# Externalities, contagious diseases and news

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## Abstract

This article discusses positive externalities and anti-rivalry, focusing on two examples: (a) Anything that could help control a contagious disease, and (b) News, especially regarding political corruption or anything else that could improve the productivity of the economy. A good has positive externalities if consumption by one benefits others. A good is anti-rivalrous if consumption by one makes it easier for another to consume it. For public health the economic question is to design public policy to minimize the present value of the disease burden in perpetuity at some reasonable discount rate. This suggests that the price to the consumer of a test, treatment, vaccine or other risk-reduction protocol for a contagious disease should be the maximum of (a) the marginal cost of producing an additional unit minus the benefit to others and (b) the minimum charge required to appropriately limit waste. Any patent royalties should be paid by taxpayers and should not be considered in the price to the consumer. Secondly, anyone who travels should be required to carry liability insurance to cover the losses suffered by others directly or indirectly infected from them. Consider smallpox eradication: In 1967 the global disease burden was estimated at $1.35 billion (USD) annually. The eradication effort cost a total of $300 million spread over 1967 to 1979. The US was the largest contributor to that eradication effort and has reportedly recouped its investment every 26 days since. For many other goods that improve public health, like diagnostic procedures to name only one, the marginal cost of an additional unit may be so low and the benefits so large that any group of countries representing some modest portion of the gross world product would be healthier and wealthier if they paid for the entire world. News also has positive externalities: If someone in power believes I may disseminate information on political corruption involving them, I could be killed like Jamal Khashoggi. I'm much healthier and wealthier if everyone else knows about that political corruption, because it's more likely to be fixed, whether I'm aware of it or not. Also, an obstacle to improving public health is that much of the money for many media organizations in the US comes from patent royalties, which gives the US media a conflict of interest in honestly discussing these issues.

## Introduction

Laurie Garrett (2000) wrote that public health is "a practical system ... rooted in two fundamental scientific tenets: the germ theory of disease and the understanding that preventing disease in the weakest elements of society ensured protection for the strongest (and richest)". She also reported that, "Vital statistics data from England, Wales, and Sweden show that in 1700 the average male lived just twenty-seven to thirty years. By 1971 male life expectancy reached seventy-five years. ... [In] the United States ... less than 4 percent of the total improvement in life expectancy since the 1700s can be attributed to twentieth century advances in medical care. It is a matter of considerable academic debate which factors were most responsible for the spectacular improvements in life expectancy and infant mortality seen in the United States and Western Europe between 1700 and 1900." Factors mentioned include improved sewers, clean water, education and government responses to epidemics. Even when direct access to improved sewers, clean water, education and government responses to epidemics is not universal, people who do not have such access may still benefit when diseases circulate less and other goods and services become easier to obtain. When that happens, the better sewers, water, education, and government response to epidemics carry positive externalities. But most of the innovations that contributed to those improvements in life expectancy "would have died in the cradle but for persuaders and activists who championed the innovation and policies", according to Pinker and Johnson. The dissemination of information that motivated those persuaders and activists carried huge positive externalities, benefitting people who may never have lifted a finger to obtain the improvements in health they enjoy as a result.
The present article starts by discussing positive externalities and the concept of rivalry in economics, including non-rivalry, and anti-rivalry. We then discuss how these concepts apply to news, especially about political corruption and research. The positive externalities from the eradication of a disease like smallpox can be enormous, benefitting every human living after the eradication. Public health systems for testing, diagnosing, tracking, treating, vaccinating for and limiting the transmission of infectious diseases also carry huge positive externalities, as explained herein.

## Externalities, Rivalry, non-rivalry, anti-rivalry

This section briefly reviews the concepts of externalities and rivalry in economics.
In economics, an externality is a cost or benefit for a third party who did not agree to it. Pollution is a negative externality.
A good in economics is called rivalrous if consumption by one precludes consumption by another. A standard example is an apple: If I eat one, you cannot eat the same one. We must produce another -- or split one, so we each eat different parts of the same apple. (In this article, we use the term "good" to include a service. For example, a haircut is rivalrous, because if I give you a haircut, I cannot give someone else the same haircut.)
Similarly a good is called non-rivalrous if consumption by one has no impact on the ability of another to consume the same good. An example is a radio or television broadcast: The consumption by one has no impact on the ability of another to consume the same broadcast.
There seems not to have been as much research on anti-rivalry, but it seems reasonable to say that a good is anti-rivalrous if consumption by one makes it easier for others to consume it. This allows us to think of rivalry as a continuum from competition to collaboration: We compete to obtain rivalrous goods. We collaborate with anti-rivalrous goods.
Languages are anti-rivalrous: When more people use a particular language, they develop more literature in that language, thereby making it easier to learn. Free and open-source software is similarly anti-rivalrous.
Nikander et al. claim that data may be anti-rivalrous. However, that may not be true if governments and major organizations use data secretly to harm their designated enemies and threaten democracy.
Efforts to combat climate change are reportedly perversely anti-rivalrous, because the countries that do not support the international efforts to combat this problem will continue to benefit from what others do without making any efforts to change themselves, unless other countries impose global warming Pigovian taxes on trade with countries that refuse to support international efforts to manage this problem.
Rivalry and externalities :
| | Externalities | Externalities | Externalities |
| | Negative | Negligible | Positive |
| Rivalrous | goods whose production or consumption pollutes the environment, e.g., fossil fuels; printed literature that is racist or inciting inappropriate violence | Organic food; printed literature that is entertaining | Vaccinations; printed literature that disseminates information on political corruption or technology for how to more easily produce goods with positive externalities. |
| Non-rivalrous | Spyware; computer viruses; broadcasts advocating racism and inciting inappropriate violence, e.g., Father Coughlin's radio broadcasts in the late 1930s and very early 1940s | Entertainment broadcasted or on the Internet (unless it helps people learn a language, in which case it's anti-rivalrous) | Broadcasts or web sites the distribute news that might help limit political corruption or help people learn how to more efficiently produce more goods with positive externalities. |
| Anti-rivalrous | Literature that is racist or inciting inappropriate violence that is freely available on the Internet that helps people learn a language or understand these alternative perspectives, e.g., Henry Ford's International Jew, Adolf Hitler's Mein Kampf. | Entertainment that is broadcasted or is free on the Internet that helps people learn a language. (NOTE: Such literature has some positive externalities but not as much as news and information on how to produce goods with positive externalities.) | Freely available historical literature that was used in the past to limit political corruption or promote public health or make people more productive; Free and open-source software (FOSS). |

## News about political corruption

News about political corruption is anti-rivalrous with positive externalities, because increased awareness of the details often leads to action reversing widely condemned cases while encouraging institutional reforms making similar instances of political corruption less frequent and costly in the future. When that happens, everyone benefits from the resulting positive externalities. Moreover the benefits are shared among people who did nothing to encourage reforms, making the access easily obtained, i.e., making the news that motivated such reforms anti-rivalrous.
McChesney and Nichols argued that the dominant position of the United State in today's international political economy is built in part on the US Postal Service Act of 1792. Under that act, newspapers were delivered up to 100 miles for a penny when first class postage was between 6 and 25 cents. That amounted to roughly 0.2 percent of national income (Gross Domestic Product, GDP), which corresponded to roughly $100 per person per year in 2012. Many if not all humans alive in the US today benefit from the improvements in literacy and limits on political corruption encouraged by nineteenth-century US newspapers: This provides positive externalities that are anti-rivalrous, because people in the US today benefit from the consumption by others in the nineteenth century without ever having accessed those newspapers themselves.
Benson and Powers (2011) surveyed the media in fifteen advanced industrialized democracies. Each had a mix of public and private media. They claimed that the public media tended to provide better coverage of news and public affairs than the commercial media, primarily because the public media had better firewalls that more effectively limited interference in the content by funders. Most had multi-year funding with oversight boards with only limited input from the current government in power. The US was the exception, whose per capita public spending is less than $4, far less than the $30 to $134 per capita for the other 14 countries examined in this study. Moreover funding for public broadcasting in the US is renewed every year, which made it the most susceptible to political interference in the content.

## Research publications

Publications advancing technology, especially regarding human health, are anti-rivalrous: Documents disseminating previous innovations in public health and health care have contributed to reducing the risks of disease and death for the vast majority of the world's population documented in Figures 1 and 2: People who have never read those documents live longer on average today because others inspired by those research reports took actions that benefitted many others.

## News and public health

The lines for Eastern Europe in Figures 1 and 2 show much slower progress in public health than the rest of the world. One possible explanation for this is that the press there has been more tightly controlled than in the rest of the world.
Similarly, it is striking that the US has lost the position it held in 1950 as one of the world leaders in life expectancy and infant mortality. Since then, Northern, Western, and Southern Europe along with Canada and Japan have improved faster. The slower rate of improvement in the US might be explained by differences in how the media in different countries are funded and governed.
Every media organization sells changes in audience behaviors to their funders, people who give them money. They all therefore have conflicts of interest in disseminating information that might offend a major funder. Benson and Powers (2011), mentioned above, note that the US has the weakest firewall between funding and content of any of the 15 advanced industrialized countries they studied. This means that media organizations in the US funded primarily by advertising must be more careful to avoid offending big pharma or the health insurance industry than their counterparts in other developed countries.
This difference could also explain the results displayed in Figure 3, that people without college degrees tend to be less well informed in the US than in the UK and Scandinavia.
The extent to which news can be anti-rivalrous is limited by constraints on funding. This suggests that the most anti-rivalrous funding structure may be something like that provided by the US Postal Service Act of 1792, mentioned above. Prior to the US Civil War, newspapers accepted advertising, but most of their funding came from readers, some directly, most indirectly in the form of the postal subsidies. After the US Civil War, advertising gradually became the primary source of funding for news in the US. To the extent that the improvements in public health documented in Figures 1 and 2 should be attributed to the media, this suggests that since World War II US media may have been more constrained than in other advanced industrialized countries that have more institutional restraints on political interference in editorial policies. (In the US, the reliance on advertising from major corporations limits media editorial independence, especially given the near elimination of investigative journalists by the major US broadcasters between 1975 and 2000 and the loss of 70 percent of advertising revenue by US newspapers since 2004, which led to a 50 percent reduction in newspaper journalists and the closure of a quarter of US newspapers.)
The quality of healthcare in Cuba is a contentious issue. People on the political left claim that the Cuban healthcare system is a model for the entire world, but others insist that data from a closed society like Communist Cuba are not to be trusted. However, if Garrett (2000, p. 10), cited above, is correct, no country need twenty-first century medicine to achieve life expectancy and infant mortality numbers like those in Figures 1 and 2: They only need to provide things like adequate nutrition, good sewers, and clean water to the poorest elements of society. To the extent that good sewers and water reduce the total disease burden of society, they are anti-rivalrous, because I'm unlikely to catch a contagious disease that few others have.

## Pricing anti-rivalrous goods

Public policy should minimize the present value of the disease burden in perpetuity at some reasonable discount rate. The optimal price to the consumer of a vaccine is often zero for two reasons: First, the benefits to everyone else (positive externalities) exceed the marginal cost of an additional unit of vaccine. Second, a negative price could mean paying people to get vaccinated, and that could create an industry of poor people being vaccinated multiple times. For most goods, reducing the price usually increases the demand. For anti-rivalrous goods, increasing the demand benefits society, even if the price to the consumer is less than the marginal cost of producing and distributing the good. For many such goods, the optimal price is zero.
A positive price for anti-rivalrous goods may be justified if they also have uses that are not anti-rivalrous like N95 respirators. The general rule is that you and I should be willing to subsidize consumption of goods by others whenever said consumption benefits us. With goods with multiple uses only some of which are anti-rivalrous, we'd ideally like to subsidize only those uses that have positive externalities. However, with some goods it may not be economically feasible to subsidize only some uses.
A mathematical framework for modeling both the benefits and the costs of producing and distributing such goods is outlined in a mathematical appendix at the end of this article. In this framework, any patent and copyright royalties should be combined with the fixed costs: Otherwise, they discourage uses that would benefit others.
With disease eradication programs, the benefits can potentially be huge. As discussed in the next section, everyone alive today pays nothing for the benefits they derive from the smallpox eradication program, which officially ended in 1979. We then consider other contagious diseases, then disease monitoring both for future previously unknown diseases like COVID was in mid-2020 and for sexually transmitted infections (STIs), then for face masks. We then briefly discuss requiring travelers to carry liability insurance for contagious diseases they may transmit with rates adjusted based on the available data on the documented effectiveness of the vaccines they've taken.

### Smallpox

One example of incredible anti-rivalry is the smallpox eradication program of the 1960s and 1970s. In the late 1960s the disease burden of smallpox was estimated at between 10 and 15 million cases costing roughly $1.35 billion (USD) annually in the losses from sickness and death plus the cost of vaccinating people. The eradication campaign spent roughly $23 million for each of the 13 years between 1967 and 1979 totalling $300 million. International donors provided $98 million, while $200 million came from the endemic countries.
The documentation I've seen of the smallpox eradication program does not mention any fee charged to those who were vaccinated, but it was presumably either zero or so low that the price was not a consideration for any of those vaccinated, especially in the latter stages of the campaign. If the price had been higher, fewer people would likely have been vaccinated when they did, which likely would have extended the duration and increased the total cost of the program. And they presumably did not pay people to get vaccinated, which could have generated a small industry of poor people getting vaccinated repeatedly for the money.
One important aspect of this for the present discussion is that everyone alive today benefits from that $300 million program that ended in 1979. We are not even asked to pay a penny for the benefits (positive externalities) we derive from that program. Some of us would not even be here. Some of us born before 1979 would have died from smallpox without it. Others born more recently not have been born, because one of their parents or grandparents would have died before they were conceived. The rest of us would have a shorter life expectancy and higher cost of health care, because of the cost of vaccinating and otherwise managing smallpox that were eliminated, presumably in perpetuity, by that program.
Similarly, any consortium of countries experiencing, e.g., 10 percent of that total annual cost of $1.35 billion could have paid the entire $300 million and gotten their money back every 2.22 years (= $300 million divided by 10 percent of $1.35 billion) in perpetuity. The United States, the largest contributor to the program, has reportedly recouped its investment every 26 days since in money not spent on (a) vaccinations and (b) the costs of incidence. If the US had paid the entire $300 million, they still would be getting an incredible return on that investment, ignoring the benefits to the rest of humanity.

### Other contagious diseases

A 2001 analysis of what the United States saves through standard childhood vaccinations estimated that, after the costs to deliver the vaccines, and the health care costs for the rare side effects that vaccines cause, society saves nearly $10 billion in direct medical costs, and $47 billion in indirect costs like lost worker productivity and permanent disability from disease; this was the total life cycle cost for all the children born in 2001 discounted at 3 percent. The US Gross Domestic Product in 2001 was $10.6 trillion with a population of 285 million. Thus, the dollar value of the anti-rivalry, positive externalities, of childhood vaccinates is roughly 0.5 percent of GDP ($57 / $10,600) and $200 per person ($57,000 / 285), not counting the increased costs to public health systems due to an epidemic or pandemic.
Other eradication programs are targeting polio, dracunculiasis (Guinea worm), yaws (caused by a spirochete similar to syphilis) and malaria. Obstacles to eradication include the need to (a) upgrade public health systems in poor countries to avoid diverting the few trained health workers from concerns that seem more pressing, and (b) guard against "reintroduction from areas where poverty, civil unrest, or lack of political will impede high vaccination coverage and sustain endemicity."
Western military activities and support for corrupt regimes in Muslim countries on top of the legacy of colonial domination have reportedly contributed to boycotts of the polio vaccine and spikes in cases in Afghanistan, Pakistan, Nigeria, Kenya, and elsewhere. An honest budget for the War in Afghanistan (2001–present) should include the negative externalities from the increased burden of disease in the US and its allies, whose military operations in Afghanistan and other support for political corruption in Muslim countries are reflected in the resistance to vaccination efforts.
Those obstacles to eradication seem likely to result from a general absence of quality news required to build a consensus for action against threats experienced by all, similar to the discussion with Figures 1 and 2 above that attributed limited progress in public health in Eastern Europe and the US to conflicts of interest in the mainstream media on those countries.
The anti-rivalrous nature of vaccines is implied by the concept of herd immunity: If everyone with whom I interact is vaccinated, I'm not likely to get a disease, even if I have not been vaccinated. Other public health measures like diagnostic testing and masks can be similarly anti-rivalrous.

### Disease testing

One of the major obstacles to managing COVID-19 has been the availability of tests, especially early in the pandemic. Before entering a retail outlet in the US in March 2021, a store employee took my temperature with a forehead scanner. I asked what it was: 70 °F (21 °C). That's Stage 3 hypothermia: I would have been unconscious or dead, not on my feet, trying to enter a retail outlet with that body temperature.
But a forehead fever thermometer is anti-rivalrous, because it reduces the risk of people being exposed to a disease when shopping -- and it would be even better if it were reasonably accurate!
Diagnostic procedures with less error usually (a) make it easier to identify and manage contagious individuals and (b) increase the value of contact tracing. Both of these tend to reduce the spread of the condition. In addition more accurate diagnostics make it easier to development vaccines, treatment modalities, and other procedures for managing the spread of a disease. When a person with a contagious condition is diagnosed, steps are usually taken to reduce the number of others who would likely catch that disease.
Even if an outbreak occurs on the other side of the planet, more accurate diagnosis and better control limits the spread and with it the chances that I will catch that disease. Better control also on average reduces disruptions to the economy from people not producing as much when sick. If the disruptions are large enough, they can reduce the availability of seemingly unrelated products (like toilet paper in the US early in the COVID-19 pandemic) and the cost of obtaining such. These positive externalities indicate that I would benefit from subsidizing the use of any such test procedure any place in the world if my subsidies sufficiently increased the use of better diagnostic procedures.
Some contagious diseases could be eradicated if anyone who didn't feel well had convenient access to a sufficiently accurate test. Such tests could help diagnose their condition and prescribe actions to maximize their rate of recovery while minimizing the chances of infecting others. This may not work if many people who are contagious are asymptomatic unless they are subjected to effective routine screening, e.g., when entering some public space like public transit, retail or office space.
There are in fact several research strains moving in this direction. Harvard Chemistry professor Whitesides predicts "Zero cost diagnostics" for almost any medical condition in the not-too-distant future. These predictions are based on rates of improvement comparable to Moore's law, which has described the doubling of the number of transistors in a microprocessor almost every two years since 1970; it is named after Gordon Moore, co-founder of Fairchild Semiconductor and Intel, who first predicted something like this in 1965.
Moore's law is a special case of experience curve effects, which is an empirical observation that each time the cumulative production of almost anything doubles, the unit cost drops by roughly a constant percentage, with the rate of improvement varying between products and industries. While it's not clear what determines this rate of improvement, it is clear that providing more money to fund research by competent experts tends to increase the rate of progress. Both the Salk and Sabin polio vaccines were funded by the March of Dimes, founded in 1938 as the National Foundation for Infantile Paralysis by Franklin D. Roosevelt, himself a polio victim and president of the US at that time. Twenty years later, two different vaccines were being administered worldwide and have since come close to eradicating polio.
Whitesides has proposed developing specially treated paper for low-cost diagnosis of health problems, analogous to litmus paper, which has been used for roughly 700 years to test acidity. Others are developing "lab-on-a-chip" devices. Both types of products hold the promise of rapid, low cost diagnosis of almost anything, including DNA sequencing of previously unknown pathogens for pennies. The genome for a single human could be sequenced in 2020 for $600, down from over $3 billion the first time it was done (1990-2003). A $100 genome is anticipated "soon"; a $10 genome is reportedly not far away. Harvard geneticist George Church predicated "one day sensors might 'sip the air' so that a genomic app on our phones can tell us if there’s a pathogen lurking in a room." The human genome has 3 billion letters but SARS-CoV-2 has only about 30,000 letters. This makes it much easier and cheaper to sequence something like a SARS-CoV-2 sample than the genome from an individual human. The widespread availability of relatively inexpensive sequencing has allowed researchers to monitor the evolution of SARS-CoV-2 essentially in real time.
Joseph DeRisi has developed a system called "IDseq" for "metagenomics", whose goal is to inventory all the viruses and living organisms in a sample of almost anything, e.g., bodily fluids or sewage. It does this by matching overlapping fragments of nucleotide sequences in the sample. The assembled genomes are then compared against a database of all the known sequences maintained by the National Center for Biotechnology Information (NCBI), part of the US government, to identify all known and previously unknown viruses and living organisms in the sample. This system has made major contributions to understanding many different diseases all over the world, including COVID.
The global burden from influenza might be dramatically reduced through low cost testing of domestic pigs and fowl. Aquatic birds are reportedly the primary reservoir of the influenza A virus, which is responsible for most cases of severe illness, epidemics and pandemics in humans. Influenza also circulates among mammals, especially pigs, which have often facilitated the transmission to humans.
Major obstacles to progress are sufficiently widespread understanding of (a) the benefits of research and (b) effective and efficient ways of managing research to benefit all.
A goal simpler than the universal diagnosis just mentioned might be reasonable diagnostics for known sexually transmitted infection (STI): We'd need something that could test for these conditions crudely like testing blood oxygen level or using saliva or some other body fluid, e.g., a drop of blood like a glucose test. If anyone could do it discreetly in the presence of a potential partner, that could become standard practice worldwide: When one partner tested positive, they might still engage in intimate behaviour that was not high risk.
Roughly 16 percent of the world population of 7.4 billion had a sexually transmitted infection other than HIV/AIDS in 2015. It may be worse in the US. A 2008 study by the US Centers for Disease Control and Prevention (CDC) reported that a quarter of US teenage girls have at least one of four infections monitored in the study.
Even people who are 100 percent monogamous would benefit from widely used and accurate test(s) for common STIs. Some partners are clandestinely unfaithful. Moreover, widespread use of such testing would reduce the likelihood that rape spreads STIs. This makes such testing substantively anti-rivalrous.

### Public health monitoring

Public health programs are anti-rivalrous, benefitting even people who are unaware of them. In December 2019, before anyone outside of China had heard of COVID-19, Charity Dean saw there was a major problem from her monitoring of internet traffic for key words. Dean was the number 2 public health official in California but was unable to convince her manager that there was a problem. Instead, her manager excluded her from key meetings, apparently believing that Dean's claims were a waste of her time. Eventually a couple of Silicon Valley executives got Dean's message through to Governor Newsom, who issued a stay-home order -- after COVID-19 was already a major problem in California. In 2020-09-28 O'Leary and Storey described how they could predict "the number of people in the USA who will become infected and die from the coronavirus" using "the number of Google searches, Twitter tweets, and Wikipedia page views". In fact this is a cheap way to monitor for all kinds of problems including emerging and evolving conflicts, natural disasters, and public health crises.
Public health officials in the US announced in August 2020 that they were creating a new tool called the "National Wastewater Surveillance System (NWSS)" that would "include a portal for state, tribal, local, and territorial health departments to share wastewater testing data, helping public health officials better understand community spread" of conditions like COVID-19. For that in particular, they are asking wastewater treatment facilities to test "sewage for RNA from SARS-CoV-2". With this they can model which strains are active where as well as the emergence of new strains.
The development in recent decades of electronic health records provide the promise of computer-assisted health care monitoring, suggesting additional tests and alternative therapies. They could also be used for public health monitoring and research. Unfortunately, there is a sad record of use by people in business and government to track and punish their perceived enemies. This has been countered in the past by an emphasis on privacy, protected in the US by the Health Insurance Portability and Accountability Act (HIPAA).
However, is Ed Snowden in Russia to avoid prosecution for exposing violations of US law by public officials? If that seems plausible, it suggests a need to change US law to make it harder for public officials to hide possible criminal activities, especially ones that the public would likely not support, with questionable claims of national security. Graves (2014) suggested we give every federal judge the authority to subpoena classified documents that may be relevant to a case in their jurisdiction and declassify them in whole or part if the judge believes the public interest is better served by openness, subject to appellate review of any declassification ruling. Currently, per the US Supreme Court decision in United States v. Reynolds (1953), no federal judge can question a claim of national security by a government official. Changing US law to overrule US v. Reynolds would have anti-rivalrous effects, including encouraging more complete and honest evaluation of questionable interference in foreign countries, like the killing of Osama bin Laden and four others of his household, without benefit of trial by jury, in a way that has had many other negative externalities, including slowing progress to the eradication of polio, mentioned earlier.

### Face masks

Face masks provide an interesting example of a product that can be used to limit the spread of contagious diseases. How should they be priced? The general rule for pricing mentioned above is the minimum of (a) the marginal cost of production minus the benefit to society and (b) a minimum charge required to limit waste. In this case, "waste" could include otherwise legitimate use in applications like painting or working in a dusty environment, which are not anti-rivalrous. The public should not be expected to pay patent royalties for uses that are not anti-rivalrous. For an outline of mathematical modeling for such applications, see the mathematical appendix at the end of this article.

### Vaccine hesitancy and liability insurance for contagious diseases

Ropeik said, "A 2008 study in Michigan found that areas with “exemption clusters” where more parents chose not to have their kids vaccinated were three times more likely to have outbreaks of pertussis than where vaccination rates matched the state average. ... A 2008 measles outbreak in San Diego triggered by an unvaccinated boy infected during a visit to Switzerland exposed 893 people... . Controlling the outbreak ... cost the community close to $900,000. A similar case that year in Tucson, Arizona, infected 14 people ... with measles. The outbreak cost two hospitals nearly $800,000, and tens of thousands more were spent by the state and local health departments to track down the cases, quarantine and treat the sick cases, and notify the thousands of people who might have been exposed." Ropeik concluded, "society has the right and responsibility to establish laws, regulations, and choice frameworks that discourage vaccine refusal. ... [V]accine refusal costs society billions of dollars, both in direct health care costs and indirectly in lost productivity and public health spending to curtail disease outbreaks. ... [I]n many communities, vaccination rates, particularly for children, have dropped below thresholds necessary to maintain herd immunity. ... A study in the United States found that in places where it is harder to opt out, fewer people do.
Becchetti and Salustri modeled disease progression in Italy with partial vaccination and concluded that herd immunity could not be reached with the prevailing rates of noncompliance with vaccines without vaccinating people under 16 years of age, though the stress on the existing hospital system could be substantially reduced.
A relatively simple solution to the problem of people refusing to get vaccinated might be to require the following:
    1. Everyone should purchase liability insurance for spreading contagious diseases to cover the losses from anyone who catches a contagious disease directly or indirectly from them.
       1.1. A simple formula might be to reduce the premium by a factor of (1-effectiveness) of a vaccine for those who are vaccinated. For example, the premium for a vaccine that is 95 percent effective should be 5 percent of the premium for someone who is not vaccinated. Similarly, the premium for a vaccine that is only 50 percent effective should be half that of the premium for someone who is not vaccinated. The premiums for both vaccinated and unvaccinated might be set to cover the cost of the burden of diseases covered including the cost of administering liability insurance for diseases acknowledge to be contagious.
       1.2. The insurance premium may also consider each individual's behavior patterns. For example, people may not have to buy the insurance unless they will be traveling to a place where the covered contagious disease may be more prevalent than it is where they currently reside and otherwise travel.
       1.3. For a disease that might plausibly be eradicated, some of the insurance premiums might be used to pay for a standard ring vaccination program as well as (a) research to facilitate understanding vaccine hesitancy, (b) appropriate action to challenge the official behaviors that contributed to the vaccination hesitancy like the fake hepatitis B immunization campaign that the US CIA used to confirm the residence of Osama bin Laden prior to killing him, and (c) public health campaign to make it easier to overcome vaccine hesitancy. After an eradication program has been declared successful, the insurance premium for that disease should drop to zero.
       1.4. This is similar to the liability insurance required to drive a car in many if not all countries in the world today. That insurance rate is higher for people in higher risk groups.
    2. Anyone with symptoms that could be due to a contagious disease should be legally required to consult a health care professional and enter quarantine if told to do so. The cost of the medical consultation, therapy and quarantine should be paid from the liability insurance for contagious diseases. This would include paying people for actual loss of income in quarantine by some formula that would be capped at some modest multiple of a prevailing minimum wage.
Requiring anyone with symptoms of a potentially contagious condition to seek medical attention and act according to the medical advice should reduce the transmission of disease by itself, thereby reducing the vaccination rate required to achieve herd immunity. It could also facilitate any eradication program.
Insurance payments for such a system could be based on actuarial calculations considering the evidence from research into which diseases are contagious. Contact tracing could identify several individuals as most likely for the outbreak and could estimate the proportion of the total burden of the outbreak that was most likely due to each individual using Bayesian inference. If more than one insurance carrier was involved, these estimated proportions could be used to allocate the total burden to the different insurance companies with no need to declare any one person as most likely responsible for the outbreak.
If you are fully vaccinated, you may get the insurance for free, paid by increasing the rates on others who are not vaccinated. If you have a condition for which certain vaccines are contra-indicated, e.g., egg allergies for vaccines produced using eggs, you may still get the insurance for free, with two stipulations: (i) Your condition is certified by a licensed medical practitioner as prescribed by law, and (ii) you comply fully with other regulations to minimize the communication of any disease you might catch, e.g., wearing an N95 or even an N99 mask in public and wearing disposable rubber gloves, which may also be provided to you for free in appropriate quantities with instructions on proper use. If you are caught not complying fully with appropriate public health measures, you can be required to pay the insurance plus a fine for noncompliance.
An insurance mandate of this nature could be introduced using a "fee and dividend" system that is revenue neutral or slightly beneficial for the poor and middle class, similar to carbon fee and dividend systems designed to increase the market prices for fossil fuels in a way that does not generate massive protests as happened in the UK, Mexico, France, Zimbabwe, Haiti, and elsewhere.
The main purpose of requiring liability insurance for contagious diseases is not to pay for the outbreaks but to help the public understand the following:
* Everyone benefits from others being vaccinated (and from others using other anti-rivalrous goods that can help control contagious diseases).
* You personally could become infected, be asymptomatic, and still be responsible for close family and associates getting sick and dying.
* Vaccines are never perfect.
This is similar to the malfunctioning forehead fever thermometer mentioned earlier: Part of the value (and in that case the only value) is to help people understand the potential impact of their actions on others.

### Vaccine cartel

Two-thirds of the epidemiologists surveyed in March 2021 thought that we had “a year or less before the virus mutates to the extent that the majority of first-generation vaccines are rendered ineffective and new or modified vaccines are required.” The mutation rate is proportional to the number of people who get the disease.
No vaccine is 100 percent effective. The effectiveness of the Pfizer and Moderna vaccines have been estimated at 90 percent. That means that in a group with some people vaccinated and some not, if 20 percent of unvaccinated people got sick, roughly 2 percent of the vaccinated got sick.
As strains develop that are resistant to a vaccine, they will increasingly threaten people who have been vaccinated. Thus, any limits on the production of vaccines increase the risks to everyone, even those already vaccinated. In particular, when distribution is limited by demands for patent royalties, it threatens the health of all. It's "penny wise and pound foolish" and will almost certainly lead to more deaths among those already vaccinated. The disease burden among people in the developed world could cost more than if they had paid reasonable patent royalties for the entire world and otherwise worked to increase the speed of distribution of the vaccines.
In this regard, it's good that the Biden administration announced May 5, 2021, that they would support "waiving intellectual property protections for coronavirus vaccines ... . The United States had been a major holdout at the World Trade Organization over a proposal to suspend some of the world economic body’s intellectual property protections, which could allow drugmakers across the globe access to the closely guarded trade secrets of how the viable vaccines have been made." Biden had previously been criticized for failing to support waiving patent royalties for coronavirus vaccines.
A couple of months earlier the Health Global Access Project (Health GAP) said that, "Expanding Vaccine Manufacturing Capacity Solely Within the Pharma Cartel is a Recipe for Perpetual Vaccine Apartheid and Artificial Scarcity". In an “unusual pact between fierce rivals”, J&J "will give Merck $268.8 million in U.S. taxpayer funding to use its capacity to manufacture J&J’s vaccine. ... Every country in the world is up in arms about inadequate supplies of COVID-19 vaccines. Rich countries had tried to ensure against delayed vaccinations by advance purchases ... . For the rest of the world, including 130 countries that as of last week had received no vaccines, artificially limited supplies means waiting in line for years, more deaths, more social and economic disruption, and development of more contagious and vaccine-resistant variants. It’s a recipe for a never-ending pandemic. The solution to the false supply scarcity should have been advance planning and early agreement to override patent protections ... . Instead vaccine monopolists schemed to maintain rigid control over supply, price, and distribution, both to increase profits and prioritize their monopolies at the risk of public health."
The vast majority of the costs associated with many patented products is in the research; the unit costs of production are often a very small part of the cost and can be made even smaller as the cumulative production increases. This increases the importance of considering having taxpayers pay any patent royalties for anti-rivalrous products and not requiring the end user to think about whether they should pay the higher cost.

## Cost and benefit

How much should countries spend on health? A 2003 discussion paper by William Savedoff for the World Health Organization notes that, "The range in per capita health spending across countries is larger than 100 to 1, and this translates into spending of anywhere between 1 percent to well over 10 percent of national income." Five percent of Gross Domestic Product (GDP) is mentioned as an unofficial target that has been used in some international comparisons and evaluations but was never officially approved. Savedoff mentioned a 1988 WHO resolution that does not mention 5 percent but does recommend taking action 'to reallocate existing resources more effectively, "reduce waste and increase efficient use of resources", etc.'
To the extent that the discussion with Figures 1 and 2 above is accurate, an important contributor to advances in public health is a free press with a substantive firewall between people with power and the editorial policies of the media, preferably with substantive citizen-directed subsidies for journalism. Subsidies like this were provided in early US history by the Postal Service Act of 1792, which was funded at roughly 0.2 percent of GDP. However, in the latter half of the nineteenth century, advertising gradually grew to represent roughly 10 times that to 2 percent of GDP, where it has been since the early twentieth century, swamping the postal subsidies.
With adequate limits on political corruption and malfeasance in government, it may then be worth reviewing the most recent Global Burden of Disease Study published by the World Health Organization (WHO). This methodology has been developed since 1990 to help guide public health investments in areas of greatest long-term need. In such studies, disease burden is often expressed in terms of Disability-adjusted life years (DALYs). DALYs can be expressed in US dollars (at Purchasing power parity, PPP) or any other currency by multiplying DALY components by the average annual income (Gross Domestic Product, GDP, per capita). However, investments even by poor countries should not be limited to selecting from currently existing options but should also consider investing in research to find lower cost and / or more effective approaches to these problems. Might we find other examples like the eradication of smallpox that could show massive returns on investments that are miniscule compared with the burden of disease? One example mentioned above might be improved diagnosis of sexually transmitted infections (STIs). Others might include health promotion and research to identify cost effective changes in health care for pregnant women and child care that could pay for themselves with a respectable interest after the children enter the workforce: Natural experiments in the US have documented a handsome return on investment from such interventions in terms of the increased taxes paid on increase income accompanied by reductions in the cost of health care and the crime rate.

## Policy implications

Knowledge is anti-rivarous, especially regarding how things work and how the public could get more from less. In particular, the following summarizes some of the most important implications of the discussion in this article:
* Citizen-directed subsidies for journalism could reduce political corruption and increase the rate of progress against many if not all of the problems facing humanity today. A reasonable target might be 2 percent of Gross Domestic Product (GDP), which is roughly what the US spent on advertising in the twentieth century and which overwhelmed the 0.2 percent of GDP devoted to newspaper subsidies under the US Postal Service Act of 1792. Two percent is also roughly what the US spends on accounting, including creative accounting, such as what contributed to infamous financial disasters such as the savings and loan crisis of the 1980s and 1990s and the Enron scandal of 2001. Two percent is also the average annual increase in productivity (GDP per capita adjusted for inflation) in the US between 1947 and 2019: We could pay for such citizen-directed subsidies from the increase on productivity from one year. More importantly, if the increased exposure of political corruption increases the rate of economic growth, which seems likely, these citizen-directed subsidies would soon become free, paid for from income we would not have without them.
* Future articles in refereed scientific journals should never be behind a paywall, because none of the research described in those articles is funded from copyrights, which means that paywalls are an obstacle to "the Progress of Science and useful Arts", which is the purpose of the Copyright Clause in the US Constitution.
* To the extent that the international pharmaceutical industry operates a vaccine cartel as suggested above, it should be broken using antitrust law.
* Other experiments should be conducted in funding research in ways that prohibit patenting the results and require all results of such publicly funded research to be placed in the public domain -- but only after adequate funding is provided for investigative journalism to limit wasting such research funding, as indicated above.
* Everyone should be required to purchase liability insurance for spreading contagious diseases with the rates adjusted based on their vaccination history, general health, location, and travel.

## Mathematical appendix

We consider the following in pricing:
* P = Price to the consumer.
* $V=V(P)$ = Volume of consumption at unit price P. V could be zero for sufficiently large P and could be unbounded for sufficiently negative P, i.e., when people are paid to consume the good. We expect $V(P)$ to be monotonically non-increasing in P.
* $B=B(V)=B(V(P))$ = The total (gross) benefits that others derive from consumption of one additional unit at consumption volume V. This could be zero when V is 0. We expect $B(V)$ to increase to a maximum then decline as additional consumption is diverted to applications that are not anti-rivalrous, e.g., with N95 face masks used to protect a person from breathing particles that are not contagious. If there is a maximum, it should be unique with the function non-decreasing prior to that maximum and non-increasing after the maximum.
* F = Fixed costs required to develop the product and associated production processes. This in theory could increase with V as people spend more money to develop more efficient production processes justified by large volumes of demand, but we will suppress those effects in this notation to simplify the discussion.
* $M=M(V)=M(V(P))$ = The marginal cost of producing and distributing an additional unit at volume V.
* $T=F+\sum _{v=1}^{V(P)}[M(v)-B(v)]$ = total cost to society at production volume V and price P.
We want to select P to minimize T. Equivalently, this would maximize the net benefits to others after subtracting fixed and total variable costs.
In many practical applications, it will be clear without a major empirical modelling effort that the benefits to society from someone consuming one additional unit, B, substantially exceeds the marginal cost of producing and distributing that unit, M. In such cases, the optimal price to the consumer, P, will be 0. This will not be true for goods like N95 respirators, which have uses that are not anti-rivalrous. For such products, it may be desirable to invest in more careful efforts to model B and M.