomiasis by treating infected cattle with trypanocidal drugs and by suppressing populations of the tsetse fly vector using odor baited traps. Ecosocial data on the project were also collected and analyzed (22, 23). Tick-borne diseases (tbd) in cattle and malaria in human, among others, are of concern in this area as are the changing patterns of land allocation to agriculture, declining soil fertility, the vagaries of environmental variables (Fig. 2).

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Fig. 1.

Two East African grasslands systems. (A) A natural system. (B) An agropastoral system with disease constraints. The dashed line in B indicates that only part of the waste is recycled back to the soil, and the symbol $ indicates the conversion of the mass/energy flow into monetary units (see ref. 20).

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Fig. 2.

A holistic view of a hypothesized closed East African agropastoral systems showing disease constraints (shaded area), land allocation, and weather and edaphic variables.

Ecological and bioeconomic models are used to analyze the effects of multiple disease constraints on this system. To simplify the analysis, the system as in other previous studies on ecosocial system resilience is assumed closed and of fixed scale (11). The models are first described and then applied to the agropastoral system.

Physiologically Based Demographic Ecosystem Models (EMs)

Mass (energy) flow in a consumer-resource population dynamics model (Eq. 1) describes the dynamic inflows and outflows in any trophic levels (Fig. 1) by using the same functions across trophic levels including the economic one (12, 13). Multiplication by a constant converts mass to number of individuals or monetary units in human economies (Fig. 1 B).

Using the notation from ref. 17, let M _i (i = 1,2,…,n) denote the mass of the ith trophic level in a food chain with the dynamics of any trophic level governed by the following equation of motion:

The components of the model are as follows: D _i is the maximum per-unit biomass demand of the ith trophic level for resource trophic level i − 1, and may be viewed as the sum of the maximum outflows for each species including consumption (C); \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} $$h({u}_{i})=(1-exp(\frac{-{\alpha }_{i}{M}_{i-1}}{{D}_{i}{M}_{i}}))$$ \end{document} is the proportions of the per unit demand D _i satisfied by search with D _i h(u _i) being resource acquisition per unit biomass by trophic level i from level i − 1 (i.e. the supply), and 0 ≤ h(u _i) < 1 equals the supply–demand ratio; α_i is the proportion of level i − 1 accessible to the ith level, and 1 − α_i is the size of the refuge of the resource; θ_i is the conversion rate of resource and includes wastage; v _i(D _i) = v _i D _i is the cost rate per unit of consumer as a function of the demand rate. In a time varying environment, v for poikilotherms increases with temperature (i.e. the Q ₁₀ rule), and has special importance in the context of studies on the effects of climate warming (16).

The function D _i h(u _i) is a ratio-dependent concave per-unit functional response model that includes interspecific competition in the exponent and the possibility of utilizing several resource species each having different α s and consumer preferences. The term D _i M _i is the maximum population demand, and D _i M _i h(u _i) ≤ α_i M _i−1 is the rate of resource depletion by the ith level, where α_i ≤ 1 sets the limits on the extraction by level i from resource level i − 1. If α_i is sufficiently small compared with the assimilation efficiency of the lower level [α_i ≤θ_i−1 D _i−1 − v _i−1(D _i−1)], then the lower tropic level will survive any population size and demand rate of its consumer. The model (Eq. 1) has been used to study resource allocation dynamics at the individual, population, metapopulation and regional levels (14).

The model is used to describe the dynamics of the East African pastoral system where M ₁ is pasture biomass, M ₂ is cattle biomass, and M ₃ is the pastoralists (Eq. 2)

Survivorship terms for trypanosomiasis (S _tryp) and tick-borne diseases (S _tbd) in cattle and malaria in pastoralists (S _malaria) are included as constants indicating the level of disease pressure (i.e., 0–1) due to the combined effects of morbidity and mortality. For specific field application, the density-dependent effects of each disease can be estimated from field data as k value functions (24), and the other parameters of the model can be estimated from field and/or laboratory data. This enables the model to be used to analyze changes in various agropastoral regions by using weather and the dynamics of soil nutrients and water as forcing variables (12 –14). Below, we analyze the general stability properties of natural and managed East African grasslands to assess the ecological consequences of human interventions.

Analysis of a Natural Grassland/Wild Herbivore/Predator System

Wildlife is tolerant of trypanosomiasis (S _tryp ≈ 1) but may carry high levels of infection (20) (Fig. 1 A). The shapes of the zero isoclines and the equilibrium properties of Eq. 2 depend on the value of the apparency rate (α_i+1) of the renewable resource to the consumer relative to the maximum per-capita growth rate of the resource (θ_i D _i) (13). The inequalities for the natural grassland system are α₂ < θ₁ D ₁ and α₃ < θ₂ D ₂ yielding the zero isoclines for levels M ₁ and M ₂ depicted in Fig. 3 A. The direction of the inequality α₂ < θ₁ D ₁ is due to the high per-unit biomass growth rate of grass relative to the ability of wild herbivores to consume it. Similarly, the biomass growth rate of herbivorous wildlife is high relative to the predation pressure (i.e., α₃ < θ₂ D ₂) yielding the zero isoclines in the (M ₂,M ₃) phase plane (Fig. 3 B). The resource species have a maximum population at (θ_i D _i)/v _i and cannot be driven below the vertical asymptotes at (θ_i D _i − α_i+1)/v _i. Stable equilibrium (·) occur in both the (M ₁,M ₂) and (M ₂,M ₃) phase planes.

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Fig. 3.

Isoclines for an East African grassland (M ₁), herbivore (M ₂), and predator (M ₃) system. (A) The grassland, herbivore phase plane. (B) The herbivore, predator phase plane, and a pasture/cattle/pastoralist system under trypanosomiasis (tryp) pressure. (C) The pasture, cattle phase plane with (+tryp) and without (w/o tryp) trypanosomiasis. (D) The cattle, pastoralist phase plane. • indicates stable equilibrium, and ○ indicates an unstable one, and the dotted arrow in C indicates a decline in soil fertility.

Analysis of a Managed Grassland/Cattle/Agropastoralist System

In contrast to natural systems, trypanosomiasis pressure in agropastoral systems (+tryp) is high, and cattle are susceptible resulting in a low value for S _tryp → 0. When healthy, cattle have an efficient search behavior and a larger per-capita demand rate than wild herbivores (i.e. α₂ > θ₁ D ₁), and hence the shape of the isoclines for the pasture (M ₁) is humped (Fig. 3 C) (15) as proposed by Noy-Meir (25). Pastoralists view herd size as a measure of wealth, and as insurance during periods of drought or high incidence of disease, and hence prefer not to consume or sell them (26). For this reason, the shape of the M ₂ isoclines (Fig. 3 C) is sigmoid as in Fig. 3 A (e.g., α₃ < θ₂ D ₂).

Under high trypanosomiasis pressure (S _tryp → 0; +tryp), cattle density (M ₂) is low (>(θ₂ D ₂ − α₃)/v ₂) (Fig. 3 D), and pasture level (M ₁) is high, yielding a stable equilibrium at point A(·, Fig. 3 C). However, suppression of tsetse/trypanosomiasis drives S _tryp → 1 and allows cattle populations to increase resulting in an unstable equilibrium (∘) that leads to overgrazing and the depletion of soil nutrients. This causes the M ₁ isocline to contract leftward (dotted arrow, Fig. 3 C) resulting in a new stable equilibrium at low M ₁ and M ₂ (point B, ·, Fig. 3 C). This is a demonstration of exceeding resilience capacity that takes the system to a new but unfavourable stable point (6).

Viewing the isoclines in the (M ₂,M ₃) phase plane shows that trypanosomiasis suppression causes a rightward shift in the M ₂ isocline that affects the level but not the shape of the M ₃ isocline (Fig. 3 D). However, overgrazing causes a reversal or leftward shift in the M ₂ isocline in the (M ₂,M ₃) phase plane that could be as extreme as the effects of high trypanosomiasis pressure (Fig. 3 D) suggesting that solving the trypanosomiasis problem may lead an overgrazing problem. The ecosocial consequences of trypanosomiasis suppression were examined by ref. 26 and are reviewed and expanded below by using the bioeconomic model.

Bioeconomic Model of Managed Grassland/Cattle/Agropastoralist Systems

For clarity, Eq. 2 is simplified to represent the dynamics of M ₂ and M ₃ given a constant amount of forage M ₁ (Eqs. 3 and 4) (see ref. 17): where G(M ₁,M ₂) = M ₂ D ₂ h(u ₂) is the quantity of M ₁ eaten by cattle, F(M ₂,M ₃) = M ₃ D ₃ h(u ₃) is the flux of M ₂ harvested by pastoralists (M ₃), and v ₂(D ₂)M ₂ and v ₃(D ₃)M ₃ are the respiration rates. The functions G(·) and F(·) satisfies the necessary concavity and positive marginal productivity conditions of economic models because both increase with resource levels and decrease with intraspecific competition among consumers [i.e., the exponent −α_i M _i−1/D _i M _i in h(u _i), (Eq. 1)] (13). This biology in reduced form is included in the bioeconomic objective function (Eq. 5).

Bioeconomic Objective Function

In economics, the objective function for resource exploitation by all individuals of M ₃ seeks to maximize the present value utility of individual consumption (C) from the revenue (energy) stream and is expressed as: subject to the dynamics constraints of the managed resource M ₂ (Eq. 3) and the pastoralists M ₃ (Eq. 4), e ^−δ_trypt is the discount factor reflecting the level of risk of trypanosomiasis, t is time, and the per-capita demand (D) and consumption (C) rates are control variables (17). C is included in the model via the monotonically increasing concave utility function of individuals U(C) that has properties U′(C) > 0, U″(C) < 0 and U′(C) → 0 as C → ∞.

By Pontryagin's maximization principle, the maximization of Eq. 5 by all consumers M ₃ subject to population dynamics constraints (Eqs. 3 and 4) is equivalent to the maximization of the current value Hamiltonian (Eq. 6) (17, 27): where λ₁ and λ₂ are costate or auxiliary variables associated with the dynamic constraints. In particular, λ₁ is the Lagrange multiplier that represents the marginal utility of income from harvesting M ₂. The necessary conditions for an optimal solution of Eq. 6 are satisfied, C*(δ) is an increasing function of δ, and because Ṁ₂do not depend on M ₃ and λ₁ ≤ U′(C*)(θ−v), this allows the analyses to be restricted to [0,U′(C*)(θ−v)] × [0,∞] in the (λ₁,M ₂) phase space. The extensive mathematical analysis is outlined in ref. 17 and is not reproduced here.

Two solutions arise: The optimal societal solution for resource exploitation by all pastoralists maximizes the present value utility of individuals expending from the revenue stream in ways that do not contribute to growth (consumption) and yet assures the persistence of the renewable resource over an infinite time horizon (i.e., renewable resource sustainability), and the competitive solution results where pastoralists pursue self-interest goals with λ₁ → 0 as δ → ∞ resulting in overexploitation of the resource.

Bioeconomic Effects of Reducing Trypanosomiasis Risk

Ecosocial Data.

The trypanosomiasis program at Luke, Ethiopia, was initiated in 1995, and by 2005, tsetse populations were very low, and the prevalence of trypanosomiasis fell from 29% to 10% (23, 26). The prevalence of disease would have been lower had infected cattle not been continually introduced from outside the suppression zone and trypanosomiasis not been endemic in wildlife. Cattle numbers including oxen increased 5-fold, calving rates 8.2-fold, milk production 13-fold, per-capita income doubled, and human populations increased 40%. Increases in highly susceptible oxen allowed cultivated land to increase from 12 ha in 1995 to 506 ha in 2005. Increased revenues enabled the building of a school and allowed the villagers to continue the tsetse/trypanosomiasis suppression program. The latter 2 items are measures of economic consumption as well as indicators of the Luke community's readiness to adopt change and reacted to new opportunities. Studies undertaken in Africa under different cultural and ecological conditions have also shown fast economic responses to tsetse control operations (28).

Predictions of the Bioeconomic Model.

The dynamics of the bioeconomic model can be reduced mathematically to the zero isoclines for the shadow prices for cattle (λ₁) and cattle populations (M ₂) at different levels of trypanosomiasis risk (δ_tryp) (see appendix in ref. 17). As observed, the model predicts that a dramatic reduction in risk (δ_tryp → 0) and increased productivity (θ₂) lead to increased cattle (M ₂) and human (M ₃) populations, and to increases in the marginal value (λ₁) of cattle. Some of the dynamics are summarized in the (λ₁,M ₂,θ₂) phase space (Fig. 4) where positive changes in λ₁,M ₂ and θ₂ along the optimal path (point A to B) are measures of increasing economic health. All of the points along the optimal path are saddle points. In contrast, M _2,c on the abscissa and points along the trace from it (λ₁ = 0,M ₂,θ₂) is the path of the competitive solution. Point M _2,e on the abscissa is a hypothetical level where the system collapses (17, 18).

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Fig. 4.

The (λ₁,M ₂) phase plane on increasing θ₂ for an East African agropastoral system (see text).

As δ_tryp decreases from an initial high level (Fig. 4, point A), the optimal trajectory (λ₁ *,M ₂*) increases on θ₂ to the point of maximal societal benefit (point B). However, overgrazing beyond B reduces natural capital (M ₁ and soil fertility) resulting in a reversal of θ₂ with the optimal path of λ₁*,M ₂* (the dashed line) declining in the direction of system collapse (i.e., M _2,e; point C). The rate of change of the optimal trajectory from A to C may be relatively fast, whereas the reversal or remediation from C back to the “maximum optimal societal benefit” at B is slow commensurate with the time required to rebuild soil structure and function. This illustrates the effects of fast and slow variables in the system (5, 7).

If the Luke villagers choose the competitive solution as suggested by their cultural view of herd size as insurance and wealth (29), the path to over exploitation will occur much sooner along the trace from M _2,c (Fig. 4).

Adding Other Disease Constraints

It is difficult to introduce the contribution of other sources of risk into the bioeconomic model and to separate their contribution to total risk (δ_total = δ_tryp + δ_tbd + δ_malaria + ⋯) (18).

It is, however, quite straightforward to analyze the separate effects by using the zero isoclines of the agropastoral system model (Eq. 2), wherein the disease effects are introduced as increased morbidity and mortality of affected hosts.

With reduced trypanosomiasis (w/o tryp) and the associated increases in cattle (M ₂), ticks and tick-borne diseases (+tbd) are expected to increase causing a reversal in cattle density (Fig. 5 A). This suggests that gains from suppression of trypanosomiasis could be lost as the independent effects of tbd are unleashed (Fig. 5 C). In addition, the cost of acaricides to control ticks (i.e., a component of v ₃ in Eq. 2) would cause the M ₃ isocline to shift downward (Fig. 5 B). As with trypanosomiasis, decreases in cattle population resulting from tbd would enhance pasture recovery (dotted line in Fig. 5 A).

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Fig. 5.

The phase plane for combinations of M ₁,M ₂ and M ₃ with (M ₁,M ₂) phase plane without tsetse/trypanosomiasis (tryp) and adding the effects of tick-borne diseases (tbd) (A), (M ₂,M ₃) phase plane adding malaria (B), and a Venn diagram of some competing disease risks in the systems (C).

With human populations increase, the incidence of malaria is expected to increase in the absence of investments in control. The effects of malaria enter the model (Eq. 2) as an increase in morbidity and mortality to pastoralists that lower the M ₃ isocline (Fig. 5 B). The model predicts an unlikely increase in cattle densities (M ₂, Fig. 5 C) only because the negative feedback of malaria to cattle herding and care is not included in the model. Last, the increase in land use for agriculture will come at the expense of grazing land (M ₁) reducing the system's carrying capacity for cattle.

Thus, the consequences of reducing risk from trypanosomiasis will increase risk from other diseases in cattle and humans (Fig. 5 C) that may cancel many of the gains of the tsetse/trypanosomiasis suppression program. On the bleak positive side, heavy disease pressure will cause a reversal, albeit slow, in the decline of pasture quality.