Over the last 20 years, cows in the UK have moved premises at a rate of one every seven seconds. How do I know this? Because since 1999 it has been a statutory requirement that every cattle movement be traced and stored electronically. As a researcher in infectious livestock disease, I have the privilege of being able to access this database.
Many diseases transmit from one animal to another through direct contact or sharing common pastures. When an animal is transported from one farm to another (often via a market) there is a risk that it may be taking the disease with it. In the early stages of an epidemic, severing these pathways of transmission is one of the simplest and most effective ways to contain the outbreak.
Knowing these cattle movements also allows us to investigate the influence of potential risk factors in the spread of livestock diseases. My colleagues at the Roslin Institute have used this data to explore the role of wildlife in the spread of bovine tuberculosis, for example, while others have studied the significance of sheep-to-cow transmission in foot-and-mouth disease (FMD). Personally, I am interested in the role of human behaviour, and the disease I study is Bovine Viral Diarrhoea (BVD).
BVD is a non-fatal disease that reduces milk production, weakens immune defences, and threatens the well-being of cattle. Unlike better known livestock diseases, it tends to fly under the radar. It does not transmit to humans, and its effect on the milk or beef quality is barely noticeable; if BVD is detected on a farm it will be thought of as a minor inconvenience rather a national emergency. Economically, however, it is one of the most burdensome diseases for the dairy industry and has been the target of many eradication campaigns. BVD has been eradicated in Switzerland, for example, thanks to extensive government funded testing and culling of infected animals.
In England, on the other hand, there are no enforced regulations restricting the management of BVD. While farmers have the option of committing to its eradication through schemes such as BVD-Free, they also retain the option to not do so and avoid investing time and money into something they may deem unnecessary. The dilemma confronting English cattle farmers is this: should I favour the short term benefit of the saved expense of BVD eradication schemes but possible disease burden, or should I favour the long term future benefits including the social good element?
Perhaps we can tackle BVD by nudging farmers towards more congenial behaviour. To do so would require a sensitive understanding of the personal and societal challenges faced by farmers and farming communities. It would also require some way to predict what the consequences of these nudges would be - this is where modelling can be useful. Modellers of infectious disease are well aware that tipping points do exist. A small decrease in vaccine coverage, for example, can lead to catastrophic epidemics. We are currently seeing a resurgence of measles precisely for this reason but we will talk about that later in this post
Our goal then, is to find out what incentives, financial or otherwise, it would take to push BVD from its current state in the UK: endemic and prevalent, to a situation where there is virtually no disease at all.
First we should acknowledge the complexity of this challenge; there is no reliable historical record of these kind of behavioural interventions, and we cannot observe this kind of behaviour in an experiment. Our analysis will instead be an exercise in imagining how individuals could behave when faced with the dilemmas that confront livestock farmers every day. In this post we will ask you to consider some of these choices and to think about what you would do. Our objectives are to understand how decisions are made in the real world, what it takes to make someone behave differently, and what the effect is of these behavioural changes on the farming community as a whole.
Suppose that you are a farmer. One day you want to buy a cow and there are two markets that you can attend - let’s call them A and B. In this hypothetical situation there are no circumstantial reasons to favour one over the other. You are aware that other farmers will also want to buy cattle and are faced with the same decision as you. To avoid overpaying for the cow, your goal is to choose the market that is chosen by the fewest other farmers (since having more potential buyers bumps up the price). What is the rational decision to make?
This is an example of what's known as the minority game - one of a number of ”games" that have been adopted to explore the relationship between behaviour and social, economic and political decision making. If you are unable to figure out the best strategy for playing the minority game, that is because there isn't one. To win the game you have to make a judgement about what the other players will do, while they in turn are making a judgement about what you will do. In the words of Brian Arthur, the originator of this game, it’s “a world of subjective beliefs, and subjective beliefs about subjective beliefs. Objective, well-defined, shared assumptions then cease to apply." .
Players of this game must rely on their memory of past outcomes to inform their decisions. Suppose the game is played many times in a row, the goal now is to try to anticipate what the majority will do based on what happened in previous rounds and make your decision accordingly. In one study, this iterative version of the game was played by 1000 automated players . Each one had a set of strategies they could potentially use, where a “strategy" here is simply a method of determining what their next move should be based on previous outcomes, and they would always play the strategy that experience tells them is most likely make them a winner.
Since the players are able to change strategies, as the game progresses we might expect them to steadily improve over time and eventually reveal what the optimal strategy is for this game. It turns out that this does not occur. In the study it was shown that an entire “ecosystem" of players can coexist; like in any predator-prey or resource-consumer system, the abundance of one type of individual can create opportunities for other types to take advantage. Some play unpredictably while others have a range of strategies to draw from, adapting to any situation. Others keep the same behaviour throughout the simulation . Diversity thrives.
In reality farmers don't have a binary choice but a choice of many suppliers to buy from, each with a different set of desirable qualities such as distance, breed, quality of stock, and, of course, the likelihood that the cattle are carrying some disease like BVD. The fact that we generally try to avoid infectious contact is a challenge for anyone trying to model and predict the progress of an epidemic. In addition to understanding how a disease can exploit a network of social, sexual, or commercial interactions, we must also try to understand how the network itself is shaped by individual awareness of the disease.
To introduce the work in this area we must first talk about how mathematicians model the spread of infectious disease. We (the mathematicians) usually think of a population of individuals, each one is in one of a number of states. In the simplest model they can be either susceptible or infected with respect to some disease. An individual in the susceptible state may transition to the infected state. The probability of this happening depends on the number of infected individuals already in the population at the time.
By asserting that the probability of becoming infected is dependent on the proportion of the population already infected, we have implicitly assumed that there is no variation in contact across the population. In reality there may be substantial distance between a susceptible individual and those who are infected. This is certainly the case when we consider the diseases that are spread through livestock trade - infected farms in the south west of Great Britain are not an immediate concern for farms in Scotland even though we might consider them to belong to the same population. For this reason, long distance trades substantially inflate disease risks. These connections can often have the property of increasing the likelihood of infection to previously unexposed regions, see for example the 2001 FMD epidemic in the UK.
For this class of problems as described above, the sub-field of network epidemiology exists. We (the network epidemiologists) usually start with some predetermined network structure, for example a social network of humans, or animals that have frequent physical contact with each other. Now the probability that an individual will transition from being susceptible to being infected depends only on the number of infected individuals that they are directly connected to in the network. Among many results from this field, perhaps the most significant is the revelation that highly connected individuals can disproportionately accelerate the spread of a disease.
Returning to the subject of awareness: the network epidemiology paradigm, as described above, considers a network that is fixed and unchanging despite a potentially deadly disease propagating through it. In the case of social networks, both humans and other animals are known to respond to the threat of infection with avoidance behaviour. We suspect that avoidance mechanisms might play a role in how farmers choose where to buy cattle from, this time driven by their concern for the well-being of their animals and by the financial losses that the disease may bring. What occurs as a result is a feedback loop: the network constantly adapts in response to the disease, while the disease propagates through the links of the network.
Is avoidance sufficient to prevent a small outbreak from becoming a large epidemic? It depends at least in part on the speed of the response. The mathematical biologist Thilo Gross, who was among theorist to consider this question, found that the factor that determines the fate of the population is the speed at which individuals sever connections with other people once they become infected. If people react quickly then only small outbreaks are possible, too slow and there is likely to be a large epidemic. In between he found a situation where the outcome is entirely unpredictable - healthy and endemic states can realised but it is random chance that determines which one .
Suppose again that you are a farmer. You have the option of joining a scheme such as BVDFree that gives you piece of mind that your farm is, indeed, free of BVD. To achieve this, however, there is a cost - you would need to vaccinate all new-born calves, test any cattle that you bring onto the farm, and cull any that tested positive for the disease. Now suppose that it’s not only you that faces this choice but every farmer in the country. Each of you must make a decision on whether to pay the costs of going BVD-free or to save your money and risk exposing your farm to the disease. What is the most prudent option?
This question has previously been asked in the context of vaccination uptake. In the early 2000s the percentage of parents giving the MMR vaccine to their kids was declining, not due to the actual risks of the vaccine, but due the perceived risks that were exacerbated by a now discredited study linking the vaccine to autism. Mathematicians Chris Bauch and David Earn asked how someone would decide whether to use the vaccine if all they are to consider is how dangerous they think it is, relative to the risk of being exposed to the disease . If the risk of vaccination is perceived to be sufficiently high, then it is possible that no members of the population will think it a good idea to vaccinate. To understand how this could happen, we can think of this problem as another version of the minority game. If everyone in the population chooses the vaccination option then a rogue player can win the game by doing the opposite, safe in the knowledge that the risk is minimal thanks to the cautious behaviour of others. If the majority choose not to vaccinate, then the risk of disease is high, and the preferred option is to vaccinate against the disease. The strategy with the smallest cost is the one that the minority of players choose.
While there are many obvious differences between an MMR vaccine and a BVD-free campaign, the same dilemma exists in both scenarios. The ideal situation in which everyone complies with the “social good" policy, whether it’s vaccinating their kids against measles or protecting their farm from BVD, inevitably creates the opportunity for some to take advantage. Currently the number of people ignoring the advice about vaccination appears to be sufficiently small, however, recent measles outbreaks have occurred in locations where a disproportionate number of people have refused to vaccinate. This may be a result of social influence. The theoretical work of Martial Ndeffo Mbah et al suggests that this may be a consequence of a social contagion of vaccine hesitancy .
At least with BVD we have enough information about the trading practices of each farm to predict the consequences of the risky decisions that farmers may make.
Putting the pieces together
Let us take all these ideas and combine them in one game: the BVD game. Each player takes the role of a farmer, each farm starts with a number of cows. They win money by selling cows to other farms. In each round of the game, a player can choose to buy cattle from any other player and sell them in later rounds. The price is determined by supply and demand; if many people all choose to buy from the same farm then more money will be exchanged for each cow bought and sold there. So far the game concerns only trade and market dynamics and is a version of the minority game - the goal is to avoid buying from the same source as everyone else*.
At the beginning of the game a number of cows are infected. When a player buys from a farm with BVD cows there is a chance they might purchase the sick ones. Additionally, cows are at risk of becoming infected if they live on the same farm as BVD infected animals; the more infected cows they live with, the higher the risk. Players lose money each round for every infected cow they own. To avoid bringing the disease onto their own farm, they may be averse to buying from farms that have a large presence of BVD. As disease spreads from farm to farm, we might expect to see the network of trading relationships adapt in response to the increased risks.
Finally we can introduce control schemes. We add in an extra option to pay a cost each round to remove all the BVD-infected animals from a player’s farm. This creates the dynamics of the vaccination game; if everyone adopts the scheme there will be a mutual benefit for everyone but also the opportunity to exploit other people’s cautious behaviour. Depending on the various costs in the game; the price of cattle, the losses incurred from infected cattle, and amount invested in biosecurity; we might expect to see a range of farmer behaviours and disease outcomes.
Although this imagined situation bears only an abstract resemblance to the real world, it focuses on the aspects of decision making that are difficult to analyse from any other angle. By putting ourselves into the game we can view risk-reward decisions from the perspective of the decision maker. By thinking in terms of strategies we can program computers to play this game for us, many times, and through adaptation discover how to minimise the decision makers’ costs. We can express the relationships between the variables as mathematical functions and derive answers to questions like; which strategies are stable and, which will produce chaos.
Ultimately, we want to know what incentives, financial or otherwise, it would take to push the disease towards eradication in the real world. We want to create an economic environment that: keeps cattle BVD-free and helps farmers resist the temptation to exploit the good behaviour of others; encourages quick response to and change their to reacting to another farm having BVD, and ; that is sensitive to the diversity of business models and the cultural circumstances that farmers operate in.
*This is actually more similar to the Kolkata Paise problem , an extension of the minority game that considers how people behave when there are many options with varying intrinsic attractiveness.
 W. B. Arthur, “Inductive reasoning and bounded rationality," The American economic review, vol. 84, no. 2, pp. 406 - 411, 1994.
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 C. T. Bauch and D. J. D. Earn, “Vaccination and the theory of games," Proceedings of the National Academy of Sciences, vol. 101, no. 36, pp. 13391 - 13394, 2004.
 M. L. Ndeffo Mbah, J. Liu, C. T. Bauch, Y. I. Tekel, J. Medlock, L. A. Meyers, and A. P. Galvani, “The impact of imitation on vaccination behaviour in social contact networks," PLOS Computational Biology, vol. 8, pp. 1- 10,04 2012.
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