By Lina Sorg
Vampire bats are leaf-nosed bats that live in Latin America, between northern Mexico and the northern parts of Chile, Argentina, and Uruguay (see Figure 1). The bats get their distinctive name from their sole food source: the blood of other mammals. In fact, they consume one blood meal per day that amounts to their entire body weight. They reside in colonies of 20 to 1,000 individuals, have a slow reproduction cycle in that females typically give birth to only one pup per year, and can live for up to 15 years.
Figure 1. Vampire bats reside in Latin America and can transmit the rabies virus to both livestock and humans in the region by feasting on mammalian blood. Public domain image.
Some vampire bats carry the rabies virus (RABV). Infected bats spread RABV to other animals via
inter-species transmission when their saliva comes into direct contact with a victim’s broken skin during the feeding process. In
intra-species transmission, one bat passes RABV to another when engaging in aggressive fighting behavior that causes saliva to enter an open wound, eye, or mucus membrane. Rabies is responsible for roughly 100,000 livestock deaths in Latin America each year, which amounts to approximately 30 million USD. In the last 60 years, it has also led to nearly 700 human fatalities. Once a rabies infection establishes itself in a human, there is no known treatment or cure.2
When farmers in Latin America discover RABV infections amongst their livestock, they sometimes destroy the nearest bat colonies or apply a poisonous paste called “vampiricide” to captured bats, which then inadvertently spread the poison to other bats during the grooming process. Existing control efforts for RABV currently employ no spatial coordination; instead, highly responsive and reactive actions prevail. During the 10th International Congress on Industrial and Applied Mathematics, which is currently taking place in Tokyo, Japan, Julie Blackwood of Williams College integrated data and modeling techniques to better understand RABV transmission dynamics in vampire bat colonies and ultimately bring a sense of control to the problem.
Blackwood’s colleague spent four consecutive summers in Peru where he sampled vampire bats, tested them for rabies exposure, and collected the resulting data. The team found that rabies persistence within colonies remained relatively constant each year, with a 10.8 percent seroprevalence level (the amount of the population that tested positive based on blood serum samples). However, all of the bats that were exposed to rabies do not necessarily die. Some remain asymptomatic, acquire temporary immunity, and make a full recovery because the virus never reaches the central nervous system. Given that conventional wisdom about RABV suggests a very high mortality rate, the constant underlying seroprevalence in vampire bat colonies is somewhat unexpected.
Figure 2. Compartmental model that describes the transmission dynamics of rabies within vampire bat colonies in Latin America. Figure courtesy of Julie Blackwood.
To understand rabies’ persistence in bat populations, Blackwood built a model that describes the transmission dynamics within a colony (see Figure 2). Susceptible \((S)\) bats become exposed \((E)\) to rabies at some rate \(\lambda\), at which point they either develop an active infection \(I_N\) or enter the temporary immune class \(T\). Bats in the \(T\) compartment recover and return to \(S\), whereas RABV-infected bats in compartment \(I_N\) eventually move to \(I_R\) with no chance of recovery. Blackwood noted that her group’s samples from Peru fall into either \(T\), \(I_N\), or \(I_R\), though the data does not differentiate between these three classes.
After acknowledging several unknowns in the model—including transmission rate, lethal transmission probability, and transmission due to immigration of bats between colonies—Blackwood utilized a method called likelihood via particle filtering. This technique simulates the model to replicate field data, then allows users to sample the model much like how one would sample directly from the field. For any given parameter set, Blackwood can simulate the model at different time points and randomly sample bats to learn their class and determine the proportion of the population that is either immune or infected.
Blackwood’s model revealed that high levels of immigration and a low lethal infection probability are key to RABV seroprevalence and population longevity within a bat colony. Contrary to previous studies and general assumptions about rabies, only about 10 percent of exposures are lethal. This rate—combined with a significant amount of immigration between colonies—ensures that the virus does not die out.
The realization that lethal infection probability is significantly lower than expected has potential implications in laboratory design and the dosing of lab bats. Blackwood concluded by mentioning that randomly culling bats—as many farmers do to prevent the spread of rabies amongst their livestock—has a negligible effect on seroprevalence and may actually cause it to increase because the bats will interact and immigrate between colonies even more than usual. She is particularly interested in the spatial coordination of control efforts and is using this study to motivate her ongoing work in ecological systems with applications to disease.
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Lina Sorg is the managing editor of SIAM News. |