Black Death in Modern Times: Assessing Spread and Potential Impact

Introduction

The topic that I chose was how the bubonic plague would spread if there was a modern-day pandemic. I chose this exploration because the bubonic plague interests me. I learned in history class about the Black Death, which wiped out around two-thirds of the world’s population during the fourteenth century (Benedictow). I wanted to know if it was possible for the bubonic plague to spread and be fatal to that degree during modern times. I have always been interested in diseases, and this gives me the perfect opportunity to look into something I am interested in. The bubonic plague was spread by fleas that had been infected by Yersinia pestis (Plague). Typically, a person who is infected wouldn’t know for about one to seven days (Plague). This allows the disease to grow and spread in the lymph nodes of the human host’s body, which could go to the lungs and kill the person (Plague). When the host has the pneumonic plague, they can spread it to the people around them. In this exploration, the math that can be used is probability, mainly conditional probability, expected value, and tree diagrams. This math can be used because I will be tracking the spread of the disease from host to host.

Body

Spread Dynamics

The Bubonic Plague is caused by the bacteria Yersinia Pestis, which is transferred by rodents or fleas (Plague). In my exploration, I am saying that there is no way to prevent the plague, such as pest control or a vaccine. Pest control would lessen the chances of fleas and rats being able to be in close proximity to people. The vaccine or other ways of treatment also need to be taken out of the equation because I am just focusing on how fast the plague could spread without those factors. I will be using New Mexico as the place for which I will be infected. New Mexico is one of the common places in the United States where the plague can occur (‘FAQ | Plague | CDC.’).

Rodents carry fleas, which can then be transferred to people. Around 63% of cases of the plague in New Mexico come directly from flea bites (PLAGUE IN NEW MEXICO ). This leaves 37% that come from other sources. The other sources can include fluids from an infected animal, being scratched, and inhaling droplets from an animal or person with pneumonic plague (PLAGUE IN NEW MEXICO ). Mexico has a population of about 2,090,708 people (‘World Population Review’). The equation that represents how many people are affected by rodents in New Mexico is y=(x100)2090708. In this equation, y is the number of people who have a rodent problem, and x is the average percentage of people who have rodent problems. I can use this equation and make a table out of it to see how many people could be affected by rats. The equation is only good when 0X100. This is because there cannot be negative people, and there cannot be more people than there already are.

Potential Impact and Mortality

Having rat problems potentially exposes people to fleas, which can carry the Yersinia Pestis bacteria, which is the cause of the Bubonic Plague. The probability of getting the plague directly from a flea bite is 63% or .63 (PLAGUE IN NEW MEXICO). If someone has a rodent problem, it can be assumed that the fleas will eventually change what they host and jump to other mammals in the household. The probability of getting the plague from anything but a direct flea bite is 37% or .37 (PLAGUE IN NEW MEXICO). A tree diagram can be used to potentially show how a family of four could possibly become infected.

From the diagram, we can see that the probability of all four people getting infected from a flea bite is .15752961. The probability of all four getting infected from anything but a flea bite is .01874161. Most people appear to get the plague from a flea bite rather than by other forms of transmission. For the next part, I will focus on how people could get infected just by getting bitten by fleas.

If the person has a dog or cat, the fleas will use the dog or cat as a host as well as people. The American Veterinary Medical Association states that “New Mexico ranks second in the nation for pet ownership with 67.6 percent of the state’s households owning a pet” (Gerew). The fleas could spread the bacteria from rat to cat or dog to human. Cats and dogs have an average of twenty fleas but can have up to 200 or 300, but 150 is a high amount (“How Many Fleas Can Live on a Cat or Dog?”). Since 300 is the maximum amount of fleas, the denominator for probability has to be 300. So the P(fleas on the cat) = 115 and the P(fleas on the dog)=115.

The probability is 115 because that is what 20300 is reduced to. Since 67.6% of people in New Mexico have pets, we can multiply the total population of New Mexico by .676, which is 67.6% in decimal form. So .6762090708=1413318.608, and since it is not a full person, I will round up; this means that 1413319 people in New Mexico will have pets. Since the average number of fleas on dogs and cats is 20 (“How Many Fleas Can Live on a Cat or Dog?”), This means that there is a 120 chance of a flea jumping onto a human from a dog or cat. With this information, I can make an expected value chart.

The expected value for the future is 143.5 or 2872 when you add the X P(X) column together. In the future, there could be more than 20 fleas on a person at once. I can also use the numbers with fleas and pets to do conditional probability.
PFleas|Has Pets=PFleasPetsPPets
PFleas=120
P(Pets)=.676
P(Fleas Pets)=1695000
PFleas|Has Pets=(169/5000).676
PFleas|Has Pets=.05

There is a 5% that a person will have at least one flea jump onto them given that they have pets. In New Mexico, 33105 species of fleas have been found to carry the Yersinia Pestis bacteria (PLAGUE IN NEW MEXICO). Based on my findings above, I can multiply 5% by the species of fleas ( .0533105=11700 ) to find out the chance of someone getting bitten by a flea that can carry the bacteria, which is a 1.57% chance. Out of the 1413319 people who have pets, 1.57% will get bitten by a flea that carries the bacteria; this is 141331911700=22209.29857, and it has to be rounded up to 22210.
In relation to rodents with fleas, 29% of people will have a rodent problem (“Of Mice and Men”). Using the earlier equation, y=(x100)2090708, I can plug in 29 as X. (29100)2090708=606305.32. There would be 606306 people in New Mexico that would have rodents in their homes. On average, each rat will carry 4.1 fleas (Frye); there is a 14 chance of the fleas jumping into people. Conditional probability can also be used here to find the percentage of people who will get bitten by fleas, given that they have a rodent problem.

PFleas|Has Rodents=PFleasRodentsPRodents
PFleas=14
P(Rodents)=.29
P(Fleas Rodents)=29400
PFleas|Has Rodents=(29/400).29
PFleas|Has Rodents=.25

Given the calculations, 25% of these people who have rodent problems will have been bitten by a flea. Since 33105 species carry the bacteria, I can multiply the number of people who have rodents by 25%, then multiply that number by 33105 to find the number of people who could get the plague just from having rodent problems.

606306.25=151576.5rounded up, that is 151577 people who will get bitten by a flea if they have a rodent problem. I can then take the 151577 people and multiply that by the number of fleas that carry the bacteria to find the number of people who will have the bacteria. 15157733105=47638.48571rounded up, this is 47639 people. Adding this number to the people who have pets and could get infected, 47639+22210=69849 people will get infected directly from a flea bite. The bubonic plague, if left untreated, is deadly about 50% of the time (PLAGUE IN NEW MEXICO). Taking the number of people infected by flea bites and multiplying by 50% or .50, 69849.50=34924.5rounded up is 34925 people will die of the plague just from getting bitten by a flea if they have a rodent problem or pets.

Conclusion

The Bubonic Plague is notorious for having been the cause of death for millions in Europe when an outbreak occurred in the fourteenth century (Benedictow). I decided that I wanted to find out whether or not the plague could be that deadly in modern times. To do this, I used New Mexico and used probability to find out the numbers. I used a tree diagram to show the different ways a small family could get the plague and the probability of each way; I used expected value as well as conditional probability. From my calculations, I have found out that the bubonic plague could come back, just not as deadly as it once had been. Only 34,925 people out of the 2,090,708 people in New Mexico would die from the bubonic plague; this is 1.67% of the population, which is not close to the 60% of the population that died in the fourteenth century (Benedictow). In conclusion, the bubonic plague currently will never be as bad as it was in the fourteenth century.

References

1. Benedictow, Ole Jørgen. “The Black Death: The Greatest Catastrophe Ever.” History Today, vol. 63, no. 3, 2013, pp. 2-8.
2. Gerew, Sam. “New Mexico Ranks Second in the Nation for Pet Ownership.” KVIA, 4 Nov. 2019, https://kvia.com/news/new-mexico/2019/11/04/new-mexico-ranks-second-in-the-nation-for-pet-ownership/.
3. Frye, Matt. “Fleas on Rats and Cats.” Pest Control Daily, 18 Feb. 2022, https://pestcontroldaily.com/fleas-on-rats-cats/.
4. “How Many Fleas Can Live on a Cat or Dog?” PetMD, 11 Mar. 2020, https://www.petmd.com/dog/general-health/how-many-fleas-can-live-cat-or-dog.
5. “PLAGUE IN NEW MEXICO.” New Mexico Department of Health, https://www.nmhealth.org/about/erd/ideb/zdp/plg/.
6. “World Population Review.” World Population Review, https://worldpopulationreview.com/states.