Explore the contents of this article with a free Wolfram SystemModeler trial. Life science teaches us to answer everything from “How can vaccines be used to indirectly protect people who haven’t been immunized?” to “Why are variations in eye color almost exclusively present among humans and domesticated animals?” You can now learn to answer these questions by using modeling with Wolfram’s virtual labs. Virtual labs are interactive course materials that are used to make teaching come alive, provide an easy way to study different concepts and promote student curiosity.

Two such virtual labs were created by MathCore’s summer intern, Anna Palmer, based on learning objectives from biology units 3 and 4 of the Victorian Certificate of Education (VCE) in the state of Victoria, Australia. Hear her talk about how she created them:

Population Models in Genetics

You’ve probably seen or heard about commercial kits where you send in a DNA sample to a company that then tells you about different things, such as your ancestry or predispositions for different diseases and genetic traits. Increasingly, we have become interested in our own genes and what stories our traits can tell us about ourselves and our ancestors. But we seldom stop to think how these genetic traits came to be in the first place.

To understand the ancestry that genetic kits tell you about, we need to go back to biology class. We need to understand how different traits, such as eye color, evolve in populations over time; the most well-known cases of this are natural selection and Darwin’s famous phrase “survival of the fittest.” But what do these actually mean?

Contrary to what you may think, “survival of the fittest” does not just mean that only the fittest members of a species will survive, but rather, it refers to the ability of an organism to survive to reproduction. If an organism does not survive to reproduction, it cannot pass on its genes to the next generation. Thus, if a group of organisms with a particular trait has a decreased chance of surviving to reproduction, there is a decreased chance that the genes for this trait will be passed on to the next generation. This in turn may lead to the extinction of the trait.

As Anna mentioned in the video, she created a system model that explains this. In the following model, two populations with different traits (A and B) compete for the same resources. The different traits will be differently adapted to the environment, and not all born with a particular trait will reach maturity. If they reach maturity, however, they will pass on their genes to a new generation.

By running this model, biology students can experiment with how different things in the model affect the outcome. In the virtual lab, this model has been embedded in a Wolfram Language notebook that contains explanations, questions and interactive interfaces using the Manipulate function, such as this:

By playing around with the interface, students can explore how even very slight differences in the survivability can cause a particular trait to overtake another within just a few generations. With this, students can try different “what-if” scenarios and instantly see if the results match their hypotheses.

Apart from ancestry, many people are also interested in knowing if they are predisposed toward certain diseases or not. There are many genes that influence just this. For example, a genetic variance causing sickle cell anemia actually protects against another disease, malaria. This explains why the gene for sickle cell anemia is found in about 7% of the population in malaria-stricken regions, but is virtually nonexistent elsewhere. In the same virtual lab, a model that explains this relationship is included.

In teaching, visualizing the complex relationship between two different diseases might be hard to do on paper; with a model and the Wolfram Language, it’s easy. Wolfram SystemModeler and the Wolfram Language make it possible for students to interact with the simulations, try different scenarios and set up experiments to instantly see if the results match their hypotheses.

We made this virtual lab available to students, educators and hobbyists alike. You can download the notebook here and learn about population genetics for yourself. In the download, you will find models of the scenarios described here, as well as a notebook providing you with the background and exercises that you can complete.

Population Models in Infectious Diseases

One of the things I really like about using SystemModeler is how easy it is to reuse the components you have created. This is especially useful in education, where the same concept can be found in many different settings. As an example, the types of population models that were used for the previous virtual lab are not only useful to illustrate genetic changes across multiple generations; among other things, they can also be used to explain how infectious diseases spread within populations. Anna developed a virtual lab for this too.

The most well known of these models, the susceptible-infectious-recovered (SIR) model, describes a disease that transmits from an infected person to a susceptible person. After a certain amount of time, the infected person recovers from the disease and can’t be infected again. In these types of diseases, our immune system is what keeps us from falling back into the infected category. The SIR model has proven very useful at explaining everything from smallpox to seasonal influenza.

By getting vaccinated, you take a shortcut that moves you from the susceptible stage into the recovered stage, without going through the infected stage. This is illustrated in the “With Vaccination” model shown above.

In this virtual lab, interactive interfaces that allow the students to adjust things such as the rate of infections, the duration of the sickness and the vaccinated rate are provided:

By comparing two scenarios (no vaccination and low vaccination), students can use the model to explain and understand things such as herd immunity. Even though there is a larger percentage of susceptible people in the first scenario, there is clearly a lower rate of infection since the vaccinated people provide an indirect form of immunity to the non-immune individuals, called herd immunity.

Of course, this exercise (together with other exercises explaining infectious diseases) is available as a virtual lab that can be used by students, educators and hobbyists alike. You can download the virtual lab notebook here and learn about it for yourself!

Biology and genetics are just two of the areas where we have created virtual labs to explain different concepts, and we are looking to create even more. Do you have a good idea for an educational area where modeling could be applied? Let us know by sending us an email at wsmcourseware@wolfram.com.