Bayesian optimisation of restriction zones for bluetongue control

Abstract

We investigate the restriction of animal movements as a method to control the spread of bluetongue, an infectious disease of livestock that is becoming increasingly prevalent due to the onset of climate change. We derive control policies for the UK that minimise the number of infected farms during an outbreak using Bayesian optimisation and a simulation-based model of BT. Two cases are presented: first, where the region of introduction is randomly selected from England and Wales to find a generalised strategy. This "national" model is shown to be just as effective at subduing the spread of bluetongue as the current strategy of the UK government. Our proposed controls are simpler to implement, affect fewer farms in the process and, in so doing, minimise the potential economic implications. Second, we consider policies that are tailored to the specific region in which the first infection was detected. Seven different regions in the UK were explored and improvements in efficiency from the use of specialised policies presented. As a consequence of the increasing temperatures associated with climate change, efficient control measures for vector-borne diseases such as this are expected to become increasingly important. Our work demonstrates the potential value of using Bayesian optimisation in developing cost-effective disease management strategies.

Figure 1

Maps showing the dispersion of infections across England and Wales at the peak of each spread (27 October—day 300) during a simulation starting with an infection of a single animal on May 1st. For each policy, the simulation was initiated with the infection of the same farm in Somerset and the same set of parameters governing disease propagation. Each point represents a single farm where the colour indicates the following states: black—susceptible; green—exposed; red—infected; blue–infected and detected. Susceptible farms within restriction zones are shaded with increasingly lighter greys as the occupying area transitions from outer to inner zones; or equivalently, from lower to higher risk.

Figure 2

Surrogate regression models generated by the Bayesian optimisation routine after 100 iterations of sampling the simulator. The x/y axes refer to the radii of the control and protection zones, respectively. The z-axis gives the (standardised) expected number of infected farms, $\mathbb{E}\left[J^{\text{NI}}\right]$, for the associated combination of $r_{\text{CZ}}$ and $r_{\text{PZ}}$ according to the Gaussian process regression model. The scale of these values is given on the right of each diagram; note that the values are standardised due to the dataset transformation specified in “Our model” section. Simulations were performed using movement and temperature data from 2013.

Figure 3

Time series evolution of the median of two metrics over 250 Monte Carlo samples. Each simulation was evaluated in Dyfed with movement data from 2013 and temperature data from 2014; the policy was trained on both movement and temperature data from 2013. Three policies are illustrated: government with (MIZ) and without (NMIZ) movement in the innermost zone, and the $J^{\text{NI}}$-optimised policy. Uncertainties are given by the 95% confidence interval of the median from bootstrapping.

Figure 4

Economic cost of three different policies in Dyfed using movement data from 2013 and temperature data from 2014: government with movement (MIZ) and no movement (NMIZ) in the control zone, and an OPT policy trained on only 2013 data. The cost weights were set to $w_0=100,w_1=5,w_{\{2,3\}}=1$, and uncertainties given by the 95% confidence interval of the median from bootstrapping (darker shaded regions) and the interquartile range (lighter shaded regions).

Figure 5

Regression plot between the density of farms within 100 km of the centre of each region and the estimated economic cost for the government (NMIZ) and derived policies. Evaluation was performed on movement data from 2013, and temperature data from both 2013 and 2014. The one OPT policy was trained on 2013 data only. Error bands are derived from bootstrapping and form the 95% confidence interval on the regression.