Modeling Epidemics: Functions to Evaluate Intervention Strategies
Inquiry Framework
Question Framework
Driving Question
The overarching question that guides the entire project.How can we use mathematical models to understand, predict, and mitigate the spread of infectious diseases in our community?Essential Questions
Supporting questions that break down major concepts.- How can mathematical functions model the spread of a disease through a population?
- What factors influence the rate of disease transmission, and how can these be represented mathematically?
- How can different intervention strategies (e.g., vaccination, quarantine) be modeled mathematically?
- How can we use mathematical models to predict the peak of an epidemic and the total number of infected individuals?
- What are the limitations of using mathematical models to represent real-world epidemics?
Standards & Learning Goals
Learning Goals
By the end of this project, students will be able to:- Students will be able to create mathematical models that represent the spread of infectious diseases.
- Students will be able to interpret and analyze mathematical models of epidemics.
- Students will be able to evaluate the effectiveness of different intervention strategies using mathematical models.
- Students will be able to predict the peak of an epidemic and the total number of infected individuals using mathematical models.
- Students will be able to understand the limitations of mathematical models in representing real-world epidemics.
Common Core Standards
Entry Events
Events that will be used to introduce the project to studentsCreate a Public Service Announcement
Challenge students to create a PSA to educate the public. The PSA needs to include a mathematical model.Portfolio Activities
Portfolio Activities
These activities progressively build towards your learning goals, with each submission contributing to the student's final portfolio.Epidemic Equation Exploration
Students will explore basic mathematical expressions and functions that are commonly used to model the spread of diseases. This activity introduces key variables and parameters involved in epidemic modeling.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA detailed table explaining mathematical functions, variables, and parameters used in epidemic modeling.Alignment
How this activity aligns with the learning objectives & standardsHSA-SSE.A (Interpret the structure of expressions)Simulating the Spread: Building a Basic Model
Students will construct a basic mathematical model (e.g., using spreadsheets or coding) to simulate the spread of a hypothetical disease in a population. They will manipulate variables to observe changes in disease transmission.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA functional simulation model and a graph showing the spread of the disease over time.Alignment
How this activity aligns with the learning objectives & standardsHSF-IF.C (Analyze functions using different representations)Intervention Investigation: Testing Mitigation Strategies
Students will modify their basic model to incorporate intervention strategies such as vaccination or quarantine. They will analyze the impact of these strategies on the spread of the disease.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA comparative analysis of different intervention strategies and their impact on disease spread, presented with graphs and explanations.Alignment
How this activity aligns with the learning objectives & standardsHSF-IF.C (Analyze functions using different representations)Predicting the Peak: Forecasting Epidemic Trends
Using their refined models, students will predict the peak of an epidemic and the total number of infected individuals. They will discuss the limitations and uncertainties of their predictions.Steps
Here is some basic scaffolding to help students complete the activity.Final Product
What students will submit as the final product of the activityA report with predictions for the epidemic peak and total infections, along with a discussion of the model's limitations.Alignment
How this activity aligns with the learning objectives & standardsHSA-SSE.A (Interpret the structure of expressions), HSF-IF.C (Analyze functions using different representations)Rubric & Reflection
Portfolio Rubric
Grading criteria for assessing the overall project portfolioMathematical Modeling of Epidemics
Mathematical Foundations
Understanding and application of mathematical functions, variables, and parameters used in epidemic modeling (HSA-SSE.A).Function Identification and Interpretation
Ability to correctly identify and interpret relevant mathematical functions (e.g., exponential, logistic) and their components in the context of epidemic modeling.
Exemplary
4 PointsAccurately identifies and explains the role of all relevant functions, variables, and parameters with sophisticated understanding and insightful connections to real-world epidemic dynamics.
Proficient
3 PointsCorrectly identifies and explains most relevant functions, variables, and parameters with a clear understanding of their role in epidemic modeling.
Developing
2 PointsIdentifies some relevant functions, variables, and parameters but demonstrates a limited understanding of their role in epidemic modeling.
Beginning
1 PointsStruggles to identify relevant functions, variables, and parameters and demonstrates a minimal understanding of their role in epidemic modeling.
Mathematical Expression and Manipulation
Skill in expressing and manipulating mathematical expressions to represent disease spread and interventions.
Exemplary
4 PointsDemonstrates sophisticated skill in expressing and manipulating complex mathematical expressions to accurately represent disease spread and interventions.
Proficient
3 PointsEffectively expresses and manipulates mathematical expressions to represent disease spread and interventions.
Developing
2 PointsShows emerging skill in expressing and manipulating mathematical expressions, but with some inaccuracies or inconsistencies.
Beginning
1 PointsStruggles to express and manipulate mathematical expressions to represent disease spread and interventions, requiring significant guidance.
Simulation and Modeling
Construction, execution, and analysis of a simulation model to represent disease spread (HSF-IF.C).Model Construction and Execution
Ability to build a functional simulation model using appropriate tools and execute it effectively.
Exemplary
4 PointsConstructs a sophisticated and accurate simulation model using appropriate tools, executes it flawlessly, and demonstrates advanced understanding of the simulation process.
Proficient
3 PointsConstructs a functional simulation model using appropriate tools and executes it effectively with minimal errors.
Developing
2 PointsConstructs a partially functional simulation model but encounters some difficulties in execution or tool usage.
Beginning
1 PointsStruggles to construct a functional simulation model and requires significant assistance with tool usage and execution.
Data Representation and Visualization
Effectiveness in representing and visualizing simulation results (e.g., through graphs) to show disease trends.
Exemplary
4 PointsPresents simulation results with exceptional clarity and insight, using advanced visualization techniques to highlight key trends and patterns.
Proficient
3 PointsEffectively represents simulation results through clear and informative graphs that accurately show disease trends.
Developing
2 PointsRepresents simulation results with some limitations in clarity or accuracy, showing a basic understanding of disease trends.
Beginning
1 PointsStruggles to effectively represent simulation results, with unclear or inaccurate graphs that provide minimal insight into disease trends.
Intervention Analysis
Evaluation of the impact of intervention strategies (e.g., vaccination, quarantine) on disease spread (HSF-IF.C).Intervention Incorporation
Ability to incorporate intervention strategies into the simulation model and adjust parameters accordingly.
Exemplary
4 PointsSkillfully incorporates multiple intervention strategies into the simulation model, accurately adjusts parameters to reflect their impact, and provides insightful justifications for the chosen values.
Proficient
3 PointsEffectively incorporates intervention strategies into the simulation model and adjusts parameters appropriately to reflect their impact.
Developing
2 PointsIncorporates intervention strategies into the simulation model with some inaccuracies or inconsistencies in parameter adjustment.
Beginning
1 PointsStruggles to incorporate intervention strategies into the simulation model and requires significant assistance with parameter adjustment.
Comparative Analysis
Thoroughness in comparing the outcomes of different intervention strategies and drawing meaningful conclusions.
Exemplary
4 PointsConducts a comprehensive comparative analysis of different intervention strategies, drawing insightful conclusions that are well-supported by evidence from the simulation results and relevant research.
Proficient
3 PointsProvides a clear and well-reasoned comparative analysis of different intervention strategies, drawing meaningful conclusions supported by evidence from the simulation results.
Developing
2 PointsCompares the outcomes of different intervention strategies but provides limited analysis or weak support for conclusions.
Beginning
1 PointsStruggles to compare the outcomes of different intervention strategies and fails to draw meaningful conclusions.
Prediction and Limitations
Forecasting epidemic trends and discussing the limitations of the model (HSA-SSE.A, HSF-IF.C).Epidemic Forecasting
Accuracy in predicting the peak of the epidemic and the total number of infected individuals.
Exemplary
4 PointsProvides highly accurate predictions for the epidemic peak and total infections, demonstrating a sophisticated understanding of the model's dynamics and its sensitivity to different parameters.
Proficient
3 PointsProvides reasonably accurate predictions for the epidemic peak and total infections, demonstrating a solid understanding of the model's behavior.
Developing
2 PointsProvides predictions for the epidemic peak and total infections with some inaccuracies, showing a basic understanding of the model.
Beginning
1 PointsStruggles to provide reasonable predictions for the epidemic peak and total infections, demonstrating a limited understanding of the model.
Limitations Discussion
Depth and critical analysis of the limitations and uncertainties of the mathematical model.
Exemplary
4 PointsProvides a comprehensive and insightful discussion of the model's limitations, including a critical analysis of its underlying assumptions and potential sources of error.
Proficient
3 PointsDiscusses the model's limitations with clarity and provides reasonable explanations for potential uncertainties.
Developing
2 PointsAcknowledges the model's limitations but provides a superficial or incomplete discussion of potential uncertainties.
Beginning
1 PointsFails to adequately address the model's limitations or potential uncertainties.