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How R Naught (R₀) Shapes an Epidemic


Grade Range
Group Size
1-2 students
Active Time
65 minutes
Total Time
65 minutes
Area of Science
Human Biology & Health
Pandemics – COVID-19
Key Concepts
R naught, basic reproduction number, epidemics, viruses, disease modeling, COVID-19
Sandra Slutz, PhD, Science Buddies
simpandemic lesson plan


What is R naught (R₀), what factors influence it, and how does it shape the infection curves of an epidemic? Students will explore these questions and more in this lesson plan. They will then use SimPandemic, a free online tool, to model what a COVID-19 outbreak looks like in communities with different R₀ values.

Remote learning adaptation: This lesson plan can be conducted remotely. Students can work independently on the Explore section of the lesson plan using the Student Worksheet as a guide. The Engage and Reflect sections can either be dropped entirely, done in writing remotely, or be conducted over a video chat.

Learning Objectives

NGSS Alignment

This lesson helps students prepare for these Next Generation Science Standards Performance Expectations:
This lesson focuses on these aspects of NGSS Three Dimensional Learning:

Science & Engineering Practices Disciplinary Core Ideas Crosscutting Concepts
Science & Engineering Practices MS
Developing and Using Models. Develop and/or use a model to generate data to test ideas about phenomena in natural or designed systems, including those representing inputs and outputs, and those at unobservable scales.

Developing and Using Models. Develop, revise, and/or use a model based on evidence to illustrate and/or predict the relationships between systems or between components of a system.

Using Mathematics and Computational Thinking. Use mathematical models and/or computer simulations to predict the effects of a design solution on systems and/or the interactions between systems
Disciplinary Core Ideas MS
LS2.A: Interdependent Relationships in Ecosystem. Organisms, and populations of organisms, are dependent on their environmental interactions both with other living things and with nonliving factors.

LS2.D: Social Interactions and Group Behavior. Group behavior has evolved because membership can increase the chances of survival for individuals and their genetic relatives.
Crosscutting Concepts MS
Cause and Effect. Cause and effect relationships may be used to predict phenomena in natural or designed systems.

Systems and System Models. Models can be used to represent systems and their interactions—such as inputs, processes, and outputs—and energy and matter flows within systems.

Cause and Effect. Cause and effect relationships can be suggested and predicted for complex natural and human designed systems by examining what is known about smaller scale mechanisms within the system.

Systems and System Models. When investigating or describing a system, the boundaries and initial conditions of the system need to be defined and their inputs and outputs analyzed and described using models.


Background Information for Teachers

This section contains a quick review for teachers of the science and concepts covered in this lesson.

R₀ (pronounced R naught) is the basic reproduction number of an infectious disease. It quantifies how many people, on average, an infected person can infect. For example, an R₀ of 3 means that an infected person will, on average, infect three more people. R₀ is the measure of how spreadable the disease is and can be used to model and understand the speed and scale of an outbreak.

Three factors contribute to the R₀ for an infectious disease:

  1. The infectious period of the disease. This is the average length of time, usually measured in days, during which an infected individual is able to pass the infection to another person.
  2. The mode of transmission of the disease. Diseases can be passed from one person to another in many ways including through direct contact with bodily fluids like blood, droplet spray from coughing or sneezing, or airborne diseases whose small particles stay suspended in the air for minutes or hours, even after the infected person has left the area.
  3. The contact rate between individuals. This is the most variable factor and depends on the population. In densely populated cities, individuals tend to have contact (interactions) with more people per day than in sparsely populated, rural areas.

Since some of the factors, like contact rate, are variable, R₀ is often given as a range. When a new contagious disease appears in a population, like COVID-19, scientists look at the data to determine the R₀ range. Knowing the R₀ helps policy makers, public health officials, and scientists determine if an epidemic is coming and what that epidemic might look like.

A disease with an R₀ below 1 will not expand into an epidemic. Instead, it dies out because, on average, not all infected individuals pass along the disease. In contrast, if R₀ is above 1, an epidemic is likely. The larger the R₀, the faster the pace of the epidemic and the larger the scope. Compared to epidemics from diseases with low R₀'s, epidemics from diseases with high basic reproduction numbers tend to be shorter in duration, but have higher numbers of infected individuals per day. Overall, the total number of individuals infected over the course of the epidemic increases as R₀ increases.

Students will learn all of this by using SimPandemic to model what a COVID-19 epidemic looks like with different R₀ values. They will observe that the infection curve appears sooner and is steeper and narrower with a high R₀ .

You will see that students obtain slightly different results, even when they have the same inputs for SimPandemic. Many events in the real world and in a simulation of the real world are based on chance. When you become infected in the real world, you often don't know when or where the infection occurred. Perhaps someone sneezed when you were randomly walking by them. A simulation cannot predict that you were going to get infected (except in special cases), but it can predict fairly well that someone would get infected. In SimPandemic there are many events where the simulation literally rolls virtual dice to determine when an infected individual will transmit the disease to another (all within the bounds specified by the input parameters). To better understand the assumptions and parameters involved, read the SimPandemic FAQ.

Prep Work (15 minutes)

Engage (15 minutes)

Explore (40 minutes)

Reflect (10 minutes)


Make Career Connections

Lesson Plan Variations

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