Mathematical Modeling of Virus Spread in Epidemiology

Mathematical Modeling of Virus Spread in Epidemiology

Find a scientific paper in an area that interests you. Write a summary of the paper. The paper must contain a mathematical model involving either an integral or differential equation. It cannot contain only a statistical or graphical analysis

Step 1: Find a scientific paper in an area that you find interesting (examples: chemistry, sociology, etc.). Any discipline from the sciences and social sciences is fine with one exception -- the paper cannot be a mathematics paper.

One way to find such an article is to search for "Mathematically modelling (something I'm interested in)" such as "Mathematically modelling the spread of a virus". You can do this by searching any of the following:

https://library.utoronto.ca/ U of T's library database
https://onesearch.library.utoronto.ca/article-databases a list of subject-specific databases through U of T
https://scholar.google.com/Links to an external site. (Also good for looking up the bibliographical information by clicking on "cite" below the search result for your paper.)
How do you read one of these papers? Advise on how to read journal articles Download Advise on how to read journal articles.

This is enough to get you started. For more detailed information, you are welcome to look at this set of instructions from 2022 Download this set of instructions from 2022. All of it still applies except for the information about ACT E, which we will not be doing this year, and the fact that there is no groupwork component for the ACTs this year.

The paper must contain a mathematical model involving either an integral or a differential equation. It cannot contain only a statistical or graphical analysis.

Step 2: Write a rough copy of your description of the journal article and bring a (hardcopy or electronic) on Feb 1 or Feb 2 to your tutorial. This write-up will be a summary of the paper in two paragraphs, as follows.

  1. The first paragraph is an introductory paragraph that answers the questions:
    Which discipline and domain is the paper about? Examples: Organic chemistry and protein folding, Sociology and the spread of rumours through a social network, Economics and the
    What specific problem is the paper trying to solve? Alternatively, what specific phenomena and/or contributing factors are being observed
  2. The second paragraph discusses the use of mathematics to analyze and/or describe the data that was collected.
    Is an integral or differential equation being used? (Do not go into detail. Simply state whether they use one or the other)
    What do each of the variables represent?
    Include the units each variable is measured in.
    Briefly explain what the integral or differential equation is meant to model.
    What conclusions did the paper arrive at, based on this mathematical model? You should be able to explain this using terms from the domain of the paper, not math terms. (Example: "The population started to decline after 2 years", not "The population function reached its maximum")
    What impact will the conclusions of the paper have on the discipline. (Example: "Since we know that a lack of sunlight has a negative impact on the population of lab rats, we can study further to see if ssimilar effects can be observed with humans who live in various geographic locations and look for ways to help people who lack sun exposure in winter.")

Find a scientific paper in an area that interests you. Write a summary of the paper. The paper must contain a mathematical model involving either an integral or differential equation. It cannot contain only a statistical or graphical analysis

Step 1: Find a scientific paper in an area that you find interesting (examples: chemistry, sociology, etc.). Any discipline from the sciences and social sciences is fine with one exception -- the paper cannot be a mathematics paper.

One way to find such an article is to search for "Mathematically modelling (something I'm interested in)" such as "Mathematically modelling the spread of a virus". You can do this by searching any of the following:

https://library.utoronto.ca/ U of T's library database
https://onesearch.library.utoronto.ca/article-databases a list of subject-specific databases through U of T
https://scholar.google.com/Links to an external site. (Also good for looking up the bibliographical information by clicking on "cite" below the search result for your paper.)
How do you read one of these papers? Advise on how to read journal articles Download Advise on how to read journal articles.

This is enough to get you started. For more detailed information, you are welcome to look at this set of instructions from 2022 Download this set of instructions from 2022. All of it still applies except for the information about ACT E, which we will not be doing this year, and the fact that there is no groupwork component for the ACTs this year.

The paper must contain a mathematical model involving either an integral or a differential equation. It cannot contain only a statistical or graphical analysis.

Step 2: Write a rough copy of your description of the journal article and bring a (hardcopy or electronic) on Feb 1 or Feb 2 to your tutorial. This write-up will be a summary of the paper in two paragraphs, as follows.

  1. The first paragraph is an introductory paragraph that answers the questions:
    Which discipline and domain is the paper about? Examples: Organic chemistry and protein folding, Sociology and the spread of rumours through a social network, Economics and the
    What specific problem is the paper trying to solve? Alternatively, what specific phenomena and/or contributing factors are being observed
  2. The second paragraph discusses the use of mathematics to analyze and/or describe the data that was collected.
    Is an integral or differential equation being used? (Do not go into detail. Simply state whether they use one or the other)
    What do each of the variables represent?
    Include the units each variable is measured in.
    Briefly explain what the integral or differential equation is meant to model.
    What conclusions did the paper arrive at, based on this mathematical model? You should be able to explain this using terms from the domain of the paper, not math terms. (Example: "The population started to decline after 2 years", not "The population function reached its maximum")
    What impact will the conclusions of the paper have on the discipline. (Example: "Since we know that a lack of sunlight has a negative impact on the population of lab rats, we can study further to see if ssimilar effects can be observed with humans who live in various geographic locations and look for ways to help people who lack sun exposure in winter.")
Title: Mathematical Modeling of Virus Spread in Epidemiology Discipline and Domain: Epidemiology and the spread of infectious diseases Specific Problem: The paper aims to understand and predict the dynamics of virus spread in a population to inform public health interventions and control strategies. The use of Mathematics: The paper utilizes a differential equation model to analyze and describe the data on virus transmission dynamics. The model incorporates variables such as the number of susceptible individuals, infected individuals, and recovered individuals over time. Each variable represents a specific population group, and the units can be measured in terms of the number of individuals or proportions. The differential equation represents the rate of change of infected individuals over time, taking into account factors such as the transmission rate, recovery rate, and contact patterns within the population. By solving the differential equation, the researchers can simulate and predict the spread of the virus under different scenarios and interventions. The conclusions drawn from the mathematical model provide insights into the effectiveness of various control measures, such as vaccination campaigns, social distancing, or quarantine strategies. For example, the model might reveal that a combination of increased vaccination rates and reduced contact rates can significantly reduce the overall infection rate within a population. These findings have important implications for public health officials and policymakers in developing targeted strategies to mitigate the spread of infectious diseases and minimize their impact on communities. The impact of this paper lies in its contribution to the field of epidemiology. By using mathematical modeling techniques, researchers can gain a deeper understanding of virus spread dynamics and inform evidence-based decisions for disease prevention and control. The insights gained from this study can guide the development of effective intervention strategies and optimize resource allocation in future outbreaks or pandemics.

Sample Answer