Fifth Blog Post

Networks and Epidemic Models

Keeling, M. J., & Eames, K. T. (2005). Networks and epidemic models. Journal of the Royal Society Interface, 2(4), 295-307.

This journal is written by Matt J. Kneeling and Ken T.D Eames. It begins by discussing the standard epidemic theory, which is a mathematical theory that I am familiar with from other journals. This journal quotes another journal that I have read, which I thought was pretty cool. Specifically, this talks about the SIR model and SIS model. The SIR model is used within diseases that result in lifelong immunity, like measles; whereas the SIS model is used for diseases where repeat infections are common, like sexually transmitted diseases. These models are based on the assumption that the population mixes at random, where each individual has an equal chance of coming into contact with another individual. This is not truly accurate, however, because individuals typically have a certain set of individuals that they are most likely to come into contact with. The random-mixing assumption is avoiding by assigning individuals to a finite set of contacts with which they can infect/become infected by. This seems to be more accurate. This journal then goes on to describe the standard network theory, something I was not already aware of. This section also cites another journal that I have read. The journal states how it is important to determine a complete mixing network, but that this is rather time consuming. It is also very difficult to sample an entire population, and even if the entire population is sampled, not everyone will be willing to give up truthful information. It is also to important which contacts are capable of disease transfer, something that is also difficult to measure. Different infections require different levels of contact. The journal uses the example of the flu versus something like an STD. This is something that seems obvious, but something that I overlooked. The journal then goes on to discuss main techniques that have been used to gather network information, and then describe each in detail. These techniques include infection tracing, complete contact tracing, and diary-based studies. It then goes on to discuss different types of networks which include random networks, lattices, small-world networks, spatial networks, scale-free networks, and exponential random graph models. These networks are defined by how individuals are distributed in space and how connections are formed. At the end of the journal, it discusses the future and how future advances will help determine networks. A specific example is the future of GPS tracking. Due to GPS, it may be possible in the future to accurately track people’s movement. This would make it possible to build a full networks for airborne diseases. I think this is really cool.

Fourth Blog Post

Thucydides and the Plague of Athens

Poole, J. C. F., & Holladay, A. J. (1979). Thucydides and the Plague of Athens. The Classical Quarterly, 29(2), 282-300.

This journal was written in 1979 by A. J. Holladay and J. C. F. Poole, and it discusses the Plague of Athens. The Plague of Athens is considered to be the first recorded epidemic. Thucydides recorded the symptoms and severity of the disease which caused this mysterious plague. The journal begins by discussing the concept of a disease, which is something that is necessary to understand. If a certain amount of people in a similar region are suffering from similar symptoms, it is possible that they are suffering from the same disease. This is something that is relevant to our paper. It also states that diseases are named by classifying illnesses, which is something that is subject to change as there are advances in the medical field. This is important to know because people can be experiencing similar symptoms and have two different diseases. This is also important to note because the symptoms that Thucydides described could be that of a modern illness, but without a modern physician examining the ancient patients, it is not possible to truly know. The journal then goes on to discuss how bacteria and viruses undergo evolution and can change over time. It notes that many infectious diseases have tended to become less severe over time, in part due to improved living conditions and medical advances. Also, a disease that quickly kills its host it less likely to infect another individual than a disease that infects its host for a more prolonged period of time. This is something that seems to be common sense, but it is something I would not have thought to mention in our paper. With all of this being said, it is almost impossible for modern scientists to identify what disease caused the Plague of Athens, which is why it still remains a mystery. The journal offers a few suggestions for specific diseases and then goes on to describe them in detail. The diseases mentioned are smallpox, bubonic plague, scarlet fever, measles, typhus fever, typhoid fever, and ergotism. It is also suggested that the Plague of Athens was due to the spread of multiple diseases at one time. In conclusion, it states that there is no one simple answer to the mystery of the Plague. The Plague of Athens is important to our paper in the fact that it was the first recorded epidemic, but the mystery surrounding what disease caused it is not relevant to our paper whatsoever. However, this journal was very interesting to read and did provide some background information that will be useful in our paper.

Third Blog Post (#2)

Third blog post

Spread of epidemic disease on networks

Newman, M. E. (2002). Spread of epidemic disease on networks. Physical review E, 66(1), 016128.

In the introduction, it states that diseases spread among humans via contact between infected and susceptible individuals. This is a common statement that I have heard repeatedly throughout my research, which is why I am making sure to include it in our paper. Also in the introduction, it suggests that these contacts form a network and that the goal of this paper is to look at the effects of these networks on the rate and pattern of disease spread. This is based on the assumption that it is equally likely for an infected individual to infect any member of the population which they belong too. This is also something I have heard repeatedly throughout research. This paper also offers a definition for epidemic, “outbreaks that affect a nonzero fraction of the population in the limit of large system size.” However, it does not give a definition for large system size. It states how it is rather obvious that an individual does not have an equal probability of infecting everyone else in a population, due to the fact that most individuals only have contact with a small fraction of the total population. This is something important that I think we should note in our paper. The focus of this paper is the class of susceptible/infective/removed (SIR) models. Susceptible refers to individuals who are able to contract the disease, infective refers to individuals who are infected by the disease and are able to infect others, and removed refers to individuals who are dead or immune to the disease by being previously infected and recovered. The paper also explains the difference between a person’s “connections” and actual contacts with others. Connections are the set of people that the individual may have contact with while they are infected. Just because two people have a connection, however, does not guarantee that they will truly have contact during the time in which the given individual is infective. This is something I really want to include in our paper because it’s important to note that just because a person can have contact with a certain number of individuals, it does not mean that they will have contact with each and every one of those individuals. Some pairs have a probability of disease transmission than others. The paper then goes on to discuss SEIR models, in which there is a period where infected individuals are not able to infect others. This is something new to me, as I have not read anything about it before. This is potentially something that could be added to our paper. The majority of this paper just discusses mathematical models, which isn’t something particularly useful in regard to our paper, but it is definitely interesting to read about. This paper also does include a lot of useful information here and there that is relevant to our paper though.

Third Blog Post

Third blog post

https://www.ancient.eu/article/939/the-plague-at-athens-430-427-bce/

Citation: Horgan, J. (2016, August 24). The Plague at Athens, 430-427 BCE. Ancient History Encyclopedia. Retrieved from https://www.ancient.eu/article/939/

This article discusses the mystery surrounding the illness which caused the Athenian Plague, which is noted to be the first recorded epidemic. The article first begins with some useful background information. The plague appeared in Athens in 430 BCE, lasting about 4 years. It is said to have originated near Ethiopia and spread to other places such as Egypt, Libya, Persia, and Greece. It also is noted that the plague started during the second year of the Peloponnesian War. Thucydides was a Greek historian who wrote extensively on the Peloponnesian War. In his work, Thucydides discussed the disease and also its severity and symptoms. The symptoms he noted were violent heats in the head, red and inflamed eyes, blood spread out over throat and tongue, unnatural and unbearable breath, sneezing, hoarseness, coughing, vomiting, retching, convulsions, cold and not red body, pustules and ulcers, extreme feverishness. Many people died within 7-9 days of contracting the disease. If one were lucky enough to survive, they often died from awful diarrhea. The people who still survived often suffered from genital, finger, and toe disfigurement, blindness, and memory loss. Doctors often fell ill after experience with affected people. Thucydides noted that birds and other animals were also falling victim to the terrible disease or were disgusted with the bodies of the infected. Both of these facts led to the belief that the mystery disease was contagious. Thucydides was not a trained medical professional, so he could not offer a full diagnosis, but his records have led many scholars to speculate on what the mystery disease was. The article then goes on to discuss different scholars and their opinions and research on the disease. To be specific, thirteen different scholars are mentioned. One that interested me the most was the theory that there were multiple diseases. This theory was offered by A.J. Holladay, J.C.F. Poole, and J. Longrigg. Longrigg noted that the research done by Thucydides does not specifically suggest one specific disease, but can apply to multiple diseases. A lot of other single diseases were ruled out on their own as well, which is another reason supporting this theory. It is noted that multiple diseases can and do exist simultaneously and surviving one disease does not guarantee that you will survive another. Other suggestions for the mystery disease include Ebola, typhoid, smallpox, measles, bubonic plague, cholera, influenza, ergot poisoning, and various animal diseases. Today, it is still a mystery. This was a very interesting article to read. It was good to read because it provided some good background information on epidemics and also gives some insight on their severity, which is a focus of our paper. This article does not specifically relate to our paper and probably will not be of much direct use. This was still an interesting read and did provide some solid background knowledge.

Second Blog Post

This article is written by W.O. Kermack and A. G. McKendrick. The first thing I noticed about this article is that it is very old, as it says it was received on May 13^th, 1927. It begins by saying that something interesting about epidemics is that it is difficult to establish a common factor. Epidemics are a worldwide problem, and it is difficult to find a link between different places and their rates of epidemics. In the introduction, it says that two scientists, Ross and Hudson, did work with a similar problem and that many references are made to their work. This article provides a general theory of epidemics. First, it discusses how disease spreads by contact infection. Based on this, it is safe to assume that a population that is higher in numbers would have a higher disease rate, since there are more chances for contact. The chances of the disease actually being spread depend on what stage of sickness the individual affected presents. The article states that as an epidemic continues to spread, the number of unaffected population members decreases. That statement was very redundant, but it helped to make things clear. This article also puts into question what determines the end of an epidemic. Can an epidemic be considered terminated while there are still susceptible individuals within the population? The two common reasons believed to end an epidemic are 1) all susceptible individuals are removed and 2) the severity of the causative organism has decreased. As a conclusion, it states that an epidemic does not end when there are no more susceptible individuals. Rather, the authors state that there is a threshold density of population. No epidemic can occur below this specific threshold value. The population of a certain area must exceed this threshold in order for an epidemic to occur. If the population density is equal to or below the threshold value, introducing an infected person to the population will not cause an epidemic. Also, the more the threshold density is exceeded, the larger the epidemic. According to the authors, what causes this is the relationship between population density, population infectivity, recovery rates, and death rates. A population close to the threshold value is extremely sensitive. This means that a slight upset in population or recovery, infectivity, and death rates can cause a major outbreak of epidemic. This accounts for the what appears to be sporadic occurrence of large epidemics. The authors of this article give an example looking at two different populations. The two populations have identical population densities, recovery rates, and death rates. The only difference was that one population had a higher infectivity rate than the other. It is stated that greater epidemics will occur within the population with the higher infectivity rate. The math portion of the article was way over my head and nearly impossible for me to comprehend. In general, I interpreted that there is no specific threshold and that the threshold depends mostly on infectivity, recovery, and death rates. In order for something to be considered an epidemic, the population must exceed this threshold value.

Kermack, W., & McKendrick, A. (n.d.). Mathematical Theory of Epidemics. Retrieved October 2017, 18, from http://rspa.royalsocietypublishing.org/content/royprsa/115/772/700.full.pdf

First Blog Post

Mollison, D. (2008). Epidemic models: their structure and relation to data. Cambridge Printing Press.

This book discusses how the transmission of an infection can depend on population size. The general focus is the possible effects of population and contact rate and the probability that contacts are between a non-infected and infected individual. It assumes that contact between infected and non-infected individuals occur at random. The name for this is mass-action kinetics. This book discusses and compares two types of mass-action kinetics: true mass-action and pseudo mass-action. Mathematical models are used to compare the two types of mass-action kinetics and show their spread of infections. The spread of infections is referred to as “force-of-infection” and is defined as the probability per some unit of time that an individual will become infected. According to the book, this is a crucial factor in using mathematical models. In pseudo mass-action, the force-of-infection is described in terms of the populations sizes of both susceptible and infectious subpopulations. The formula for this is bXY. b is the transmission constant and X and Y are the sizes of susceptible and infectious subpopulations. In true mass-action, the formula is bXY/N with N being the total population size. The authors of this book hypothesize that total population size does have an effect, and so true mass-action is correct. First, the authors use three factors to examine force-of infection. The first factor is contact rate, which is the average number of relevant contacts with other individuals per unit of time. The second is the probability that if there is contact, it is with an infected individual. The third and last factor is the probability that contact with individual leads to infection being transmitted. These are all based on the assumption that the probability that someone gets infected given that contact occurs between that individual and someone who is infected, is constant. In true mass-action, contact rate increases linearly with population density, but total area, hence, population size, does not affect it. In pseudo mass-action, the probability that someone gets infected is proportional to the population size. To test their hypothesis, the authors of this book use preexisting data. However, it is noted that there have only been few attempts at using epidemic models with actual data. An experiment done in 1981 by two scientists named Becker and Angulo used data from a smallpox outbreak in Brazil. They estimated that the transmission parameter would be different between household and community data. There estimate did not agree with pseudo mass-action, but neither did the results. The results showed that the transmission parameter did indeed change proportionally to population size. This agreed with the authors of this book and their hypothesis. At the end, it states that true mass-action is a building block for epidemic models.