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.