Modelled vaccination strategies.

<p> All campaigns were annual unless specified in the analyses.</p

Model description.

<p>(A) Secondary cases are drawn from the (i) offspring distribution, and become infectious at a date drawn from the (ii) generation interval distribution: here four secondary cases are generated by the index case (black dot) which become infectious on day 14, 21, 23, and 35. The occurrence of secondary cases depends on vaccination coverage in the grid cell at the time of transmission. (iii) With probability 1–<i>p</i> each offspring occurs at a location generated from the local dispersal kernel (solid black arrows). (iv) With probability <i>p</i>, each offspring occurs on any randomly chosen grid cell (broken black arrow). It took 2.2 years for rabies to be detected in all nine Regencies (grey band), consistent with <i>p</i> = 0.05–0.09 (black dots are medians with 95% PIs from 100 simulations). See <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-t001" target="_blank">Table 1</a> for parameterization of distributions. (v) Human rabies deaths versus confirmed dog rabies cases, showing the best-fit relationship (black line, see <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#s3" target="_blank">Results</a> for equation) and 95% confidence intervals (grey area). (B) 95% PI envelope of simulated cases (grey area) with annual campaigns of the ‘random’ mass vaccination strategy (green line, <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-t002" target="_blank">Table 2</a>), which is rolled out when cumulative cases reach 7,000 and from which point the time to eradication is measured.</p

Key epidemiological and operational variables determining the success of rabies vaccination programmes in terms of the predicted probability of eradication (grey y–axis and line) and time to eradication (black y–axis, medians and 95% PI), showing sensitivity to: (A) the basic reproductive number, <i>R</i>₀, (B) vaccination coverage (achieved at the time and location of the campaign (see Fig. 4)), (C) annual dog population turnover, with conversion into birth/death rate assuming constant population size (birth rates equal to death rates), and (D) duration of immunity provided by vaccine.

<p>Based on 1000 simulations generated using parameters in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-t001" target="_blank">Table 1</a> (unless specified) and annual campaigns of the ‘random’ mass vaccination strategy (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-t002" target="_blank">Table 2</a>).</p

Vaccination strategies.

<p>The probability of eradication following: (Ai) 1; (Aii) 2; (Aiii) 3 campaigns under a range of coverages (40, 60, 80%) and inter–campaign intervals (0, 6, 12 months); (Aiv) vaccination as implemented on Bali, and projected from January 2012 when rabies was still circulating. The time to eradication (medians with 95% PI) for a range of: (B) frequencies of human–mediated transport of dogs (<i>p</i> = 0, 0.02 or 0.05) and campaign strategies (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-t002" target="_blank">Table 2</a>). 95% PI of the one-month ‘sync’ strategy is highlighted (grey band) for comparison with the six–month strategies; (C) coverages when campaigns last 1 month or 6 months. (D) The probability of eradication with % island area left unvaccinated, made up of either randomly chosen 1 km squares (solid lines) or randomly chosen blocks, and when human-mediated movement of dogs was either infrequent (<i>p</i> = 0.02, grey) or frequent (<i>p</i> = 0.05, black).</p

Parameters values and distributions used to model rabid dog movement and transmission processes.

<p>Parameters values and distributions used to model rabid dog movement and transmission processes.</p

Rabies incidence and spread in Bali prior to island-wide mass vaccination.

<p>(A) Cases in humans and dogs and corresponding control efforts. (B) The month that rabies was first confirmed in each village. The black dot marks the village where the index case occurred. Regencies are outlined in black.</p

Trajectories of vaccination coverage achieved at the island-wide level during modeled vaccination campaigns and in relation to levels of coverage required for herd immunity.

<p>Three types of coverage are referred to in the text: target coverage achieved in the subset of the population at the time and location of a local campaign (i.e. within a block); island-wide vaccination coverage (y-axis); and critical vaccination coverage (<i>P_crit</i>) which is required for herd immunity and is determined by <i>R</i>₀, the basic reproductive number of rabies in Bali, <i>P_crit</i> = 1-(1/<i>R</i>₀). <i>R</i>₀ estimated for Bali is 1·2, which corresponds to a <i>P_crit</i> of 17% (grey solid line). A 40% coverage campaign resulted in a trajectory that stayed above 17% (black solid line) and the probability of eradication was 1 (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-g003" target="_blank">Fig. 3B</a>), whereas 30% coverage resulted in a trajectory that dipped below 17% (black dashed line) and the probability of eradication was less than 1 (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-g003" target="_blank">Fig. 3B</a>). Annual campaigns were modeled, using parameters in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-t001" target="_blank">Table 1</a> and the ‘random’ six-month strategy (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-t002" target="_blank">Table 2</a>). Blocks are assumed to be vaccinated at the end of the month hence coverage increments jaggedly. Coverage declines between vaccinations due to waning of immunity and dog population turnover.</p

The vaccination campaigns on Bali and prospects for rabies eradication.

<p>Observed confirmed dog cases up to December 2011 (solid red line) overlay model confirmed cases (grey area, shaded according to confidence level) simulated from estimated vaccination coverage in the Bali dog population (solid blue line) and assuming 0.07 probability of confirming a case <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd.0002372-Townsend1" target="_blank">[6]</a>. For 3 scenarios, vaccination coverage was projected forward to December 2014 (broken blue lines), and implemented in the model to project upper percentile limits for confirmed cases (broken red lines) and the probability of island-wide eradication (see legend and <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0002372#pntd-0002372-g003" target="_blank">Fig. 3Aiv</a>). The increase in cases in Dec 2011 may have been due to a substantial improvement in surveillance involving follow up of suspected animal bite cases by outbreak investigation teams.</p