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Targeted pre-emptive rabies vaccination strategies in a susceptible domestic dog population with heterogeneous roaming patterns
Preventive Veterinary Medicine 172 (2019) 104774
Contents lists available at ScienceDirect
Preventive Veterinary Medicine journal homepage: www.elsevier.com/locate/prevetmed
Targeted pre-emptive rabies vaccination strategies in a susceptible domestic dog population with heterogeneous roaming patterns
T
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Emily G. Hudsona, , Victoria J. Brookesa,b, Salome Dürrc, Michael P. Warda a
Sydney School of Veterinary Science, The University of Sydney, Camden, Australia School of Animal and Veterinary Sciences, Charles Sturt University, Wagga Wagga, Australia c Veterinary Public Health Institute, University of Bern, Liebefeld, Switzerland b
A R T I C LE I N FO
A B S T R A C T
Keywords: Canine rabies Free-roaming dogs Rabies spread Pre-emptive vaccination Australia Disease modelling Prevention
Australia is free of canine rabies, however northern regions – such as the Northern Peninsula Area (NPA), Queensland – are at risk of an incursion from nearby rabies-infected Indonesian islands. Early detection and reactive vaccination is the current Australian policy to eradicate an incursion. Early detection in this region is challenging, so pre-emptive vaccination might be an effective strategy. The NPA dog population also has a heterogenous contact structure, with three roaming categories previously characterised, which could be exploited in targeted pre-emptive vaccination strategies for more efficient use of limited resources. To evaluate the effectiveness of a pre-emptive vaccination program, an agent-based rabies spread simulation model was used to simulate outbreaks with a range of pre-emptive vaccination coverages. Increasing proportions (10% increments) of the dog population randomly vaccinated were modelled, and at the most efficient random vaccination coverage we then explored 10 pre-emptive vaccination strategies targeting different dog roaming categories (whilst maintaining the same overall population level vaccination coverage). All pre-emptive vaccination strategies were simulated 2000 times without and with a 70% random reactive vaccination strategy, following rabies detection. All random pre-emptive vaccination coverages reduced outbreak size and duration compared to no pre-emptive vaccination. A 40% random coverage was most efficient. Targeted strategies that pre-emptively vaccinated proportionally more roaming dogs were more effective than a random 40% vaccination coverage and strategies that targeted non-roaming dogs. The pre-emptive vaccination strategies that targeted non-roaming dogs produced significantly larger and longer outbreaks. These results suggest that pre-emptive vaccination can reduce potential rabies outbreaks in this region and that such a strategy should not just focus on easily accessible dogs that do not roam often or at all. A cost-benefit analysis is required to determine whether the implementation of such pre-emptive vaccination strategies is also cost-effective, which is essential in the resourcepoor communities of this region.
1. Introduction Australia is free of canine rabies (WHO, 2013). However, northern Indigenous communities of Australia – such as the Northern Peninsula Area (NPA) – are at risk of canine rabies entry and establishment due to their large populations of unvaccinated free-roaming domestic dogs and their proximity to rabies endemic Indonesian islands (Hudson et al., 2017a). One pathway that has been assessed as high-risk is the illegal transportation of infected dogs from Indonesia to the NPA on fishing boats (Hudson et al., 2017a). Vaccination is the most cost effective and efficient method to prevent, control and eliminate canine rabies (WHO, 2013; Hampson et al., 2015). However, in rabies-free Australia, only legally imported animals are vaccinated (Animal Health Australia,
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2011). Consequently, the NPA dog population is likely entirely susceptible to rabies infection. Currently, Australia relies on early detection and immediate reactive vaccination to prevent and control rabies outbreaks (Animal Health Australia, 2011). Early detection is important for rabies control and potential eradication because it enables timely implementation of control measures, without which rabies could become endemic. Modelling has shown that a low detection probability (and subsequent long detection time) causes longer and larger rabies outbreaks and reduces the probability of rabies elimination within a 2-year period (Townsend et al., 2013). However, there are specific challenges to rabies detection in the NPA that make early detection difficult. For example, rabies awareness in remote Indigenous communities is likely to be very low or
Corresponding author. E-mail address: [email protected] (E.G. Hudson).
https://doi.org/10.1016/j.prevetmed.2019.104774 Received 6 May 2019; Received in revised form 12 September 2019; Accepted 13 September 2019 0167-5877/ © 2019 Elsevier B.V. All rights reserved.
Preventive Veterinary Medicine 172 (2019) 104774
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implemented reactively after detection of rabies; the use of pre-emptive vaccination remains unexplored. Similar to the reactive vaccination strategies, the heterogeneous roaming patterns and subsequent contacts in the NPA dog population could be exploited to develop efficient preemptive vaccination strategies. The objective of this study was to evaluate the benefits of a preemptive vaccination program in terms of predicted rabies outbreak duration and size (number of infected dogs). Roaming behaviours and contact structure were exploited to develop targeted pre-emptive vaccination strategies which were compared to a random vaccination strategy. The results of this study can be used by decision makers to justify further research into the practical feasibility of pre-emptive vaccination programs, including cost-benefit analyses.
non-existent due to the rabies free-status of Australia, and dogs that present with clinical signs of rabies would likely be mistaken by dogowners for other diseases or ignored completely; the first detected case might not be the primary case and rabies could have already infected several other dogs. Also, there are no veterinary or diagnostic facilities in the NPA to confirm a rabies diagnosis, which could further delay a definitive detection (Hudson et al., 2016). Therefore, with potentially difficult early detection due to only passive surveillance in the area, alternative strategies might need to be employed to protect the dog population and facilitate rabies control, if an incursion occurred. Pre-emptive vaccination has been predicted to be an effective rabies control response in areas where surveillance and detection probability is low because it reduces the susceptible population (Townsend et al., 2013). A reduced susceptible population could subsequently reduce the probability of rabies establishment and the impacts of an outbreak. Japan is an example of a rabies-free country that employs a mandatory annual (anytime at a registered veterinary clinic or during council run campaigns between April – June) pre-emptive vaccination program for domestic dogs against canine rabies virus. Modelling has predicted that this program will reduce outbreak size (Kadowaki et al., 2018; Kwan et al., 2018). However, an analysis of the Japanese pre-emptive vaccination program suggested that it is cost inefficient (Kadowaki et al., 2018), because the risk of rabies entry into Japan is extremely low and the program is implemented nation-wide, which might be unnecessary (Kadowaki et al., 2018). The NPA has a higher estimated risk of rabies entry and exposure than Japan (Hudson et al., 2017a; Kwan et al., 2016, 2017), and localised pre-emptive vaccination of free-roaming domestic dogs in the NPA could be considered rather than a nationwide pre-emptive vaccination program in Australia. Tailoring preemptive vaccination strategies for the roaming behaviours found in the NPA dog population would help achieve and maintain effective vaccination coverage with the limited resources that are available in the NPA. An agent-based simulation model that can describe potential rabies outbreaks in the NPA has been developed (Dürr and Ward, 2015). Recently, the simulation model was updated to reflect the heterogeneous contact structure caused by different roaming patterns found in the NPA dog population; explorer dogs, which roam frequently to different places that can be far from their residence; roamer dogs, which roam infrequently; and stay-at-home dogs, which spend most (if not all) of their time around their residence and rarely, if ever, roam (Hudson et al., 2017b, 2019a). These roaming behaviours are represented in the rabies simulation model as contact kernels which describe the probability of contact between pairs of dogs, dependent on the distance between their residences (Hudson et al., 2019a). Contact kernels that involve an explorer dog in the pair have a lower probability of contact with their closest neighbours but longer distances at which contact is possible (maximum distance for contact 1000 m, 741 m and 881 m for the explorer-explorer, explorer-roamer and explorer-stay-at-home kernels, respectively), which increases the total number of dogs available for contact. In contrast, contact kernels that involve a stay-at-home dog have a high probability to contact their close neighbours but shorter distances for possible contact (maximum distance for contact 721 m, 361 m and 271 m for the roamer-roamer, stay-at-home-roamer and stayat-home-stay-at-home kernels, respectively), which limits the number of total contacts (Hudson et al., 2019a, b). These roaming patterns were then exploited to develop targeted reactive vaccination strategies for more efficient resource allocation; prioritising explorer and roamer dogs for reactive vaccination more efficiently reduced outbreak size and duration than prioritising stay-at-home dogs (Hudson et al., 2019b). Similarly, a network model simulating rabies transmission in a dog population in Chad demonstrated that prioritised dogs showing social interactive behaviours with high betweenness centrality and high degree centrality, plus large area roaming movements, reduced outbreak probability and size compared to random vaccination (Laager et al., 2018). In these studies, the simulated vaccination strategies were
2. Methods 2.1. Study site The Northern Peninsula Area (NPA) is located at the tip of Cape York Peninsula in Queensland, Australia. The closest major Australian city is Cairns, located approximately 1000 km south-east; travel is via unsealed roads during the dry season. The NPA consists of five Indigenous communities – Bamaga, Injinoo, New Mapoon, Seisia and Umagico. The entire NPA local government area covers approximately 1060 sq.km. However, community size ranges between 2.2–10.2 sq.km (Australian Bureau of Statistics, 2016) and the road distance between the two furthest communities (Seisia and Injinoo) is 15 km. Dogs in these communities are owned and are mostly unrestrained (opened gates or poor-quality fences) which facilitates free-roaming (Dürr and Ward, 2014; Hudson et al., 2016, 2017b). There are no stray or unowned dogs in these communities (Hudson et al., 2016). Humanmediated movements of dogs between communities is commonplace and is likely to constitute the majority of inter-community dog movements (Dürr and Ward, 2014; Hudson et al., 2016, 2018). There are no veterinarians or veterinary facilities in the NPA, and therefore, the proportion of sterilised dogs is low (approximately 14%; Hudson et al., 2016, 2018). 2.2. Rabies simulation model Full details of the simulation model can be found in Dürr and Ward (2015). The model is an agent-based, stochastic spatially explicit simulation model which simulates rabies spread in the free-roaming domestic dog population. Recent studies on the dog population has led to updates to how the model describes contacts between dogs with different roaming patterns populations. The most recent version of the simulation model used in the current study – which features heterogeneous roaming category contact structure and an initial dog population of 813 dogs with equal birth and death rates – can be found in Hudson et al. (2019a). The field population structure used in Hudson et al. (2019b) was also used in this study; 42% of the dog population are stay-at-home dogs (n = 341), 29% (n = 236) are explorer dogs and 29% (n = 236) are roamer dogs. The heterogenous roaming patterns and subsequent contact rates are describe by six contact kernels which describes the probability of contact between pairs of dogs based on the distance between the dogs’ houses. 2.3. Random pre-emptive vaccination To create a random pre-emptive vaccination strategy, all simulations began with the original population size (n = 813) and a proportion of this original population was randomly selected to be vaccinated before the rabies outbreak was initiated. Dogs were assumed to remain fully immune for the duration of the simulated outbreaks. For example, within a 50% pre-emptive vaccination strategy, approximately 406 dogs were randomly selected as rabies vaccinated, leaving a susceptible 2
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random pre-emptive vaccination strategy are shown in Figs. 1 and 2, respectively. Without pre-emptive vaccination (0% random coverage) median outbreak duration was 99 days (range 27–510 days) and 542.5 days (range 28–1607 days), with and without 70% reactive vaccination, respectively. The median outbreak size without pre-emptive vaccination was 6 dogs (range 1–81 dogs) and 530.5 dogs (1–670 dogs) with and without 70% reactive vaccination, respectively. All random preemptive vaccination strategies produced significantly smaller outbreaks compared to no pre-emptive vaccination scenarios, both with and without reactive vaccination. All strategies – except 10% pre-emptive coverage without reactive vaccination – also produced shorter outbreaks compared to no pre-emptive vaccination. For both reactive vaccination scenarios, a 50% pre-emptive coverage was the most effective at reducing both outbreak size (median 3 dogs, range 1–36; median 3 dogs, range 1–273, with and without reactive vaccination, respectively) and duration (median 64 days, range 28–298; median 87 days, range 29–1120, with and without reactive vaccination, respectively). However, for the scenarios with reactive vaccination, there was no significant difference between a 50% and 40% random pre-emptive coverage for both outbreak size (median 3 dogs, range 1–35) and duration (median 65 days, range 28–302). Reactive vaccination would always be implemented during an outbreak. Therefore, based on this result, a 40% overall coverage was chosen to further explore targeted pre-emptive vaccination strategies.
population of 407 dogs. Additional vaccination strategies were created as increments of 10% vaccination coverage – starting at 0% – were modelled as the proportion of the original dog population to be vaccinated, until there was no significant difference in model outputs (outbreak size and duration) with increased coverages. In the AUSVETPLAN for a rabies outbreak, reactive vaccination is the foundation of outbreak control (Animal Health Australia, 2011). A 70% vaccination coverage has been recommended to eliminate rabies spread (Coleman and Dye, 1996; WHO, 2013); therefore, each pre-emptive vaccination coverage was simulated both without further vaccination and with a reactive random vaccination strategy of 70% coverage of the remaining non-preemptively vaccinated dogs. Consistent with previous studies using this model, all pre-emptive strategies were simulated 2000 times (based on previous convergence tests using coefficient of variation; Hudson et al., 2019a) and a Kruskal-Wallis Test and a post-hoc Dunns Test were used to compare model outputs (outbreak size and duration) with a significance level of P = 0.01. All simulations were run until no infected dogs remained in the population 2.4. Targeted pre-emptive vaccination The overall random population pre-emptive vaccination coverage from which there was no significant difference compared to the next higher random population coverage was chosen to further explore 10 targeted pre-emptive vaccination strategies. The pre-emptive vaccination strategies were developed by distributing the available number of vaccines amongst the roaming categories in different proportions. The vaccination strategies varied in coverage for each roaming category within the population whilst the overall population coverage remained at the same level for each of the 10 strategies. There were three approaches to allocate the vaccines between the roaming categories: 1) give the maximum number of vaccines to one category (up to 90% of one category vaccinated) and any remaining vaccines to one of the other categories, 2) use the vaccines evenly between combinations of two categories, and 3) use the vaccines evenly between all three categories. The targeted pre-emptive vaccination strategies were implemented using the same method as the random preemptive vaccination strategies and also simulated with and without a 70% random reactive vaccination. A strategy in which no pre-emptive vaccination and a strategy with the random coverage were added as controls to produce 12 strategies in total (Table 1).
3.2. Targeted pre-emptive vaccination To produce a 40% pre-emptive coverage in the study population, approximately 325 dogs need to be vaccinated before an outbreak occurs. The pre-emptive vaccination strategies developed are shown in Table 1 and boxplots of the resulting outbreak duration and size are shown in Figs. 3 and 4 respectively. For all strategies mentioned below, the pre-emptive vaccination coverages of the three roaming categories are reported (in brackets) immediately following the strategy number in the order of explorer, roamer and stay-at-home. For example, Strategy 1 (90–48–0) represents Strategy 1 that pre-emptively vaccinated explorer dogs at 90%, roamer dogs at 48% and stay-at-home dogs at 0% coverage. All pre-emptive vaccination strategies significantly reduced outbreak size and duration compared to the no pre-emptive vaccination strategy (Strategy 12) when simulated with and without reactive vaccination. Without reactive vaccination, Strategy 1 (90–48–0), Strategy 2 (48–90–0) and Strategy 5 (69–69–0) – in which explorer and roamer dogs were prioritised for pre-emptive vaccination and no stay-at-home dogs were pre-emptively vaccinated – all had significantly smaller and shorter outbreaks compared to the random 40% vaccination strategy (Strategy 11 [40–40–40]). Strategy 8 (0–8–90) and Strategy 9 (8–0–90) – which prioritised stay-at-home dogs for pre-emptive vaccination –
3. Results 3.1. Random pre-emptive vaccination Boxplots of the resulting outbreak duration and size for each
Table 1 Pre-emptive vaccination strategies based on various vaccination coverages for each roaming category in the Northern Peninsula Area dog population. The strategies were tested in a rabies-spread simulation model for the Northern Peninsula Area, Queensland, Australia. Each strategy was run 2000 times. Pre-emptive vaccination coverage (%)
1 2 3 4 5 6 7 8 9 10 11 12
Number of vaccinations
Explorer dogs
Roamer dogs
Stay-at-home dogs
Overall
Explorer dogs
Roamer dogs
Stay-at-home dogs
Overall
90 48 90 0 69 69 0 0 8 46 40 0
48 90 0 90 69 0 69 8 0 46 40 0
0 0 33 33 0 48 48 90 90 32 40 0
40 40 40 40 40 40 40 40 40 40 40 0
212 113 212 0 163 163 0 0 19 109 95 0
113 212 0 212 163 0 163 19 0 109 95 0
0 0 113 113 0 163 163 306 306 109 135 0
325 325 325 325 326 326 326 325 325 327 325 0
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Fig. 1. Boxplots of rabies outbreak durations (days) from 6 random pre-emptive vaccination strategies, simulated with (A) and without (B) a 70% reactive vaccination coverage and predicted by a rabies-spread model for the Northern Peninsula Area, Queensland, Australia.
Fig. 2. Boxplots of rabies outbreak size (number of rabid dogs) from 6 random pre-emptive vaccination strategies, simulated with (A) and without (B) a 70% reactive vaccination coverage and predicted by a rabies-spread model for the Northern Peninsula Area, Queensland, Australia.
other half either explorer or roamer dogs, respectively – also performed worse than the other strategies (Figs. 3 and 4). However, this difference was not significant.
both had significantly larger and longer outbreaks compared to Strategy 11 (40–40–40). The differences between the targeted pre-emptive vaccination strategies were less pronounced when a 70% random reactive vaccination was also simulated. With a reactive vaccination strategy, there were no pre-emptive strategies that performed significantly better than the random 40% pre-emptive strategy (Strategy 11 [40–40–40]). However, similar to scenarios without reactive vaccination, Strategy 8 (0–8–90) and Strategy 9 (8–0–90) both produced significantly larger and longer outbreaks compared to Strategy 11. Strategy 6 (69–0–48) and Strategy 7 (0–69–48) – in which half the available vaccines were used to vaccinate stay-at-home dogs and the
4. Discussion Study results suggest pre-emptive vaccination is a beneficial control strategy against canine rabies outbreaks in NPA dog populations because all pre-emptive strategies had significantly smaller and shorter outbreaks compared to the no pre-emptive vaccination strategy, even when reactive vaccination was simulated. However, consistent with 4
Preventive Veterinary Medicine 172 (2019) 104774
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Fig. 3. Boxplots of rabies outbreak durations (days) from 10 targeted pre-emptive vaccination strategies totalling a 40% vaccination coverage (shown in Table 1), a random 40% coverage and no pre-emptive vaccination, simulated with (A) and without (B) a 70% reactive vaccination coverage and predicted by a rabies-spread model for the Northern Peninsula Area, Queensland, Australia.
in which almost no explorer or roamer dogs were vaccinated pre-emptively, performed significantly worse than the random 40% coverage and the other high-risk dog targeted strategies. Even Strategy 6 (69–0–48) and Strategy 7 (0–69–48) – in which half the available vaccines were used to vaccinate stay-at-home dogs and the other half on either explorer or roamer dogs, respectively – tended to perform worse than the other strategies. This suggests that a concerted effort to at least uniformly vaccinate all roaming dog categories and not just focus on the most easily accessible stay-at-home dogs is required for an efficient and effective pre-emptive vaccination strategy in conjunction with a reactive vaccination strategy. A cost-benefit analysis needs to be performed for the NPA before a pre-emptive vaccination program is implemented to determine requirements and highlight areas for improved cost efficiency (frequency of vaccinations, house-to-house or centre-point vaccination, potential use of oral vaccinations). For example, a cost-benefit analysis of Japan’s
Hudson et al. (2019b) in which targeting explorer and roamer dogs versus stay-at-home dogs was more effective, pre-emptive strategies that targeted these roaming dogs outperformed strategies that targeted stayat-home dogs. Without a reactive vaccination strategy, pre-emptive vaccination strategies that heavily prioritised explorer and roamer dogs (Strategy 1 [90–48–0], Strategy 2 [48–90–0] and Strategy 5 [69–69–0]) outperformed the random pre-emptive strategy, again consistent with Hudson et al. (2019b). However, in an actual outbreak, reactive vaccination would always be implemented, and in these simulated scenarios the effect on outbreak size and duration of targeting the high-risk dogs was less pronounced. Therefore, a random pre-emptive vaccination strategy – which could be more time efficient because there is less effort in trying to vaccinate potentially hard-to-catch roaming dogs – would be sufficient to control rabies outbreaks in the NPA in conjunction with a reactive vaccination campaign. However, pre-emptive strategies that heavily targeted stay-at-home dogs (Strategies 8 and 9),
Fig. 4. Boxplots of rabies outbreak size (number of rabid dogs) from 10 targeted preemptive vaccination strategies totalling a 40% vaccination coverage (shown in Table 1), a random 40% coverage and no pre-emptive vaccination, simulated with (A) and without (B) a 70% reactive vaccination coverage and predicted by a rabies-spread model for the Northern Peninsula Area, Queensland, Australia.
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despite different population structures, vaccination strategies that targeted explorer and roamer dogs reduced outbreak size and duration compared to strategies that targeted stay-at-home dogs. The extent to which vaccination strategies that targeted explorer and roamer dogs reduced rabies outbreaks varied with population structure (Hudson et al., 2019b), and we expect that similar results are likely to be predicted for pre-emptive vaccination strategies. This paper can be used to direct and justify further investigation into the effects of population structure on pre-emptive vaccination strategies in the NPA. With the knowledge of the benefits of pre-emptive vaccination in the NPA, further cost-benefit analyses undertaken by decision makers to determine the feasibility in implementing such pre-emptive vaccination programs is justified.
annual mandatory pre-emptive vaccination strategy estimated that although abolition of the program would result in a 3-fold increase in economic loss if a single outbreak occurred, the program itself was relatively cost inefficient because the risk of rabies entry into Japan is extremely low and the program is implemented nation-wide (Kwan et al., 2018). Improvements in cost-efficiency could be made by reducing vaccination frequency to every 2―3 years and focussing on high risk areas only (Kwan et al., 2018). The current study can be used to justify and direct such cost-benefit analyses because the results suggest that a pre-emptive vaccination program would reduce a potential rabies outbreak in the NPA and targeting explorer and roamer dogs is a more effective strategy than targeting stay-at-home dogs. Although a costbenefit analysis is important for implementation and to highlight economic efficiencies, the cost of preventing a rabies outbreak is relatively unimportant due to the fatal zoonotic potential of rabies and Australia’s GDP. During incremental assessment of blanket pre-emptive vaccination coverages, there was no significant difference between a 40% and 50% random pre-emptive vaccination coverage; therefore a 40% coverage was chosen to further explore targeted pre-emptive vaccination strategies. A pre-emptive coverage greater than 50% could further decrease outbreak size and duration. However, reaching and maintaining a higher pre-emptive vaccination coverage in the NPA would be difficult due remoteness, the limited resources and potentially high turnover and population growth facilitated by a low sterilised proportion in the NPA dog population (Hudson et al., 2016, 2018). For comparison, in Japan the mandatory rabies vaccination coverage is only approximately 43.2% of the dog population, despite having regulations for pet registration and sterilisation, and availability and accessibility to resources such as veterinary facilities (Kwan et al., 2018). Currently, there are no permanent veterinarians or veterinary clinics in the NPA (Hudson et al., 2016). Therefore, resources such as veterinary facilities and trained vaccinators would need to be provided for successful implementation of a pre-emptive vaccination program in the NPA. Increasing education in the communities would also complement a vaccination campaign and help increase detection times. Methods to increase community engagement and education in the NPA have been explored in a previous study (Degeling et al., 2018). In addition, a policy change that allows vaccination of dogs against rabies also needs to be implemented. Currently, only dogs that are being exported are allowed to be vaccinated in Australia using the Nobivac™ rabies vaccine and only in the event of an outbreak is this vaccine permitted to be used on permanent Australian dogs (Animal Health Australia, 2011). Introduction of a humane dog population management plan by increasing sterilisation in the NPA – approximately 14% of NPA dogs are sterilised (Hudson et al., 2018) – would also complement pre-emptive vaccination. Such a program would reduce the susceptible population over time and reduce the probability of rabies establishment. It would also reduce the resources needed to implement a pre-emptive vaccination program, by decreasing the number of vaccines needed to reach the desired pre-emptive coverage. Population management would also limit population turn-over (Taylor et al., 2017), helping to maintain the desired pre-emptive vaccination coverage. Additionally, interactions between dingoes and domestic dogs are evident in the NPA (Bombara et al., 2017a, b), which could affect how rabies spreads within the population and subsequently affect the efficacy of vaccination strategies. However, the current study focussed on the domestic dog population because this population is the most atrisk population for rabies introduction and immediate spread (Hudson et al., 2017a). This study focussed on only one population structure in terms of proportions of dogs in each roaming category. Variation in this population structure could affect the results in this study. However, Hudson et al. (2019b) tested various population structures in terms of proportion of dogs in each roaming category for reactive rabies vaccination scenarios in the NPA using the same simulation model and found that
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Contents lists available at ScienceDirect
Preventive Veterinary Medicine journal homepage: www.elsevier.com/locate/prevetmed
Targeted pre-emptive rabies vaccination strategies in a susceptible domestic dog population with heterogeneous roaming patterns
T
⁎
Emily G. Hudsona, , Victoria J. Brookesa,b, Salome Dürrc, Michael P. Warda a
Sydney School of Veterinary Science, The University of Sydney, Camden, Australia School of Animal and Veterinary Sciences, Charles Sturt University, Wagga Wagga, Australia c Veterinary Public Health Institute, University of Bern, Liebefeld, Switzerland b
A R T I C LE I N FO
A B S T R A C T
Keywords: Canine rabies Free-roaming dogs Rabies spread Pre-emptive vaccination Australia Disease modelling Prevention
Australia is free of canine rabies, however northern regions – such as the Northern Peninsula Area (NPA), Queensland – are at risk of an incursion from nearby rabies-infected Indonesian islands. Early detection and reactive vaccination is the current Australian policy to eradicate an incursion. Early detection in this region is challenging, so pre-emptive vaccination might be an effective strategy. The NPA dog population also has a heterogenous contact structure, with three roaming categories previously characterised, which could be exploited in targeted pre-emptive vaccination strategies for more efficient use of limited resources. To evaluate the effectiveness of a pre-emptive vaccination program, an agent-based rabies spread simulation model was used to simulate outbreaks with a range of pre-emptive vaccination coverages. Increasing proportions (10% increments) of the dog population randomly vaccinated were modelled, and at the most efficient random vaccination coverage we then explored 10 pre-emptive vaccination strategies targeting different dog roaming categories (whilst maintaining the same overall population level vaccination coverage). All pre-emptive vaccination strategies were simulated 2000 times without and with a 70% random reactive vaccination strategy, following rabies detection. All random pre-emptive vaccination coverages reduced outbreak size and duration compared to no pre-emptive vaccination. A 40% random coverage was most efficient. Targeted strategies that pre-emptively vaccinated proportionally more roaming dogs were more effective than a random 40% vaccination coverage and strategies that targeted non-roaming dogs. The pre-emptive vaccination strategies that targeted non-roaming dogs produced significantly larger and longer outbreaks. These results suggest that pre-emptive vaccination can reduce potential rabies outbreaks in this region and that such a strategy should not just focus on easily accessible dogs that do not roam often or at all. A cost-benefit analysis is required to determine whether the implementation of such pre-emptive vaccination strategies is also cost-effective, which is essential in the resourcepoor communities of this region.
1. Introduction Australia is free of canine rabies (WHO, 2013). However, northern Indigenous communities of Australia – such as the Northern Peninsula Area (NPA) – are at risk of canine rabies entry and establishment due to their large populations of unvaccinated free-roaming domestic dogs and their proximity to rabies endemic Indonesian islands (Hudson et al., 2017a). One pathway that has been assessed as high-risk is the illegal transportation of infected dogs from Indonesia to the NPA on fishing boats (Hudson et al., 2017a). Vaccination is the most cost effective and efficient method to prevent, control and eliminate canine rabies (WHO, 2013; Hampson et al., 2015). However, in rabies-free Australia, only legally imported animals are vaccinated (Animal Health Australia,
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2011). Consequently, the NPA dog population is likely entirely susceptible to rabies infection. Currently, Australia relies on early detection and immediate reactive vaccination to prevent and control rabies outbreaks (Animal Health Australia, 2011). Early detection is important for rabies control and potential eradication because it enables timely implementation of control measures, without which rabies could become endemic. Modelling has shown that a low detection probability (and subsequent long detection time) causes longer and larger rabies outbreaks and reduces the probability of rabies elimination within a 2-year period (Townsend et al., 2013). However, there are specific challenges to rabies detection in the NPA that make early detection difficult. For example, rabies awareness in remote Indigenous communities is likely to be very low or
Corresponding author. E-mail address: [email protected] (E.G. Hudson).
https://doi.org/10.1016/j.prevetmed.2019.104774 Received 6 May 2019; Received in revised form 12 September 2019; Accepted 13 September 2019 0167-5877/ © 2019 Elsevier B.V. All rights reserved.
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implemented reactively after detection of rabies; the use of pre-emptive vaccination remains unexplored. Similar to the reactive vaccination strategies, the heterogeneous roaming patterns and subsequent contacts in the NPA dog population could be exploited to develop efficient preemptive vaccination strategies. The objective of this study was to evaluate the benefits of a preemptive vaccination program in terms of predicted rabies outbreak duration and size (number of infected dogs). Roaming behaviours and contact structure were exploited to develop targeted pre-emptive vaccination strategies which were compared to a random vaccination strategy. The results of this study can be used by decision makers to justify further research into the practical feasibility of pre-emptive vaccination programs, including cost-benefit analyses.
non-existent due to the rabies free-status of Australia, and dogs that present with clinical signs of rabies would likely be mistaken by dogowners for other diseases or ignored completely; the first detected case might not be the primary case and rabies could have already infected several other dogs. Also, there are no veterinary or diagnostic facilities in the NPA to confirm a rabies diagnosis, which could further delay a definitive detection (Hudson et al., 2016). Therefore, with potentially difficult early detection due to only passive surveillance in the area, alternative strategies might need to be employed to protect the dog population and facilitate rabies control, if an incursion occurred. Pre-emptive vaccination has been predicted to be an effective rabies control response in areas where surveillance and detection probability is low because it reduces the susceptible population (Townsend et al., 2013). A reduced susceptible population could subsequently reduce the probability of rabies establishment and the impacts of an outbreak. Japan is an example of a rabies-free country that employs a mandatory annual (anytime at a registered veterinary clinic or during council run campaigns between April – June) pre-emptive vaccination program for domestic dogs against canine rabies virus. Modelling has predicted that this program will reduce outbreak size (Kadowaki et al., 2018; Kwan et al., 2018). However, an analysis of the Japanese pre-emptive vaccination program suggested that it is cost inefficient (Kadowaki et al., 2018), because the risk of rabies entry into Japan is extremely low and the program is implemented nation-wide, which might be unnecessary (Kadowaki et al., 2018). The NPA has a higher estimated risk of rabies entry and exposure than Japan (Hudson et al., 2017a; Kwan et al., 2016, 2017), and localised pre-emptive vaccination of free-roaming domestic dogs in the NPA could be considered rather than a nationwide pre-emptive vaccination program in Australia. Tailoring preemptive vaccination strategies for the roaming behaviours found in the NPA dog population would help achieve and maintain effective vaccination coverage with the limited resources that are available in the NPA. An agent-based simulation model that can describe potential rabies outbreaks in the NPA has been developed (Dürr and Ward, 2015). Recently, the simulation model was updated to reflect the heterogeneous contact structure caused by different roaming patterns found in the NPA dog population; explorer dogs, which roam frequently to different places that can be far from their residence; roamer dogs, which roam infrequently; and stay-at-home dogs, which spend most (if not all) of their time around their residence and rarely, if ever, roam (Hudson et al., 2017b, 2019a). These roaming behaviours are represented in the rabies simulation model as contact kernels which describe the probability of contact between pairs of dogs, dependent on the distance between their residences (Hudson et al., 2019a). Contact kernels that involve an explorer dog in the pair have a lower probability of contact with their closest neighbours but longer distances at which contact is possible (maximum distance for contact 1000 m, 741 m and 881 m for the explorer-explorer, explorer-roamer and explorer-stay-at-home kernels, respectively), which increases the total number of dogs available for contact. In contrast, contact kernels that involve a stay-at-home dog have a high probability to contact their close neighbours but shorter distances for possible contact (maximum distance for contact 721 m, 361 m and 271 m for the roamer-roamer, stay-at-home-roamer and stayat-home-stay-at-home kernels, respectively), which limits the number of total contacts (Hudson et al., 2019a, b). These roaming patterns were then exploited to develop targeted reactive vaccination strategies for more efficient resource allocation; prioritising explorer and roamer dogs for reactive vaccination more efficiently reduced outbreak size and duration than prioritising stay-at-home dogs (Hudson et al., 2019b). Similarly, a network model simulating rabies transmission in a dog population in Chad demonstrated that prioritised dogs showing social interactive behaviours with high betweenness centrality and high degree centrality, plus large area roaming movements, reduced outbreak probability and size compared to random vaccination (Laager et al., 2018). In these studies, the simulated vaccination strategies were
2. Methods 2.1. Study site The Northern Peninsula Area (NPA) is located at the tip of Cape York Peninsula in Queensland, Australia. The closest major Australian city is Cairns, located approximately 1000 km south-east; travel is via unsealed roads during the dry season. The NPA consists of five Indigenous communities – Bamaga, Injinoo, New Mapoon, Seisia and Umagico. The entire NPA local government area covers approximately 1060 sq.km. However, community size ranges between 2.2–10.2 sq.km (Australian Bureau of Statistics, 2016) and the road distance between the two furthest communities (Seisia and Injinoo) is 15 km. Dogs in these communities are owned and are mostly unrestrained (opened gates or poor-quality fences) which facilitates free-roaming (Dürr and Ward, 2014; Hudson et al., 2016, 2017b). There are no stray or unowned dogs in these communities (Hudson et al., 2016). Humanmediated movements of dogs between communities is commonplace and is likely to constitute the majority of inter-community dog movements (Dürr and Ward, 2014; Hudson et al., 2016, 2018). There are no veterinarians or veterinary facilities in the NPA, and therefore, the proportion of sterilised dogs is low (approximately 14%; Hudson et al., 2016, 2018). 2.2. Rabies simulation model Full details of the simulation model can be found in Dürr and Ward (2015). The model is an agent-based, stochastic spatially explicit simulation model which simulates rabies spread in the free-roaming domestic dog population. Recent studies on the dog population has led to updates to how the model describes contacts between dogs with different roaming patterns populations. The most recent version of the simulation model used in the current study – which features heterogeneous roaming category contact structure and an initial dog population of 813 dogs with equal birth and death rates – can be found in Hudson et al. (2019a). The field population structure used in Hudson et al. (2019b) was also used in this study; 42% of the dog population are stay-at-home dogs (n = 341), 29% (n = 236) are explorer dogs and 29% (n = 236) are roamer dogs. The heterogenous roaming patterns and subsequent contact rates are describe by six contact kernels which describes the probability of contact between pairs of dogs based on the distance between the dogs’ houses. 2.3. Random pre-emptive vaccination To create a random pre-emptive vaccination strategy, all simulations began with the original population size (n = 813) and a proportion of this original population was randomly selected to be vaccinated before the rabies outbreak was initiated. Dogs were assumed to remain fully immune for the duration of the simulated outbreaks. For example, within a 50% pre-emptive vaccination strategy, approximately 406 dogs were randomly selected as rabies vaccinated, leaving a susceptible 2
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random pre-emptive vaccination strategy are shown in Figs. 1 and 2, respectively. Without pre-emptive vaccination (0% random coverage) median outbreak duration was 99 days (range 27–510 days) and 542.5 days (range 28–1607 days), with and without 70% reactive vaccination, respectively. The median outbreak size without pre-emptive vaccination was 6 dogs (range 1–81 dogs) and 530.5 dogs (1–670 dogs) with and without 70% reactive vaccination, respectively. All random preemptive vaccination strategies produced significantly smaller outbreaks compared to no pre-emptive vaccination scenarios, both with and without reactive vaccination. All strategies – except 10% pre-emptive coverage without reactive vaccination – also produced shorter outbreaks compared to no pre-emptive vaccination. For both reactive vaccination scenarios, a 50% pre-emptive coverage was the most effective at reducing both outbreak size (median 3 dogs, range 1–36; median 3 dogs, range 1–273, with and without reactive vaccination, respectively) and duration (median 64 days, range 28–298; median 87 days, range 29–1120, with and without reactive vaccination, respectively). However, for the scenarios with reactive vaccination, there was no significant difference between a 50% and 40% random pre-emptive coverage for both outbreak size (median 3 dogs, range 1–35) and duration (median 65 days, range 28–302). Reactive vaccination would always be implemented during an outbreak. Therefore, based on this result, a 40% overall coverage was chosen to further explore targeted pre-emptive vaccination strategies.
population of 407 dogs. Additional vaccination strategies were created as increments of 10% vaccination coverage – starting at 0% – were modelled as the proportion of the original dog population to be vaccinated, until there was no significant difference in model outputs (outbreak size and duration) with increased coverages. In the AUSVETPLAN for a rabies outbreak, reactive vaccination is the foundation of outbreak control (Animal Health Australia, 2011). A 70% vaccination coverage has been recommended to eliminate rabies spread (Coleman and Dye, 1996; WHO, 2013); therefore, each pre-emptive vaccination coverage was simulated both without further vaccination and with a reactive random vaccination strategy of 70% coverage of the remaining non-preemptively vaccinated dogs. Consistent with previous studies using this model, all pre-emptive strategies were simulated 2000 times (based on previous convergence tests using coefficient of variation; Hudson et al., 2019a) and a Kruskal-Wallis Test and a post-hoc Dunns Test were used to compare model outputs (outbreak size and duration) with a significance level of P = 0.01. All simulations were run until no infected dogs remained in the population 2.4. Targeted pre-emptive vaccination The overall random population pre-emptive vaccination coverage from which there was no significant difference compared to the next higher random population coverage was chosen to further explore 10 targeted pre-emptive vaccination strategies. The pre-emptive vaccination strategies were developed by distributing the available number of vaccines amongst the roaming categories in different proportions. The vaccination strategies varied in coverage for each roaming category within the population whilst the overall population coverage remained at the same level for each of the 10 strategies. There were three approaches to allocate the vaccines between the roaming categories: 1) give the maximum number of vaccines to one category (up to 90% of one category vaccinated) and any remaining vaccines to one of the other categories, 2) use the vaccines evenly between combinations of two categories, and 3) use the vaccines evenly between all three categories. The targeted pre-emptive vaccination strategies were implemented using the same method as the random preemptive vaccination strategies and also simulated with and without a 70% random reactive vaccination. A strategy in which no pre-emptive vaccination and a strategy with the random coverage were added as controls to produce 12 strategies in total (Table 1).
3.2. Targeted pre-emptive vaccination To produce a 40% pre-emptive coverage in the study population, approximately 325 dogs need to be vaccinated before an outbreak occurs. The pre-emptive vaccination strategies developed are shown in Table 1 and boxplots of the resulting outbreak duration and size are shown in Figs. 3 and 4 respectively. For all strategies mentioned below, the pre-emptive vaccination coverages of the three roaming categories are reported (in brackets) immediately following the strategy number in the order of explorer, roamer and stay-at-home. For example, Strategy 1 (90–48–0) represents Strategy 1 that pre-emptively vaccinated explorer dogs at 90%, roamer dogs at 48% and stay-at-home dogs at 0% coverage. All pre-emptive vaccination strategies significantly reduced outbreak size and duration compared to the no pre-emptive vaccination strategy (Strategy 12) when simulated with and without reactive vaccination. Without reactive vaccination, Strategy 1 (90–48–0), Strategy 2 (48–90–0) and Strategy 5 (69–69–0) – in which explorer and roamer dogs were prioritised for pre-emptive vaccination and no stay-at-home dogs were pre-emptively vaccinated – all had significantly smaller and shorter outbreaks compared to the random 40% vaccination strategy (Strategy 11 [40–40–40]). Strategy 8 (0–8–90) and Strategy 9 (8–0–90) – which prioritised stay-at-home dogs for pre-emptive vaccination –
3. Results 3.1. Random pre-emptive vaccination Boxplots of the resulting outbreak duration and size for each
Table 1 Pre-emptive vaccination strategies based on various vaccination coverages for each roaming category in the Northern Peninsula Area dog population. The strategies were tested in a rabies-spread simulation model for the Northern Peninsula Area, Queensland, Australia. Each strategy was run 2000 times. Pre-emptive vaccination coverage (%)
1 2 3 4 5 6 7 8 9 10 11 12
Number of vaccinations
Explorer dogs
Roamer dogs
Stay-at-home dogs
Overall
Explorer dogs
Roamer dogs
Stay-at-home dogs
Overall
90 48 90 0 69 69 0 0 8 46 40 0
48 90 0 90 69 0 69 8 0 46 40 0
0 0 33 33 0 48 48 90 90 32 40 0
40 40 40 40 40 40 40 40 40 40 40 0
212 113 212 0 163 163 0 0 19 109 95 0
113 212 0 212 163 0 163 19 0 109 95 0
0 0 113 113 0 163 163 306 306 109 135 0
325 325 325 325 326 326 326 325 325 327 325 0
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Fig. 1. Boxplots of rabies outbreak durations (days) from 6 random pre-emptive vaccination strategies, simulated with (A) and without (B) a 70% reactive vaccination coverage and predicted by a rabies-spread model for the Northern Peninsula Area, Queensland, Australia.
Fig. 2. Boxplots of rabies outbreak size (number of rabid dogs) from 6 random pre-emptive vaccination strategies, simulated with (A) and without (B) a 70% reactive vaccination coverage and predicted by a rabies-spread model for the Northern Peninsula Area, Queensland, Australia.
other half either explorer or roamer dogs, respectively – also performed worse than the other strategies (Figs. 3 and 4). However, this difference was not significant.
both had significantly larger and longer outbreaks compared to Strategy 11 (40–40–40). The differences between the targeted pre-emptive vaccination strategies were less pronounced when a 70% random reactive vaccination was also simulated. With a reactive vaccination strategy, there were no pre-emptive strategies that performed significantly better than the random 40% pre-emptive strategy (Strategy 11 [40–40–40]). However, similar to scenarios without reactive vaccination, Strategy 8 (0–8–90) and Strategy 9 (8–0–90) both produced significantly larger and longer outbreaks compared to Strategy 11. Strategy 6 (69–0–48) and Strategy 7 (0–69–48) – in which half the available vaccines were used to vaccinate stay-at-home dogs and the
4. Discussion Study results suggest pre-emptive vaccination is a beneficial control strategy against canine rabies outbreaks in NPA dog populations because all pre-emptive strategies had significantly smaller and shorter outbreaks compared to the no pre-emptive vaccination strategy, even when reactive vaccination was simulated. However, consistent with 4
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Fig. 3. Boxplots of rabies outbreak durations (days) from 10 targeted pre-emptive vaccination strategies totalling a 40% vaccination coverage (shown in Table 1), a random 40% coverage and no pre-emptive vaccination, simulated with (A) and without (B) a 70% reactive vaccination coverage and predicted by a rabies-spread model for the Northern Peninsula Area, Queensland, Australia.
in which almost no explorer or roamer dogs were vaccinated pre-emptively, performed significantly worse than the random 40% coverage and the other high-risk dog targeted strategies. Even Strategy 6 (69–0–48) and Strategy 7 (0–69–48) – in which half the available vaccines were used to vaccinate stay-at-home dogs and the other half on either explorer or roamer dogs, respectively – tended to perform worse than the other strategies. This suggests that a concerted effort to at least uniformly vaccinate all roaming dog categories and not just focus on the most easily accessible stay-at-home dogs is required for an efficient and effective pre-emptive vaccination strategy in conjunction with a reactive vaccination strategy. A cost-benefit analysis needs to be performed for the NPA before a pre-emptive vaccination program is implemented to determine requirements and highlight areas for improved cost efficiency (frequency of vaccinations, house-to-house or centre-point vaccination, potential use of oral vaccinations). For example, a cost-benefit analysis of Japan’s
Hudson et al. (2019b) in which targeting explorer and roamer dogs versus stay-at-home dogs was more effective, pre-emptive strategies that targeted these roaming dogs outperformed strategies that targeted stayat-home dogs. Without a reactive vaccination strategy, pre-emptive vaccination strategies that heavily prioritised explorer and roamer dogs (Strategy 1 [90–48–0], Strategy 2 [48–90–0] and Strategy 5 [69–69–0]) outperformed the random pre-emptive strategy, again consistent with Hudson et al. (2019b). However, in an actual outbreak, reactive vaccination would always be implemented, and in these simulated scenarios the effect on outbreak size and duration of targeting the high-risk dogs was less pronounced. Therefore, a random pre-emptive vaccination strategy – which could be more time efficient because there is less effort in trying to vaccinate potentially hard-to-catch roaming dogs – would be sufficient to control rabies outbreaks in the NPA in conjunction with a reactive vaccination campaign. However, pre-emptive strategies that heavily targeted stay-at-home dogs (Strategies 8 and 9),
Fig. 4. Boxplots of rabies outbreak size (number of rabid dogs) from 10 targeted preemptive vaccination strategies totalling a 40% vaccination coverage (shown in Table 1), a random 40% coverage and no pre-emptive vaccination, simulated with (A) and without (B) a 70% reactive vaccination coverage and predicted by a rabies-spread model for the Northern Peninsula Area, Queensland, Australia.
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despite different population structures, vaccination strategies that targeted explorer and roamer dogs reduced outbreak size and duration compared to strategies that targeted stay-at-home dogs. The extent to which vaccination strategies that targeted explorer and roamer dogs reduced rabies outbreaks varied with population structure (Hudson et al., 2019b), and we expect that similar results are likely to be predicted for pre-emptive vaccination strategies. This paper can be used to direct and justify further investigation into the effects of population structure on pre-emptive vaccination strategies in the NPA. With the knowledge of the benefits of pre-emptive vaccination in the NPA, further cost-benefit analyses undertaken by decision makers to determine the feasibility in implementing such pre-emptive vaccination programs is justified.
annual mandatory pre-emptive vaccination strategy estimated that although abolition of the program would result in a 3-fold increase in economic loss if a single outbreak occurred, the program itself was relatively cost inefficient because the risk of rabies entry into Japan is extremely low and the program is implemented nation-wide (Kwan et al., 2018). Improvements in cost-efficiency could be made by reducing vaccination frequency to every 2―3 years and focussing on high risk areas only (Kwan et al., 2018). The current study can be used to justify and direct such cost-benefit analyses because the results suggest that a pre-emptive vaccination program would reduce a potential rabies outbreak in the NPA and targeting explorer and roamer dogs is a more effective strategy than targeting stay-at-home dogs. Although a costbenefit analysis is important for implementation and to highlight economic efficiencies, the cost of preventing a rabies outbreak is relatively unimportant due to the fatal zoonotic potential of rabies and Australia’s GDP. During incremental assessment of blanket pre-emptive vaccination coverages, there was no significant difference between a 40% and 50% random pre-emptive vaccination coverage; therefore a 40% coverage was chosen to further explore targeted pre-emptive vaccination strategies. A pre-emptive coverage greater than 50% could further decrease outbreak size and duration. However, reaching and maintaining a higher pre-emptive vaccination coverage in the NPA would be difficult due remoteness, the limited resources and potentially high turnover and population growth facilitated by a low sterilised proportion in the NPA dog population (Hudson et al., 2016, 2018). For comparison, in Japan the mandatory rabies vaccination coverage is only approximately 43.2% of the dog population, despite having regulations for pet registration and sterilisation, and availability and accessibility to resources such as veterinary facilities (Kwan et al., 2018). Currently, there are no permanent veterinarians or veterinary clinics in the NPA (Hudson et al., 2016). Therefore, resources such as veterinary facilities and trained vaccinators would need to be provided for successful implementation of a pre-emptive vaccination program in the NPA. Increasing education in the communities would also complement a vaccination campaign and help increase detection times. Methods to increase community engagement and education in the NPA have been explored in a previous study (Degeling et al., 2018). In addition, a policy change that allows vaccination of dogs against rabies also needs to be implemented. Currently, only dogs that are being exported are allowed to be vaccinated in Australia using the Nobivac™ rabies vaccine and only in the event of an outbreak is this vaccine permitted to be used on permanent Australian dogs (Animal Health Australia, 2011). Introduction of a humane dog population management plan by increasing sterilisation in the NPA – approximately 14% of NPA dogs are sterilised (Hudson et al., 2018) – would also complement pre-emptive vaccination. Such a program would reduce the susceptible population over time and reduce the probability of rabies establishment. It would also reduce the resources needed to implement a pre-emptive vaccination program, by decreasing the number of vaccines needed to reach the desired pre-emptive coverage. Population management would also limit population turn-over (Taylor et al., 2017), helping to maintain the desired pre-emptive vaccination coverage. Additionally, interactions between dingoes and domestic dogs are evident in the NPA (Bombara et al., 2017a, b), which could affect how rabies spreads within the population and subsequently affect the efficacy of vaccination strategies. However, the current study focussed on the domestic dog population because this population is the most atrisk population for rabies introduction and immediate spread (Hudson et al., 2017a). This study focussed on only one population structure in terms of proportions of dogs in each roaming category. Variation in this population structure could affect the results in this study. However, Hudson et al. (2019b) tested various population structures in terms of proportion of dogs in each roaming category for reactive rabies vaccination scenarios in the NPA using the same simulation model and found that
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