PS-FutureMathematical and Computational Methods for

Planning a Sustainable Future

Going BattyA Module in Planning for Sustainability

STUDENT EDITION

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DIMACS

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PS-Future Mathematical & Computational Methods for Planning a Sustainable Future

A Module in Planning for Sustainability STUDENT EDITION

Going Batty Modeling White Nose Syndrome in Bats

By David Black, The Groton School Dan Taylor, Bats International

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Going Batty: Modeling White Nose Syndrome in Bats A Module in Planning for Sustainability

What is sustainability?

The most frequently quoted definition related to sustainability is from the World Commission on Environment and Development’s 1987 report Our Common Future. It says, “Sustainable development is development that meets the needs of the present without compromising the ability of future generations to meet their own needs.”

At the heart of sustainability is the need to ensure the long-term persistence and vitality of both humans and the natural environment. Sustainability focuses on interactions between nature and society. These interactions are complex and do not abide disciplinary boundaries. They require understanding of physical and biological processes that are overlaid by human social, political, and economic concerns. A popular view is that sustainability balances on three pillars—environmental, social, and economic—and that failure or weakness of any one compromises future sustainability. To be sustainable, a practice must be environmentally, economically, and socially sustainable.

Sustainable behaviors and practices are those that can be continued (or sustained) indefinitely. To do this, they must balance limits imposed by human systems with those imposed by environmental ones.

What is planning for sustainability? Sustainability is forward-looking, and natural resources are finite. Planning for sustainability therefore involves making decisions about how we use limited resources in the light of the continuing future needs for those resources. Planning for sustainability seeks to identify practices that can continue indefinitely without critically damaging natural resources, people, or economies, especially those that are at risk.

While it is tempting (and simpler) to base decisions purely on their immediate economic impacts, doing so can easily overlook the long-term environmental (and social) consequences that can undermine sustainability. In planning for sustainability, it is important to consider that human economic and social systems exist within and are dependent on the environment. Decision makers need to identify how their choices impact both human and environmental systems, as well as whether such choices could persist indefinitely into the future.

Making complex decisions often involves the use of mathematical and computational methods to measure and model interconnected real-world systems. Planning for an unknown future heightens the need to use mathematical and computational methods to simulate, for example, the effect of choices within the context of a wide range of potential future scenarios.

It is especially important to note that planning for sustainability can be done at any level—global, national, municipal, or individual.

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1. Summary White nose syndrome (WNS), a disease caused by an introduced fungus, currently threatens the persistence of many species of bats across North America. At present, much about the disease remains a mystery. In this module, students will develop models to predict the persistence of individual bat populations across the landscape, as well as the possible extinction of certain species. 2. Overview Introductory Video:

Battle for Bats: Surviving White Nose Syndrome https://vimeo.com/76705033

We live in what geoscientists now refer to as the Anthropocene Epoch of the Cenozoic Era in the history of the Earth. It is a time when the world’s ecosystems are dominated by a single species, Homo sapiens, better known as humans. During this epoch, some species will thrive in the new environment while many others will disappear from the planet. Science writers, like best-selling author Elizabeth Kolbert, have characterized this as the sixth great extinction in the history of life. Many factors have caused an increase in extinctions, including habitat loss, overharvesting for subsistence and commercial markets, the introduction of new (i.e., invasive) species, pollution of the air and the water, and climate change, which interacts with and, in many cases, exacerbates the effects of these and other stressors. Globalization has changed the way that bacteria, viruses, and fungi move from place to place, bringing these disease-causing agents into contact with populations that had never encountered them before. In much the same way that human epidemics have wreaked havoc on humans over the millennia, ecologists are also studying how these new diseases have devastated populations of plants and animals in all corners of the world. For example, ecologists have found that chytrid fungus may result in the loss of many of the world’s amphibians (Vrendenburg et al. 2010). In this module, we will explore a disease caused by an introduced fungus that is devastating several species of North American bats. We will use various epidemic models to predict possible outcomes, including the loss of populations and extinction of species. 3. Introduction Diseases and epidemics have done much to shape our planet and have occupied the attention of scientists for millennia. The Black Death of the fourteenth century may have killed more than half of the population of Europe, smallpox wreaked havoc on the native populations of North America, and the great flu pandemic of 1918 killed far more people than the World War that was going on at the same time. In 2016, public health officials at the World Health Organization declared the Ebola epidemic to be over after more than 11,000 people had died from the disease. Despite such attention and study, concerns about pandemics persist, and the study of disease remains the focus of tremendous effort by epidemiologists working at public health agencies, hospitals, and universities worldwide.

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Disease also threatens biodiversity when bacteria, viruses, fungi, and protists attack a population. One such disease is White Nose Syndrome (WNS), which threatens to wipe out North American bats. In 2006, Alan Hicks, a wildlife biologist and mammal specialist at the U.S. Fish and Wildlife Service (FWS), discovered thousands of little brown bats (Myotis lucifugus) dead outside their hibernating caves and abandoned mines in New York State, with a whitish fungal growth on their muzzles. The fungus, Pseudogymnoascus destructans (Pd), was on bats as well as cave/mine surfaces and was determined to be growing in the soil of the bats’ hibernacula (hibernating sites). In Europe, however, microbiologists, veterinary pathologists, and wildlife researchers1 have not seen the fungus cause similar devastation. By early 2016, biologists and mycologists (scientists who specialize in the study of fungi) at the U.S. National Wildlife Services found that the fungus had spread north and northeast throughout much of New England and Eastern Canada and south and southwest through the mid-Atlantic, southern, and midwestern states, and as far west as Eastern Nebraska. In April 2016, the fungus was detected on a dead little brown bat found by hikers in Washington State, a jump of nearly 1,300 miles west (Figure 1). Since the appearance in 2006 of WNS, wildlife biologists estimate that it has killed more than 5,000,000 bats in North America.

1 www.ncbi.nlm.nih.gov/pmc/articles/PMC3298319/

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Figure 1. Spread of White Nose Syndrome in the United States as mapped by cartographers and

GIS analysts at wildlife agencies and organizations.

4. The Causative Agent, Pseudogymnoascus destructans Pseudogymnoascus destructans (Pd) is a psychrophilic (cold-loving) fungus with active growth limited to cool environments, between 0°C and 20°C, with optimal growth rates between 12.5°C and 15.8°C, and while it has not been supported by data from experiments conducted by lab scientists and lab technicians, anecdotally, the fungus appears to grow better at higher humidity levels. The fungus produces brown and grey colonies, secretes a brownish pigment, and reproduces asexually (sporulate) via characteristically curved conidia, specialized hyphal structures on which arthroconidia are formed and supported (Figure 2). The spores (arthroconidia) live and persist in caves and abandoned mines used as hibernacula for bats, but it can also live, grow, and sporulate asexually, perhaps for years, as a saprotroph on dead organic matter (e.g., wood, mushrooms, dead insects, etc.) in a host-free environment. Repopulating a WNS-affected cave with bats therefore has the potential to facilitate infection of the new colony. The spores can be carried on the fur of bats or other animals or on humans and their clothing or

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equipment. Microbiologists, veterinary pathologists, and wildlife researchers have also found Pd in Europe2 and, most recently, in China, but no large mortality events have been documented there. However, researchers have yet to determine why European (and Asian) bats do contract WNS but don’t die of it. The current Pd European distribution includes Austria, Belgium, Denmark, Estonia, Poland, France, Germany, Hungary, the Netherlands, Slovakia, Switzerland, Turkey, Ukraine, and the United Kingdom. Bats are not known and have never been documented to cross the Atlantic Ocean; therefore, it is hypothesized that humans, most likely cavers (spelunkers), carried the Pd fungal spores to the United States on their clothes or caving equipment. The subsequent spread of the spores, and associated WNS, closely matches the known migratory pathways of the affected bat species and is therefore considered “animal mediated” dispersal. The recent 1,500-mile jump to Washington State is also assumed to be human-mediated dispersal. Pd’s fungal hyphae invade the skin and wing membranes of hibernating bats when their immune response is greatly suppressed, leaving bats unable to adequately fight off the infection damaging their wings and their associated role in water balance and gas exchange. The fungus also causes frequent arousals from torpor, a metabolically expensive process that depletes the fat reserves bats need to survive until spring.

Figure 2. Structure of Pseudogymnoascus destructans

2 www.nature.com/articles/srep19829

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5. Effects on Bat Populations Seven bat species found in the eastern United States have suffered mortality due to WNS: the little brown bats, northern long-eared myotis (Myotis septentrionalis), tri-colored bat (Perimyotis subflavus), eastern small-footed myotis (Myotis leibii), Indiana myotis (Myotis sodalis), big brown bat (Eptesicus fuscus), gray bat (Myotis grisescens), with the first three suffering the greatest losses, and another, the southeastern myotis has tested positive for the fungus but has not been documented with WNS. Wildlife biologists estimate that more than 5,000,0000 bats have died since WNS was first detected in the United States. Losses of up to 99% of hibernating colonies have been reported for the little brown myotis. The devastation is so significant to the bat population that the U.S. Fish and Wildlife Service is considering listing the little brown myotis, once one of the most pervasive bats in the United States and Canada, as a threatened species. In 2016, the same agency added the northern long-eared bat to the list because of high recent mortality rates. 6. Effects on Ecosystems and Humans Fifty years ago, when bats were “ranked between rattlesnakes and cockroaches in a national public opinion poll, and traditional conservation organizations were avoiding them as hopelessly unpopular,” a small and diverse group of people, including a Milwaukee museum curator began to bring the public’s attention to the importance of bats for insect control.3 They worked to help the public understand that bats play a key role in ecosystems and are important to humans economically for the value that they provide our societies in controlling insect populations. Beyond this, many cultures embrace a species’ right to exist and argue for the preservation of biodiversity for its own sake. Bats may provide between $3.7 and $53 billion dollars in nontoxic pest control each year, with a single colony of big brown bats estimated to consume 1.3 million insect pests each year. Teams of entomologists, ecologists, and conservation biologists found that little brown bats can consume between 4 and 8 grams of insects each night, which suggests an annual reduction of up to 1,320 metric tons of insects removed because of population losses attributable to WNS (Boyles et al. 2011). Of the 47 species of bats known from the United States and Canada, three pollinate and disperse the seeds of agave, saguaro, and other columnar cactus in the desert southwest, while the other 44 species are insectivores, able to consume on average 25% to 100% of their body weight in insects nightly. Research conducted by ecologists, conservation biologists, and entomologists from Boston University and the University of Illinois have demonstrated that predation by bats on moths, beetles, flies, cicadas, and hemipterans (true bugs) saves the U.S. agriculture industry, especially corn and cotton crops, more than $3 billion annually. One little brown myotis can consume between four and eight grams of insects nightly. With several million little brown bats lost to WNS, insect predation has been reduced by more than 1,300 metric tons in areas impacted by WNS. Not only are bats worth millions of dollars in ecosystem services in the form of pest control, this service reduces the amount of pesticides necessary, keeping often harmful chemicals out of our air, water, and food chain. While bats are commonly touted as being nature’s mosquito 3 www.merlintuttle.com/what-is-mtbc/history/

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control system, research indicates that mosquitoes make up only a small portion of the diet of most North American bats, though one study in an experimental setting showed that predation by northern long-eared bats, one of the species most heavily impacted by WNS, significantly reduced the number of eggs laid by mosquitoes. Given the role of mosquitoes as vectors of human diseases such as the Zika and West Nile viruses, some public health officials are encouraging the use of bats in their efforts to mitigate the frequency and transmission of these diseases.4 Studying how WNS, the mortality rate of bats, and pest control interact is one example of a cycle called ecosystem services. Understanding ecosystem services is an important step in learning about sustainability. In 2005, ecologists, botanists, and agriculture scientists from across the world collaborated to publish the United Nations’ Millennium Ecosystem Assessment (MEA), which assessed human interaction with the environment. The MEA report popularized the concept of ecosystem services, which can be broken into four categories: provisioning services, regulating services, cultural services, and supporting services.5 Provisioning services are benefits humans can take from nature, such as water, fruit, timber, and so on. Regulating services are benefits that naturally moderate a natural process, such as pollination, water purification, and erosion prevention. Cultural services are benefits that are nonmaterial, such as recreation or religious and spiritual benefits. Supporting services, which enable each of the other services to occur, sustain the natural process, such as photosynthesis and the water cycle.6 Each category provides a different reason for conservation. Agricultural economists, wildlife botanists, epidemiologists, anthropologists, and policy makers focus on the role of bats and biodiversity conservation as tools of providing ecosystem services, of preserving the environment for sustainability of human communities. Ecosystem services is an anthropocentric, or human-based, perspective on the importance of protecting and preserving the environment. As discussed above, bats play an essential role in pest control and disease prevention, which is why protecting them is important to our society. Another argument in support of preserving bat populations is that there are ethical reasons to protect nonhuman life, for its own inherent value, often referred to as the “biocentric” approach or perspective. With this perspective, nature does not exist simply to be used or consumed by humans; rather, humans are simply one species, not inherently better than any other, and all species have equal intrinsic value. While the anthropocentric and biocentric perspectives are not mutually exclusive, a potential pitfall of taking a wholly anthropocentric approach to the conservation of biodiversity is that there are organisms that it may be difficult or impossible to assign an economic value to and, therefore, it will be difficult to justify their conservation. 4 https://thinkprogress.org/climate-change-bats-and-zika-2016s-weirdest-relationship-5e44aaaf084/ 5 https://en.wikipedia.org/wiki/Ecosystem_services 6 https://www.nwf.org/Wildlife/Wildlife-Conservation/Ecosystem-Services.aspx

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7. Classroom Activity 1: The Biology of an Epidemic (student handout attached) Epidemiologists have been studying disease for at least three millennia and have worked to understand how a disease will run its course through a population. An understanding of disease is predicated on the use of a mathematical model. This model assumes that there is an infecting agent (usually a bacterium, virus, fungus, or protist) and a host (whatever gets sick) and that they interact in a defined environment. In this activity, students will model an epidemiological study to explore the most important variables that determine how a disease will affect the host population. Each student will receive a badge holder that contains three cards showing which state he or she is in. Susceptible (S): has not been exposed to the disease

• Infected (I): has been exposed to the disease and is now sick (note that it is possible to be exposed and not to get sick)

• Recovered (R): has been infected, has recovered, and can no longer be infected A student may also be “dead” in which case he or she will leave the area. Each student will also carry a 10-sided die. These are rolled to determine if a susceptible person becomes infected upon exposure and if an infected person stays infected, recovers, or dies. Prior to each round, we will set three critical parameters:

1. Probability of infection 2. Probability of recovery 3. Probability of death

Rules of the Game:

1. Begin by making sure that your tag has the “S” (Susceptible/Yellow) sign showing. 2. Each turn, you may move into any empty square within two spots of where you are

standing. 3. If you are “Susceptible” and are within two squares of an infected person (“I”/Red), roll

the die. If the value is less than or equal to the “probability of infection,” change your tag to “I”.

4. If you are “Infected” throw the die. If the value is less than or equal to the “probability of recovery” value, change your tag to “R”. Otherwise, throw the die a second time; if the value is less than or equal to the “probability of death,” sit on the bottom step.

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Plotting the Data:

Access the Google sheet using the link provided, and download this onto your device. There is much data on this spreadsheet and we can make several graphs to explore the changes in the different scenarios. We will produce three separate graphs, each showing the change in the numbers of susceptible, infected, and recovered individuals. To begin, we will produce these graphs on the paper provided. Upon completion of the exercise, answer the following questions working as a group:

1. Produce a line graph showing the changes in each of the three populations (S, I, and R) over the 20 rounds in each scenario.

2. How does the number of susceptible people change over time and what variables in the model most affect this change?

3. Discuss three factors that might affect an individual’s probability of infection. 4. Over time, what will happen to each of the three groups if no individuals are introduced

to the population?

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Scenario:

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Scenario:

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Scenario:

8. Classroom Activity 2: Exploring Epidemics with an Agent-based Model Agent-based modeling extends the type of exercise that we just completed and allows for many different scenarios to be run quickly and efficiently. For this exercise, we will use the NetLogo programming language, which is freely available. The code required for these models is straightforward; however, we will use a model that has already been developed that will allow us to vary the parameters of a disease and explore the patterns that appear under different scenarios. 1. Download NetLogo from this site: http://ccl.northwestern.edu/netlogo/download.shtml 2. Go to the “File” heading, select “Models Library,” select “Biology,” and double-click on

“Virus.”

If there are problems with this download, this model can also be run in most browsers: http://netlogoweb.org/launch#http://netlogoweb.org/assets/modelslib/Sample%20Models/

Biology/Virus.nlogo. 3. Click on the “setup” button and click on “go.” Leave the other values unchanged and observe

the changes in the three populations.

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4. Alter the values of the “infectiousness” and the “chance-recover” sliders and answer the

following questions:

a. This model looks at death a bit differently. You define the “duration” of the disease and if a person has not recovered within that period, the person dies. Change the values of “duration” and discuss how a long duration may not only increase the chances of a person surviving but also increase the number of infections.

b. In this model, new people are added to the population up to a maximum number

(in this case, 300). Explain why the addition of these new people can allow for a disease to persist in a population indefinitely. .

c. Work to set the variables in the model so that the disease disappears from the

population completely. Note the values of the parameters that you used and explain how the disease could reappear in the future.

9. Classroom Activity 3: Building the WNS SIR Model (S for the number susceptible, I for the number of infectious, and R for the number recovered)

Researchers use other types of models to predict outbreaks and to explore different strategies for managing an outbreak. But we will construct a simple model of a WNS outbreak that we can use

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to determine the probability of a colony’s survival under varying conditions. In order to do this, we will create variables that we can manipulate so that we can look at the probability of infection, the probability of recovery, and the probability of death. We will assume that the probability of infection depends to some extent on the density of the population, although, as we will discuss, this may not be a valid assumption. As we have discussed, it is also unclear whether bats develop resistance or if there are some bats that are more naturally resistant to the fungus. Building the Spreadsheet Model: In preparation for building your model, answer the following questions: 1. Write out the mathematical equations for the change to each of the groups (SIRD) at each time

interval, using the rates of change variables that we have discussed (probability of infection, probability of recovery, probability of death) in Table 1. For example:

Number of Susceptible Individuals Time 2 = Number of Susceptible Individuals Time 1 – (Probability of Infection * Number of Susceptible Individuals Time 1)

or

Table 1. SIR equations for the WNS analysis

S2 = S1 – (PI * S1)

I2 =

R2 =

D2 =

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The Spreadsheet: 1. Working with a partner, launch the spreadsheet program on your computer. 2. Create an “Input table” in the first two columns of your spreadsheet. The first column should

contain the variables that you will use, and the second should contain boxes into which different values can be inserted (Figure 3).

Figure 3. Input Table for WNS Analysis

3. Beginning with the first row of the fourth column, add row headings to show the total

population size (N), the number susceptible (PS), the number infected (PI), the number recovered (PR), and the number dead (Figure 4).

Figure 4. Columns showing population change over time

4. Now things get more challenging. We would like to have your spreadsheet calculate the

changing values over time under different scenarios. Entering equations into spreadsheet cells generally begins by putting an “equals” sign into the cell (“=”). You then need to tell the spreadsheet where to look for the values that it needs to calculate the change over time. This is shown in Figure 5, with the colors in the equation corresponding to the highlighted colors in the cells.

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Figure 5. Entering SIR equations into the spreadsheet

5. Enter the equations that you created in Table 1 into the second row of values. We will use the

fill down command to track the changes in the numbers of the groups over time. 6. When the values are filled in, insert a line graph showing the changes in each of the three

groups over time. Different programs do this in slightly different ways; however, in most cases selecting the three columns (PS, PI, PR) and using the “insert chart” command will produce the results that we want.

Questions: 1. After the winter break, students return to school infected with many different viruses. While

the population is healthy for the first few days, within a week many are coughing and sneezing. Plot the course of a virus that has a 50% chance of infection, an 80% chance of recovery, and a 0.01% chance of death. Several students decide to attach hand sanitizer to their bags; what part of the model are they trying to manipulate? How do eating a good breakfast and getting enough sleep affect the progress of the disease?

2. White nose syndrome is causing tremendous concerns among conservation biologists and

others charged with protecting natural resources and biodiversity. Using your model as the basis of your analysis, what characteristics of bats and disease make this disease so devastating?

3. Assuming that we have little control over the development of resistance, what steps could be

taken to increase the chances of bats persisting in the future? 4. With WNS, there appears to be a high probability of death, and this will result in smaller

populations. Discuss one way that this could lead to the persistence of bats over time, again looking at the parameters of your model.

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10. Looking at Possible Solutions Because Pd appears to be able to persist in suitable environments for long periods of time without its host and because its host is cryptic, gregarious, and highly mobile, Pd continues to spread rapidly. The primary actions taken to date to slow its spread have focused on preventing human-mediated dispersal by restricting access to caves and abandoned mines within and adjacent to the range of the disease and by developing and requiring decontamination procedures for those who do enter underground habitats. These procedures involve some combination of washing clothing or equipment that may have come in contact with the fungus at high temperatures, or treating them with a liquid fungicide, such as a dilute bleach solution. One challenge of coming up with an antifungal, decontamination procedure that actually kills or reduces the density of Pd in the hibernacula environment and on the infected bats themselves is that it must also be harmless against non-target organisms in natural cave ecosystems. Fortunately, there has been recent progress in that direction, with natural microbes occurring both in the soil and on a bat’s skin. Recent studies have shown that mammals, including humans, have a natural external microbial community that acts as a first line of defense against pathogens. Researchers at the University of New Mexico found that microbes called Actinobacteria, from the skin of some bat species, produce chemicals that act as antifungals, and may represent a natural defense system against Pd. Ten of these bacteria, all Streptomyces species (the same bacteria used to produce antibiotics for strep throat) appear to inhibit the growth of Pd. Researchers at the University of Georgia have found similar results with a soil bacterium, Rhodococcus, which has actually been shown to inhibit the growth of the fungus and prevent the spores from germinating, without actually touching infected bats or the cave soil but just by being placed in close proximity. Additional research and questions must be answered before any of these treatments can be put into practice, such as how they will be produced in large quantities; how they will be applied; and how they will impact other bats, organisms, and the cave environment, but they at least offer a glimmer of hope in stopping the spread of WNS. Questions: 1. In a time when resources are limited, people working to protect bats have limited resources.

Explain why mathematical models are important in making the decision about whether to focus on controlling the spread of Pd to new caves or on the development of treatments that will reduce the lethality of the syndrome.

2. Could you make an economic argument for the government’s taking action on both types of

possible approaches? Are there other actions that you would suggest to reduce the impact of the disease?

3. In many parts of the United States, a debate rages about vaccinations. Some people are

concerned about possible health problems associated with vaccines (although these have largely been shown not to exist) and choose not to vaccinate their children. Using the SIR approach, discuss why certain disease outbreaks are becoming more common in communities with a large portion of vaccinated children for the first time in decades.

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“Going Batty” Glossary bats’ hibernacula bats’ hibernating sites ecosystem services the many and varied benefits that humans and other animals freely gain from the natural environment and from properly functioning ecosytems hyphae long tubular structures resembling garden hoses. They have rigid cell walls that may be reinforced by perforated cross-walls called septa. Hyphae absorb nutrients from the environment and transport them to other parts of the thallus (fungus body). They may become bound together or modified to form more complex structures. infected affected with a disease-causing organism mycologists scientists who specialize in the study of fungi population a group of individuals taken from the general population who share a common characteristic, from which samples are drawn to study a disease, for example probability a measure of the likelihood an event will occur; mathematically, it is the number of occurrences of the event divided by the total number of possible outcomes Pseudogymnoascus destructans (Pd) is a psychrophilic (cold-loving) fungus with active growth limited to cool environments susceptible likely or liable to be influenced or harmed by a particular thing white nose syndrome (WNS) a disease caused by an introduced fungus, which currently threatens the persistence of many species of bats across North America WNS SIR model a model consisting of three compartments: S for the number susceptible, I for the number of infectious, and R for the number recovered (or immune), and which is reasonably predictive for infectious diseases that are transmitted from bats to bats, and where recovery confers lasting resistance

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11. Literature Cited and Additional Resources Boyles, J. G., Cryan, P. M., McCracken, G. F., Kunz, T. H. 2011. The economic value of bats. Science 332: 41– 42. www.biologicaldiversity.org/campaigns/bat_crisis_white-nose_syndrome/pdfs/Boyles2011EconomicsofBats.pdf. Langwig, K. E., Frick, W. F., Reynolds, R., Parise, K. L., Drees, K. P., Hoyt, J. R., Cheng, T. L., Kunz, T. H., Foster J. T., Kilpatrick, A. M. 2015. Host and pathogen ecology drive the seasonal

dynamics of a fungal disease, white-nose syndrome. Proc. R. Soc. B 282: 20142335. Reeder, D. M., Frank, C. L., Turner, G. G., Meteyer, C. U., Kurta, A., Britzke, E. R. 2012. Frequent arousal from hibernation linked to severity of infection and mortality in bats with

white-nose syndrome. PLoS ONE, 7, e38920. Tuttle, M. D. 2006. Bats, artificial roosts, and mosquito control. Bat Conservation International.

www.batcon.org/pdfs/bathouses/MosquitoControl.pdf. Verant, M. L., Boyles, J. G., Waldrep Jr., W., Wibbelt, G., Blehert, D. S. 2012. Temperature-dependent growth of Geomyces destructans, the fungus that causes bat white-nose

syndrome. PLoS ONE, 7, e46280. General Resources www.whitenosesyndrome.org/ The WNS page maintained by the U.S. Fish and Wildlife Service, the federal agency coordinating the national WNS response. www.batcon.org/wns Bat Conservation International’s white-nose syndrome page. https://caves.org/WNS/ The National Speleological Society’s WNS page. Videos Battle for Bats: Surviving White Nose Syndrome

https://vimeo.com/76705033 Smithsonian Channel: What Is White Nose Syndrome? www.smithsonianchannel.com/videos/what-is-white-nose-syndrome/20456

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Epidemics and White Nose Syndrome Name_______________________________ Classroom Activity 1 Upon completion of the exercise, answer the following questions working as a group:

1. Produce a line graph showing the changes in each of the three populations (S, I, and R) over the 20 rounds in each scenario.

Scenario:

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Scenario:

Scenario:

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2. How does the number of susceptible people change over time and what variables in the model most affect this change?

3. Discuss three factors that might affect an individual’s probability of infection.

4. Over time, what will happen to each of the three groups if no individuals are introduced to the population?

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Epidemics and White Nose Syndrome Name_______________________________ Classroom Activity 2 1. Download NetLogo from this site: http://ccl.northwestern.edu/netlogo/download.shtml. 2. Go to the “File” heading, select “Models Library,” select “Virus,” and double-click on “Disease.”

If there are problems with this download, this model can also be run in most browsers: http://netlogoweb.org/launch#http://netlogoweb.org/assets/modelslib/Sample%20Models/Biology/Virus.nlogo.

3. Click on the “setup” button and click on “go.” Leave the other values unchanged and observe the changes in the three populations. 4. Alter the values of the “infectiousness” and the “chance-recover” sliders and answer the questions below:

a. This model looks at death a bit differently. You define the “duration” of the disease and if a person has not recovered within that period, he or she dies. Change the values of “duration” and discuss how a long duration may increase not only the chances of a person surviving but also the number of infections.

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b. In this model, new people are added to the population up to a maximum number (in this

case, 300). Explain why the addition of these new people can allow for a disease to persist in a population indefinitely.

c. Work to set the variables in the model so that the disease disappears from the population completely. Note the values of the parameters that you used and explain how the disease could reappear in the future.

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Epidemics and White Nose Syndrome Name_______________________________ Classroom Activity 3 Use your model to predict the outcome of a new outbreak of WNS in a cave system. Assume that the probability of infection is 0.9, the probability of death is 0.3, and the probability of recovery is 0.05. 1. After the winter break, students return to school infected with many different viruses. While

the population is healthy for the first few days, within a week many are coughing and sneezing. Plot the course of a virus that has a 50% chance of infection, an 80% chance of recovery, and a 0.01% chance of death. Several students decide to attach hand sanitizer to their bags; what part of the model are they trying to manipulate? How do eating a good breakfast and getting enough sleep affect the progress of the disease?

2. White nose syndrome is causing tremendous concerns among conservation biologists and

others charged with protecting natural resources and biodiversity. Using your model as the basis of your analysis, what characteristics of bats and disease make this disease so devastating?

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3. Assuming that we have little control over the development of resistance, what steps could be

taken to increase the chances of bats persisting in the future? 4. With WNS, there appears to be a high probability of death, and this will result in smaller

populations. Discuss one way that this could lead to the persistence of bats over time, again looking at the parameters of your model.

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Epidemics and White Nose Syndrome Name_______________________________ Final Questions 1. In a time when resources are limited, people working to protect bats have limited resources.

Explain why mathematical models are important in making the decision about whether to focus on controlling the spread of Pd to new caves or on the development of treatments that will reduce the lethality of the syndrome.

2. Could you make an economic argument for the government’s taking action on both types of

possible approaches? Are there other actions that you would suggest to reduce the impact of the disease?

3. In many parts of the United States, a debate rages about vaccinations. Some people are

concerned about possible health problems associated with vaccines (although these have largely been shown not to exist) and choose not to vaccinate their children. Using the SIR approach, discuss why certain disease outbreaks are becoming more common in communities with a large portion of vaccinated children for the first time in decades.