Notes:1Calibrated with distances in meters.2SI stands for Supporting Information.
Model calibration
The model was calibrated to the data available from the region of São
Paulo acquired in 2017-2018 when vaccination of farms, but no roost
control, was performed in the area. Two model parameters, the
roost-to-roost transmission rate, βRR , and the
roost-to-farm transmission rate, βRF , were fitted
(see below); the remaining parameters were extracted from the literature
(Table 1).
Model fitting was carried out using a regression-based conditional
density Approximate Bayesian Computation algorithm, such as implemented
in Prada et al. (2014), following Beaumont et al. (2002) and Lopes and
Beaumont (2010). Briefly, summary statistics were calculated from the
2017-2018 data, and we ran a total of 7,800 simulations to calibrate the
roost-to-roost and roost-to-farm transmission rates,\(\beta_{\text{RR}}\) and \(\beta_{\text{RF}}\), respectively. Due to
the high number of nodes in the network, the fitting process was carried
out in two phases. First, the roost-to-roost transmission rate parameter
was calibrated to reach 1% prevalence across all roosts in the network
by simulation of 100 of years of transmission between roosts. The
spillover to farms was not considered in this phase, therefore, no
intervention was allowed. Second, the roost-to-farm transmission rate
parameter was fitted to generate 226 outbreaks in farms across a
five-year period, as we calibrated the parameters using the data
collected in 2017-2018 when only farm vaccination was performed, only
this intervention was allowed in the second phase of calibration, see
Model calibration in Supporting Information for more details.
Bat-rabies control scenarios
Using the calibrated model, we explored several VBR control scenarios,
assessing the effect over the spread of VBR from a single introduction
in a randomly selected roost. We considered three initial settings of
suitability environments, depending on whether the single initial
introduction was in either a high, middle, or low suitability
environment (limited to roosts connected to at least five other roosts,
to ensure simulations are not initiated in isolated locations). We
define these three initial sets of roosts, so that the roosts with the
suitability index, calculated through the ENM (Anderson, 2013; Owens et
al., 2013; Soberón and Peterson, 2005), within upper decile (after
excluding isolated locations) form a set of roosts in high suitability
environment, roosts with the suitability index of +/-5% around the
median form the middle, and within bottom decile form the low
suitability environment sets of roosts (Supporting Information Figure
S6).
In each initial setting, in response to VBR being detected in farms, we
consider all combinations of two reactive interventions included in the
model: a combination of roost control and farm vaccination, each
intervention alone, or no intervention. Consequently, we simulate 12
different control scenarios (three initial settings of suitability
environment with four different intervention strategies, Figure 3). This
enables a comparison of the impact of environmental suitability on virus
transmission and intervention effectiveness. With the model calibration,
we selected the best posterior draws (107 selected), and we ran 50
simulations with each posterior, 5,350 simulations in total per control
scenario.
We assessed two different outcomes: (i) the number of detected outbreaks
in farms, and (ii) the distance of virus spread from initial infection
in a roost to a farm in one year, for the different control scenarios.
We determined whether there are any statistically significant
differences between the means of the outcomes for different intervention
strategies by the Welch’s one-way heteroscedastic F test, an
alternative to ANOVA robust to the violation of variance homogeneity
assumption, which we observed for both outcomes. The Welch’s test has
one of the highest adjusted power among one-way tests for positively
skewed data, which we observed for the numbers of outbreaks, and for
approximately normally distributed data, that we observed for the
distances (Dag et al., 2018). Since we do not confirm the hypotheses of
equal means, we perform the Games-Howell post-hoc tests to recognize
which pairs of intervention strategies significantly differ, assessed
through the Holm-corrected p-values. Tests and visualization are
performed using the ggstatsplot package of R (Patil, 2021).
Areas at persistently high risk of VBR transmission and spillover in the
state of São Paulo after random introductions can be highlighted by
mapping spillover events. We divided the state of São Paulo into squares
of 3’ latitude times 3’ longitude (30km2). Spillover risk of farms was calculated as a
proportion of (detected and undetected) infections among all simulations
of a particular scenario.
Results
The average number of detected outbreaks in farms in a year, from a
single introduction, is decreased significantly when an intervention
strategy is implemented (being either cattle vaccination, roost control,
or both), across all three suitability environments considered (Figure
4A-C). The maximal distances of virus spread from a single infection in
a roost to a farm in one year, for the different intervention strategies
are shown in Figure 4D-F.
The F statistics and the p -values of Welch’s F test
are summarized for each comparison in Table S3 in Supporting
Information, with all p -values close to zero, i.e. for both
outcomes, across all three initial suitability settings, we do not
confirm the hypothesis of equal means in the four intervention
strategies. The Games-Howell post-hoc tests identify which pairs of
intervention strategies significantly differ. The Holm-correctedp -values indicate that the outcomes for the combination of farm
vaccination and roost control, versus roost control alone, are not
significantly different, Figure 4A-F. Additionally, when infection
starts in a low suitability environment, the number of outbreaks in
farms do not significantly differ between the combination of farm
vaccination and roost control, versus farm vaccination alone, Figure 4C.
The most ecologically suitable areas for bats, and thus where spread is
likely to be higher, are concentrated in the east side of São Paulo
state. The infection risk decreases dramatically with any intervention
(whether it is farm vaccination, roost control, or both); the
probability of an outbreak occurring in farms, after a single
introduction, can be as high as 3.81% of the simulations ran without
intervention and 1.02% of the simulations with the roost control, the
most effective intervention strategy (Figure 5). High infection risk
probabilities in farms were also observed in the middle and low
suitability environments, which could be as high as 7.12% (Supporting
Information Figure S7).
Discussion
The aim of this study was to explore the spatio-temporal dynamics of
vampire-bat-driven rabies (VBR) in São Paulo, Brazil, and identify
high-risk areas of spillover to cattle farms. This was achieved through
the development of a novel stochastic network two-species metapopulation
model. The model was used to explore the impact of current
interventions, ring vaccination of farms and/or ring roost control
(either bat culling or bat vaccination) around a positive farm. Our
results suggest that either strategy can prevent substantial number of
on-farm outbreaks, as well as significantly reduce the geographical
spread of the virus. However, roost control alone or combined with farm
vaccination in general leads to more significant control results than
cattle vaccination alone. Interestingly, combination of both
intervention did not provide a significant benefit comparable to roost
control alone. We also found areas of consistently high infection risk
in high roost suitability environments, and in middle and low
suitability environments for bat roosting.
As possibly, the most diverse, abundant, and geographically dispersed
vertebrate, bats are unique in their ability to fly, long lifespans,
migratory patterns, and in hosting a diverse suite of pathogens
including rabies virus (Calisher et al., 2006; Luis et al., 2013). Some
of these factors contribute towards the efficacy of bats as zoonosis
transmitters, but also towards the lack of data about pathogen
circulation, in particular their high level of mobility and vast
geographic ranges, as field data are often collected from a subset of a
species geographic range over a small timescale (Benavides et al.,
2016). While keeping the model relatively simple in terms of bat
demography, we reproduce several important environmental drivers of
disease transmission, such as elevation driving the explicit range of
contact between roots and farms, male-driven transmission between bat
roosts, flight distance and environmental suitability. This is key to
generate useful risk maps that can support policy implementation. For
example, Benavides et al. (2020) highlighted the challenge of applying
bat vaccines across many roosts, which could be mitigated by focusing
efforts on the areas estimated by the model to be at higher risk, which
could in addition reduce cross-species exposure while reducing the
impact on bat communities.
Bat culling remains a controversial approach to VBR control (Streicker
et al, 2012). Alternatively, a spreadable vaccine may be administrated
similar as the vampiricide. Laboratory and model results showed that the
oral vaccination could be effective (Standing et al., 2017; Bakker et
al., 2019). In the model we considered the implementation of a roost
control, which can either represent bat culling or bat vaccination.
Either way, it is modeled so that if a roost receives the intervention,
all transmission ceases for at least one year. In the case of culling,
the spread of the poison due to intensive grooming leads to an empty
roost (Linhrat et al, 1972), which would likely be repopulated in the
future, but this could potentially take a long time and has dangerous
ecological implications. Furthermore, it was suggested that culling may
increase recruitment of susceptible juveniles into the system, making
the intervention ineffective or counterproductive, therefore, the
efficacy simulated here is likely overestimated in case of culling
(Streicker et al., 2012; Gentles et al., 2020). To study this in more
detail, model would need to be modified to include within roost
dynamics. Bat vaccination, being spread the same way, will lead to the
entire roost population immune, arguably for at least one year. This
type of control would not change the population structure within the
roost, on the other hand, it will not reduce the impacts of bats as
pests causing harm to animals by bat bites independently of rabies,
including skin damage, anemia, loss of vision, loss of weight and
productivity, and predisposition to other infection (Delpietro et al.,
2021).
Nevertheless, cattle vaccination has also achieved considerable
reduction in on-farm outbreaks and geographical spread of infection
across the three initial suitability environments. Either way, a spatial
mathematical model simulating the impact of these interventions, for
example extending the one presented here, could be used before hand to
evaluate the consequences of their introduction, and identify the most
suitable locations to cover with the campaign for the successfully
control, or even eradication, of the virus. As concluded by Blackwood et
al. (2013), who developed several stochastic SEIR models examining viral
persistence, bat population migration, and the effects of bat population
culling; the mechanisms to reduce spillover via viral elimination,
likely need to be spatially coordinated to be effective as we
demonstrated here.
In the model we considered the minimum delay in the detection of
outbreaks in the cattle farms to be 25 days, with a mean detection time
around 75 days, and the most frequently observed delay (mode) of 30
days. We assumed a relatively over dispersed distribution to capture
both the latency period and delay in detection. As the interventions
simulated here are reactive, reducing the delay in detection could
generate significant gains in reducing transmission. Alternatively, the
farm or roost control could be administered in a prospective manner, for
example focusing on high-risk areas. The challenge would be to justify
the investment to stakeholders (whether it is the farmers paying for the
cattle vaccine, or the government paying for either farm or roost
control), when the risk might not be perceived.
We followed prior work made in the region (Rocha et al., 2020; Rocha and
Dias, 2020), building a similar contact network as in Rocha and Dias
(2020), with a consistent assumption of up to 10 km flight distance
(Benavides at al., 2016), and dependence of bat foraging migration
pattern on altitude (Rocha et al., 2020). How far within the 10 km
distance the bats fly is determined by the number of individuals in the
roost, since individuals may fly to more distant feeding sources and/or
roosts to minimize competition with conspecifics (Kunz and Fenton, 2003;
Rocha et al., 2020). We address these spatial interactions by utilizing
a gravity model. In addition, we incorporate knowledge of favorable
conditions for bats using the roost locations and an ecological niche
model to capture the environmental suitability (Ecological niche model
in Supporting Information). Our approach has however a number of
limitations; the contact network is assumed to be time-invariant and we
are examining outbreaks over a one year time-period from a single
introduction. Assuming a unique infected roost at random (potentially in
the middle of the region) as a starting point is unrealistic, however it
allows us to better capture the expected spatial spread from a single
point. The model focuses only on spillover to cattle, however, other
animals are in risk (e.g. horses), and since rabies virus is zoonosis
also spillover to humans occurs.
The reactive interventions depend on reports from the producers which is
influenced by many socio-ecological factors, similarly adherence to
intervention and thus vaccination of the animals when infection nearby
is reported might be conditioned by various factors (Benavides et al.,
2017). The behavior effects on intervention needs to be accounted for in
model if we want more realistic predictions. Furthermore, the
intervention strategies effective to reach programmatic goals needs to
be evaluated in economic manner as the government and farmers financial
sources are limited (Janoušková et al., 2022). For example, anemia from
bat bites may reduce livestock productivity (Bakker et al., 2019), hence
making a difference in bat culling compare to bat vaccination. The roost
control might be more cost-efficient to the official service since a
smaller number of locations should be visited and vaccine delivery (for
example as a paste) is more straight-forward than cattle vaccination.
The model presented here, does not evaluate the economic implications,
therefore distinguish only between susceptible, exposed, and infected
farms, ignoring how many number of animals and to which extent are
affected by bites and/or infection. The cumulative losses due to bites
if no culling is performed, and even deaths if no roost control is in
place might markedly change the cost-effectiveness. Last, but not least,
the trust, support and commitment of stakeholders and involved
institutions is necessary to reach the expected results (Janoušková et
al., 2022). For instance, vaccination of vampire bats without population
reduction will be unacceptable to some stakeholders since uncontrolled
bat depredation sustains exposures to non-rabies pathogens (Bakker et
al., 2019). The stakeholder’s preferences have to be taken into account
when assessing the sustainability of the interventions.
Conclusion
We have developed a novel stochastic network two-species metapopulation
model, that captures transmission of VBR between bat roost, as well as
spillover events to cattle farms. After exploring two alternative
control strategies, namely reactive ring roost control (i.e. bat culling
or bat vaccination) and reactive ring cattle farm vaccination, we found
no large differences in their expected efficacy, however interventions
in roosts were statistically significantly better in all settings
considered across both outcomes (number of outbreaks and spatial spread
from initial introduction). Such mathematical frameworks can prove
useful to inform control interventions, particularly identifying
high-risk areas where prospective vaccination, either in cattle or in
bats, could take place. This will support ongoing programs, leading to
more effective control. Nonetheless, to reach long-term strategies and
sustainability that could move beyond control to potential local
elimination and eradication, human behavior, for example, in context of
interventions uptake and response to VBR infection in farms, needs to be
incorporated in model to get more accurate predictions. In addition to
assessing intervention strategies effectiveness and high-risk areas such
as provided in this study, economic evaluation is essential before
decision is made on interventions.
Acknowledgements
This work was funded by the
University Global Partnership
Network Research Collaboration Fund (UGPN)