With the recent scare of a so-called Severe acute respiratory syndrome-like (SARS) virus called Middle East Respiratory Syndrome coronavirus (MERS – CoV) that so far has unknown origins and has a astounding mortality rate of 47.6% , I began to wonder about the complexities of disease outbreaks and the mathematics behind epidemics. That’s when research led me to realize that it was possible to model epidemics using calculus. As a pathofobiac, I’ve always been intrigued, and scared, of, diseases - constantly reading statistics regarding different diseases, examining how they spread an calculating the chances of any of them ever infecting me or any of my loved ones. So when the opportunity came to do a math exploration, I thought it would be interesting to look into the mathematics behind disease spread.
The aim of this exploration is to investigate and examine one epidemic model and then attempt to apply it to a scenario and determine if it’s a realistic and accurate model.
The Initial model
Although Epidemic modeling depends on a variety of factors, which will be discussed later on (such as the type of disease and its rate of spread) the initial model takes into account the major factors to produce a simplistic model.
Firstly, the initial model takes into account the very basic assumptions that are listed below
“1. SIR: All individuals fit into one of the following categories:
Susceptible: those who can catch the disease.
Infectious: those who can spread the disease.
Removed: those who are immune and cannot spread the disease
2. The population is large confined to a well-defined region. You might imagine the population to be a large university during the semester, when relatively little outside travel takes place.
3. The popu...
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...culty of The University of Iowa)
Centers for Disease Control and Prevention. Middle East Respiratory Syndrome (MERS). 3 September 2013. 3 September 2013 .
Department of Statistics at Columbia University. Introduction to Epidemic Modelling. Unknown Unknown Unknown. 28 August 2013 .
KidsHealth. Chickenpox. Unknown Unknown Uknown. 1 September 2013 .
Maps of World. Population Mexico (Poblacion de Mexico]). Unknown Unknown Unknown. 2 September 2013 .
Mathematics Faculty of The University of Iowa. Using Calculus to Model Epidemics. Unknown Unknown Unknown. 24 August 2013 .
Communicable diseases are one of the major concerns in public health, as it poses a significant threat to the population. The study of epidemiology allows nurses to understand the cause of the disease and helps determine the levels of prevention to be implemented in order to limit the spread of the disease (Lundy & Janes, 2016). The purpose of this paper is to: a) use an epidemiological model to identify the organism involved in the case study, as well as its pathology, etiology, diagnosis, and prognosis; b) describe the distribution of health events within Schenectady; c) identify the determinants affecting morbidity and mortality; d) determine the deterrents that exists within the affected population; e) calculate the outbreak’s incubation period; f) identify the individuals affected during endemic levels; g) provide a list of foods that were most susceptible to mass contamination; and h) determine the people involved in the food borne outbreak and analyze the possible cause of this occurrence.
“Plague Fact Sheet.” Centers for Disease Control and Prevention. Department of Health and Human Services. 30 March, 2005. 26 July, 2006. .
Before I go any further, I feel that I should clarify the difference between the terms epidemic and endemic disease. An epidemic disease is a disease that enters into a population and completely ravages it. Epidemics are particularly destructive because they are usually diseases that have never been introduced into that specific population. A good example of an epidemic is the bubonic plague, or smallpox. Smallpox uncontrollably ravaged Europe for more than two hundred years....
Mathematical models and computer simulations are important tool to investigate spread and control of infectious diseases. These two jointly build and test theories that are involved with complex biological systems related disease, getting quantitative conjectures, determining parameter sensitivities due to change and estimating parameters from data. It is important to state that modeling is very crucial in epidemiology since in most cases we cannot do experiments. Modelling gives better idea in e-epidemiology when the system is simulated with various parameters because conducting experiments in e-epidemiology is critical.
In this paper I plan on focusing on a public health epidemic that is taking over the U.S.
“The Influenza Pandemic of 1918.” Billings, Molly. Stanford University Virology. June 1, 1997. retrieved from http://virus.stanford.edu/uda/
The increase of population density over the past century due to an overall increase in population and the desire of many to live in major city centres. This population density has an adverse affect on the spread of infectious disease as the more people the larger amount of contact between individuals. Due to this increased contact it only takes one sick individual to spread a disease to potentially thousands through the transferal of microbes. A well known example that demonstrates just how quickly this can occur is the influenza virus. New strains of this virus are constantly emerging and the spread of these strains is aided by the close proximity of people living in cities. One of the latest flu strains to break out is the H7N9 a type of bird flu which broke out in china in the 2013 flu season. China has one of the highest population densities in the world and this is possibly the reason they see such a high rate of outbreaks. The H7N9 influenza strain infected 28 people and killed 8 in the first 9 days of the virus being recognized. Once the virus was tracked back to its source, a poultry market in shanghai, the outbreak was contained. The SIR model is used to track the spread of fl...
Ebola, a major threat to today's society, is threatening all parts of today's culture. In this paper one will be presented with six major points of analyses. The first an outbreak timeline, the next three are a basic overview of the deadly virus. In the fifth, one will be presented with what things are being blamed for these violent outbreaks. And in the sixth and final point one will be shown what is being done to better the situation.
Epidemiological transition theory is the idea that there are complex changes in patterns of health and disease in relation with demographic and technologic transitions. The original three phases include the age of pestilence and famine, the age of receding pandemics, and the age of degenerative and man-made diseases (Omran, 2005). The age of pestilence and famine is characterized by high mortality due to war, famine, and epidemic outbreaks (Omran, 2005). Very few countries are in this phase as average life expectancy has increased globally. However, in Africa, ongoing conflict and famine continue to plague many populations. In the age of receding pandemics, average life expectancy increases and infectious disease outbreaks become fewer in frequency
Until the global outbreak of the Ebola virus in 2014, I heard of a real-life present-day killer virus. Of course, I learned about the Black Plague that occurred centuries ago killing millions of people. But in the modern day, no. It was horrifying. This paper will explore the origins, types, causes/effects, and what is being done to fight the spread of the Ebola virus – the Black Plague of 2014.
The movie Outbreak is a wonderful portrayal of how the Chain of Infection works in an epidemic and pandemic outbreak of a disease. The shows how quickly the disease gained power and was responsible for sickness and death in a small community. Pathogens that invade the body have 5 requirements for a successful invasion on their host whether it is a human or animal. I will further review how the movie successfully reflects the reservoir/host, portal of exit, mode of transmission, portal of entry and susceptible host to provide the perfect Outbreak of the disease. The same model still used today in science.
Murray, M.2006. The epidemiology of SARS. In SARS in China: Prelude to pandemic?, ed. A. Kleinman and J. Watson, 17-30. Stanford, Calif.: Stanford University Press.
Medical anthropologists examine epidemic outbreaks through numerous approaches. According to Joralemon, “Epidemics offer particularly vivid demonstrations of the interconnections between biological, social, and cultural components in the human experience of disease” (2010:29). Many times these approaches cannot function on their own accord and rely on each other to solve the epidemic. It is the job of the medical anthropologist to put all the pieces of the disease puzzle together.
Hoff, Brent, Carter Smith, and Charles H. Calisher. Mapping Epidemics: A Historical Atlas of Disease. New York: Franklin Watts, 2000. Print.
The field of medicine is another high subscriber to this forecasting technique. Potential diagnoses are frequently made based on a patient’s history or that of his ancestors and the calculated likelihood of him/her acquiring certain conditions. Statistics and probability aid in the decision making process of which test may be required for a given symptom and how a possible outbreak may be detected and contained. Strategies for isolating and dealing with diseases are often made with the aid of statistics on the percentage of a population that may have been infected and the probability of its escalation.