Correspondence author
Dr. Joaquín M Prada
Email: j.prada@surrey.ac.uk
Summary
Vampire bat-transmitted rabies has recently become the leading cause of
rabies mortality in both humans and livestock in Latin America.
Evaluating risk of transmission from bats to other animal species has
thus become a priority in the region. An integrated bat-rabies dynamic
modeling framework quantifying spillover risk to cattle farms was
developed. The model is spatially explicit, and is calibrated to the
state of São Paulo, using real roost and farm locations. Roosts and
farms characteristics, as well as environmental data through ecological
niche model, are used to modulate rabies transmission. Interventions in
roosts (such as culling or vaccination) and in farms (vaccination) where
considered as control strategies implemented to reduce risk. Both
interventions significantly reduce the number of outbreaks in farms and
disease spread (based on distance from source), with control in roosts
being a significantly better intervention. High risk areas where also
identified, which can support ongoing programs, leading to more
effective control interventions.
keywords: bat rabies, infectious disease transmission, mathematical
model, spillover
Introduction
Bats have long been associated with highly pathogenic zoonoses affecting
domestic animal and human hosts (van Brussel and Holmes, 2022). Despite
attempts to understand cross-species pathogen transmission from
reservoir hosts to recipient hosts, there are still gaps in knowledge
regarding the environmental conditions and mechanisms necessary for
spillover events to occur (Ruiz-Averna et al., 2021).
In Latin America, vampire-bat-driven rabies (VBR) has come to attention
as both an underappreciated and growing threat (Benavides et al., 2016),
and is now the leading cause of both human and livestock rabies
mortality in Latin America (Benavides et al., 2020; Horta et al., 2022).
VBR is responsible for substantial agricultural and subsequent monetary
losses, disproportionately affecting resource-poor farming communities
that depend on agricultural economy (Benavides et al., 2017). It has
been recently estimated that tens of thousands of livestock die of VBR
annually, corresponding to financial losses between 30 to 50 million USD
in the region (Benavides et al., 2020; Bakker et al., 2019). VBR is a
member of the Lyssavirus genus; and similar to other
lyssaviruses, disease pathology is marked by acute fatal encephalitis
(Banyard et al., 2011; Rupprecht et al., 2017). Of the three species of
hematophagous bats, Desmodus rotundus (Chiroptera:
Phyllostomidae) is the most abundant and prefers to feed on livestock
blood (Kuzmin & Rupprecht, 2015; Horta et al., 2022); this preference
displays the species ability to adapt to anthropogenic ecological
changes as it is believed during the pre-Columbian era D.
rotundus fed upon large terrestrial mammals (Rocha et al. 2020).
Instead of being negatively impacted by urbanization, deforestation, and
a resultant decrease in wild prey, D. rotundus adapted to the new
food sources resulting in an artificially high population (Delpietro et
al. 1992; Rocha et al., 2020). The population changes might have
implications for disease dynamics.
Mathematical modeling has been used extensively to understand spread
dynamics and improve surveillance and control strategies for many
infectious diseases (Grassly and Fraser, 2008; Chowell et al., 2016;
Dorratoltaj et al., 2017; Bornaa et al., 2020). Several frameworks have
been proposed to model the dynamics of rabies transmission, approaching
the problem from different perspectives (Dimitrov et al., 2007;
Blackwood et al., 2013; Ruan, 2017; Gentles et al., 2020; Dias and
Ulloa-Stanojlovic, 2021). Here we present a stochastic network model
designed to capture the spatial heterogeneity of VBR transmission
between known bat roosts in the state of São Paulo, Brazil, and
spillover events into the local cattle farms. We explore the effect of
different combinations of current reactive interventions, namely
vaccination of cattle in confirmed VBR positive farms and other nearby
farms, and vampire bat roost control in surrounding areas (Rocha and
Dias, 2020). Currently, as a roost control, Warfarin is applied on the
back of the captured vampire bats as anticoagulant paste that is spread
between bats by themselves during socializing and grooming, they
subsequently die of hemorrhage (Rocha et al., 2020). Both ethical and
scientific arguments exist against bat culling (Olival, 2016). Moreover,
indiscriminate culling may lead to social disruptions in the roosts,
which facilitates pathogen spread (Benavides et al., 2020; Rocha and
Dias, 2020). As a less controversial alternative and arguably more
effective, spreadable vaccine may be administrated in a similar manner
(Standing et al., 2017; Bakker et al., 2019; Griffiths et al., 2022).
Risk maps for each combination of current control measures used in the
area of interest, the state of São Paulo, Brazil, are provided.
Materials and methods
Study area and databases
A mathematical modeling framework was developed that broadly represents
disease dynamics of VBR transmitted between D. rotundus roosts
and cattle farms within the state of São Paulo, Brazil. Data on bats and
roosts ecology, have been generated from long-term studies carried out
in the state of São Paulo, Brazil, for the past 20 years (Rocha et al.,
2020; Rocha and Dias, 2020). The data on roosts and farms used in this
study were collated from the surveillance survey carried out in
2017-2018 by the Coordenadoria de Defesa Agropecuária (CDA), the São
Paulo State animal health service. The data contain information such as
location (municipality, latitude and longitude coordinates, elevation),
information about the farms (number of cattle), and roosts
specifications (roost types with information about population
demographics) on 132,787 farms and 5,170 roosts in São Paulo. The roosts
were categorized as either “harems”, if occupied mostly by females and
pups; “bachelor”, if dominated by young males; “overnight” if it is
only a transit location to rest during foraging and digestion; and
“empty” if the location is never occupied by vampire bats (Rocha and
Dias, 2020). Cattle farm locations were obtained from the Ministry of
Agriculture and Livestock. The farms with no cattle (50,556 farms), as
well as empty and overnight roosts (971 roosts), were removed from the
data set, as this study focuses on infection spillover exclusively to
cattle and it is believed that the empty and overnight roosts contribute
negligibly to rabies transmission. After data cleaning and data quality
control checks (i.e. correcting longitude/latitude entry errors where
possible, and removing data where it is not possible to correct the
entry errors, along with removing of duplicated or incomplete records;
6,956 farms and 32 roots removed), our modeling simulations were carried
out on 4,167 bat roosts (2,186 bachelors and1,981 harems) and 75,275
cattle farms (Figure 1).
Model description
We have developed a stochastic network two-species metapopulation model,
linking bat populations (roosts) to cattle populations (farms), through
a discrete-time state-based Markov-chain model. The state of each
population (roost or farm) changes at every discrete daily time step in
a probabilistic manner according to a set of rules, see Model details in
Supporting Information.
We consider two possible states for the roosts, and three possible
states for the farms, Figure 2A. A roost is defined as susceptible,SR , when rabies is not present and infectious,IR , otherwise, i.e. when there is at least one
infectious bat in the roost, hence the infection spread from the roost
is possible. Susceptible roosts become infectious by interacting with an
infectious roost and can recover (i.e. become susceptible again) after a
period of time (Table 1 and Recovery in Supporting Information).
Similarly, a farm is susceptible, SF , if there
is no infected cattle animal with rabies. Farms where an animal is
infected by a bat from an infectious roost become exposed,EF , with infection present, but undetected. The
detection time period is drawn from lognormal distribution for
the farm once its status changed from susceptible to exposed. After this
time to detection has past, the infection can be detected in the farm,
and thus the farm will be considered infected,IF (Table 1, Detection time period in farms in
Supporting Information, and Supporting Information Figure S1). A farm
with a detected infection can recover and become susceptible again
(Figure 2A, Table 1, and Recovery in Supporting Information).
Roosts can be composed of young males (i.e. a bachelor roost,
RB) or be female dominated (i.e. a harem roost,
RH). We assume the driver of rabies transmission are the
bachelor roosts, such that bachelors can transmit and acquire the
infection from other roosts (bachelor or harem), while the harems can
only acquire and transmit the infection to bachelors, as male bats are
generally the ones traveling between bachelors and harems (Streicker et
al., 2016; Becker et al., 2020). The recovery rate differ between
bachelor and harem as the longevity of male and female bats differ
(Figure 2B, Table 1 and Recovery in Supporting Information). Roost sizes
are assumed to be fixed and relatively small (20 individuals in bachelor
roosts, 100 in harems), in line with the data collected in the region
(Rocha et al., 2020).
The populations, roosts and farms, are connected through a distance
based contact network, assumed to be time-invariant (Rocha and Dias,
2020). Only contacts that could lead to disease transmission are
considered, such as interactions between two roosts representing males
competing for access to females or to roosts with females, i.e.
male-driven transmission, or between a roost and a farm representing
bats feeding on cattle, expressed by the edges in the network. The
transmission is limited up to 10 kilometers flight distance (Benavides
at al., 2016). The bats are expected to feed only in farms at a lower
altitude than their roost (Rocha et al., 2020), thus spillover events
are limited by this in the model as well. Contacts between two farms
were not considered, transmission usually occurs via a bite or scratch
of an infected bat, consequently, rabies transmission between farms via
movement of infected animals is highly unlikely (Network in Supporting
Information, and Supporting Information Figure S2).
The risk of rabies virus transmission depends on spatial interactions
subjected to a gravity model. The probability of bat movement decreases
with longer distance to minimize spent energy, however increases with
higher number of bats within the roost, harems in our model, as they may
fly to further distance due to increased competition, and the roosts
with more individuals attract more bats contacts (Spatial interaction in
Supporting Information). Within-population dynamics are not considered.
We assume that the between-roost transmission risk is further modified
according to the environmental drivers of location suitability of both
roosts; vegetation, elevation, temperature, precipitation, and night
time light. These environmental data on roosts were used to calculate
suitability indexes by ecological niche model (ENM) (Ecological niche
model in Supporting Information, and Supporting Information Figure S3)
(Anderson, 2013; Owens et al., 2013; Soberón and Peterson, 2005). The
more suitable locations of roosts are expected to attract more bats. The
edges in the network are weighted by the risk of rabies virus
transmission and between two roosts also by their average environment
suitability, where the edges does not exist as described above, i.e. the
risk of transmission is negligible, it is expressed as zero weight of
the edge (Network weights in Supporting Information). The network
weights drive the probability of transmission. The probability of a
susceptible population to become infectious or exposed, if it is a roost
or a farm, respectively, depends on the sum of the weights of all edges
connecting the population with an infectious roost (Probability of
status changes due to bats behavior in Supporting Information).
We considered two possible rabies interventions in the model: A reactive
vaccination of animals in the infected premise, and all surrounding
farms in a 10 km radius; and/or a reactive roost control in the
surrounding area within a 10 km radius from the infected premise, see
Supporting Information Figure S4 for model schematic for the
transmission of bat rabies virus between bat roosts and cattle farms
including both interventions.
The reactive vaccination of farms is modeled as providing immunity to
all farms vaccinated for a year (viz., 365 days). During this time, the
vaccinated farms cannot be infected. After a year, the farm looses the
immunity, it will likely be susceptible, however, if the farm was
vaccinated while already exposed to infection, but not detected, the
farm might be still exposed or infected. If there is a new outbreak in
10 km radius from the vaccinated farm, and it is more than a half of
year (viz., 182 days) since last vaccination, the animals on the farm
are re-vaccinated.
The roost control is currently based on the administration of a warfarin
paste in the back of the captured vampire bats so that during social
grooming conspecifics ingest the paste and indistinctly die of hemorrhage
(Rocha et al., 2020; Rocha and Dias, 2020). Such roost control results
in the death of nearly all vampire bats in the roost (Linhart et al.,
1972), hence we assume that it leads to an empty roost, which likely
will not be repopulated for a long time, and will not contribute to the
virus transmission until is repopulated. Under the assumption of at
least one year of immunity, and as a result, prevention of the roost to
contribute to transmission, the spreadable vaccine can be considered as
a roost control as well (Standing et al., 2017; Bakker et al., 2019).
Consequently, for the purposes of modeling the roost control for one
year, we assume that if a roost receives an intervention (culling or
vaccination), all transmission ceases. To account for a reduced
infection pressure when roosts are controlled, we assumed an increased
recovery rate for farms when the roost control is carried out (Table 1).
Table 1 Summary of model parameters.