Quantitative comparison of vaccination policies.

<p>A uniform vaccination policy is compared with one that targets only the transhumance herds and one that only targets the sedentary herds. At low resource levels, the vaccination policy targeted to the transhumance herds outperforms the uniform one, while the uniform policy becomes more effective at higher resource levels. Both outperform sedentary-herd vaccination.</p

Simulation of nominal spread model from an initial infection in a sedentary herd.

<p>The nominal model for brucellosis spread is again simulated for the 20-herd example, without control, but the disease is initiated in a small and sedentary herd (herd 20). The disease again becomes prevalent, but the spread is much slower. Interestingly, brucellosis becomes more prevalent in the large nomadic herds than the small or sedentary ones even though the infection was initiated in a small sedentary herd. This model characteristic matches with field measurements for brucellosis prevalence in pastoralist communities, e.g. in the Tigray region of Ethiopia <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001259#pntd.0001259-Berhe1" target="_blank">[17]</a>.</p

Simulation of nominal spread model from an initial infection in a transhumance herd.

<p>Brucellosis among herds of cattle is simulated in a non-intensive agricultural system, in the nominal case that controls are not used. In this small example, a network of transhumance herds (shown as circles) and stationary herds (shown as squares) are considered, with varying herd sizes but otherwise comparable intra-herd transmission conditions. Tranhumance herds commingle with other transhumance and sedentary herds, as indicated by the spread graph (which is overlayed on the dynamics). In this example, the possibility for and frequency of spread between herds is specified based on a distance measure between the herds, although other models can be used alternatively. The simulation is initiated with a small number of infected cattle in the largest transhumance herd (Herd 1). The dynamics of the spread with time is shown (with the time axis representing months), with the extent of infection in each herd indicated by the intensity of the red color for that herd. As expected, since the basic reproductive number for the spread is greater than , the infection becomes widespread quickly.</p

Comparison of animal-level and animal-to-human controls.

<p>The subdivision of resources between animal-level control policies and animal-to-human control policies is examined, in the -herd example. In particular, assuming a particular relative cost of human infection vs. animal infection (per individual), the optimal division of resources between ainimal surveillance/control and pasteurization is determined. This resource allocation is plotted against the relative cost. If human illness costs are higher, additional resource allocation in pasteurization is beneficial, but the bulk of resources should still be allocated to animal control.</p

Model identification from snapshot data.

<p>Using a heuristic method, a nonlinear SIR model for brucellosis transmission within a herd has been developed, using snapshot herd-size and seroprevalence data from several West-African countries as well as from the Jackson Bison Herd (JBH). The ability of the model to predict seroprevalence vs. herd size is shown <i>(top)</i>. Also, for two non-intensive farming districts in Guinea which have similar herd sizes, the amount of inter-herd interaction and hence the comparative rate of outside-herd infection can roughly be guessed, from a description of the prevalent agricultural practices. The model is shown to provide a better indication of prevalence, once this variation is accounted for <i>(bottom)</i>.</p

Robustness.

<p>Given the very limited and uncertain data available for model parameterization, the robustness of the model to parameter variations is of importance. As a first step in this direction, we have studied the ability of the model to predict single-herd brucellosis prevalence, when there is up to error in each identified model parameter. The above plot shows that the model remains accurate in predicting single-herd brucellosis prevalences despite such variability.</p

Designing an optimal vaccination policy.

<p>In the upper plot, The basic reproductive number when the optimal vaccination policy is used is shown, for the twenty-herd example. Here, the three light, solid lines indicate the performance of the only-transhumance, only-sedentary, and uniform vaccination policies as developed in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001259#pntd-0001259-g004" target="_blank">Figure 4</a>. The performance of the optimal resource allocation is highlighted as a bold, dashed line. Also, the fraction of resources allocated to the sedentary herds at the optimum is shown.</p

Model identification from time-course data.

<p>An SIR model for brucellosis transmission is identified, based on time-course data from the Jackson bison herd upon initiation of a vaccination program. This simple model is not as accurate as the multi-state model described in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0001259#pntd.0001259-Peterson1" target="_blank">[31]</a>, but is sufficient for the broad policy-design efforts undertaken in this research.</p

Basic reproductive ratio for optimal design.

<p>The basic reproductive number for the optimal surveillance/control policy is shown as a function of the resource level, for the twenty-herd example.</p

Analysis of a surveillance and control policy.

<p>Improvement of brucellosis surveillance procedures so as to permit fast/cheap distributed surveillance and culling is an important policy goal. The model permits computation of infection costs as a function of the surveillance and culling rate, and hence indicates the cost benefit of improving surveillance/culling techniques.</p