How is modelling like making a cake?

How vaccine modelling works: a cake analogy

Mathematical models help researchers and policymakers think about how infections spread and how vaccination might help. One way to explain this is to compare modelling to baking a cake: you need to know what you are trying to make, choose the right recipe, check you have the right ingredients, work through problems if something is not going to plan, and then see whether the final result makes sense.

This resource also explains why PPIE (patient and public involvement and engagement) matters in vaccination modelling. Models are stronger when they are informed not only by technical expertise, but also by public perspectives, lived experience, and practical knowledge about how vaccination works in real life.

Why use mathematical models for vaccination?

When policymakers plan vaccination programmes, they need to make decisions that rely on predicting what they think might happen in the future. Mathematical models are tools that help with this. They cannot predict exactly what will happen, but they can show what might happen using different assumptions.

A model can help answer questions like:

- How quickly could an infection spread?

- Which groups are most at risk?

- What difference might vaccination make?

- Would a new vaccination strategy be a good use of resources?

Public contributors can help at the very start by asking whether the questions being modelled are the questions that matter most to patients, families, and communities.

A simple way to explain this is to think about baking a cake.

Step 1: What cake are we making, and why?

Before you start baking, you need to know what kind of cake you are making. Is it a birthday cake? A Christmas cake? A simple sponge or something more complicated?

In the same way, before building a model, researchers need to understand the disease itself.

They might ask:

- How does it spread?

- How serious is it?

- Who is most affected?

- Does it affect children, older adults, or specific communities more than others?

- Is it seasonal?

- Does vaccination stop infection, reduce severe illness, or both?

Cake analogy: if you choose the wrong kind of cake - for example, a wedding cake or a birthday cake - it may look fine but won't meet your needs.

This is the context for the model. If you don't understand the disease you're trying to represent, you may end up with a model that doesn't answer the questions you need it to.

PPIE can help by bringing real-world knowledge about what the disease is like, which impacts matter most, and how vaccination is experienced in everyday life. Public contributors may highlight issues that are easy to miss in routine data alone, such as the effect on family life, work, confidence, access to care, or trust in vaccination.

Step 2: How are we making the cake?

Once you know what you are trying to make, you need the right recipe and equipment. In modelling, this means choosing the right kind of model.

Different questions need different kinds of models.

Three common types are:

1. Compartmental models

These group people into broad categories, such as:

- people who can catch the infection

- people who are infected

- people who have recovered

- people who are vaccinated

This kind of model is useful when you want a big-picture view of how infection moves through a population.

Cake analogy: this is like following a basic recipe with clear steps and simple ingredients.

2. Network models

These look more closely at who comes into contact with each other. They are useful when patterns of contact matter, for example in households, schools, or close social groups.

Cake analogy: this is like paying close attention to who adds which ingredient, in what order, and how each step affects the final cake.

3. Spatial models

These take place and distance into account. They can help when infection patterns vary between areas, regions, or settings.

Cake analogy: this is like knowing that where the cake is baked matters too - different ovens, temperatures, or kitchens may change the result.

There is no single “best” model for every situation. The best model depends on the disease, the data available, and the question being asked.

PPIE can help researchers think about whether a model reflects real life well enough. For example, public contributors may point out that behaviour, local context, family structures, barriers to access, or differences between communities need more attention. This can help the team judge whether the model choice fits the question properly.

Step 3: Do we have all the ingredients?

A model is only as useful as the information that goes into it. Just as baking needs ingredients, modelling needs data.

Researchers may need information about:

- how many people are getting infected

- how infection spreads

- how many people are vaccinated

- how well the vaccine works

- how long protection lasts

- which age groups or communities are most affected

- how serious the illness is

- how often people need hospital care

If important information is missing, the model may be less reliable.

Cake analogy: if you leave out flour, eggs, or the oven temperature, the cake may not turn out as expected.

What information do you think scientists need before they can model the effect of a vaccine?

PPIE can help identify missing information, especially where routine data do not capture lived experience well. Public contributors may raise questions about how quality of life has been measured, barriers to vaccine uptake, impacts on people and families that may not be included, or whether important groups are being overlooked. They can also help challenge whether the available evidence feels complete and relevant.

Step 4: What if something doesn't look right?

Even with the right question, the right model, and good ingredients, the process does not always run smoothly first time.

Researchers often need a troubleshooting stage. This means stopping to check what is working, what is not, and what may need to change before the model is ready.

At this point, they might ask questions like:

- Are we using the right kind of model for this question?

- Is the model too simple, or too complicated?

- Are the data strong enough to support the assumptions we are making?

- Have we missed an important factor, such as age, behaviour, or differences between communities?

- Do small changes in the numbers lead to very different results?

- Do we need more data, different data, or a different way of organising the model?

Sometimes this stage leads to small changes. Sometimes it means going back and rethinking part of the model.

Cake analogy: sometimes the recipe looks fine at first, but when you start mixing, you realise something needs adjusting. The mixture may be too dry, too wet, or not behaving as expected. You may need to check the measurements, adjust the ingredients, or change the oven temperature.

This step matters because a model is not just written once and left alone. It is usually built up gradually, tested, adjusted, and improved. That is a normal part of good modelling.

PPIE can be especially valuable in troubleshooting. Public contributors can ask simple but important questions that test whether assumptions feel realistic. They may notice when the model leaves out practical issues, social differences, communication problems, or patterns of behaviour that affect vaccination in real life. This can help the team refine the model before moving on to the final interpretation.

Step 5: How does it look?

After mixing everything together, you need to check the cake. Did it rise properly? Does it look like it should? Does it match what you expected?

Researchers do the same with a model. They ask whether the model output looks sensible when compared with:

- what has happened in the past

- what is already known about the disease

- real-world data

- expert knowledge

- practical experience of how vaccination works in communities

This step is sometimes called validation or checking the model.

If a model suggests something very different from past experience (or from other models), that does not always mean it is wrong. But it does mean the team needs to look carefully at the assumptions and the data.

PPIE can help by asking whether the model results feel believable and relevant from a community point of view. Public contributors may help spot when a result makes technical sense but does not seem to fit real-world experience. They can also help researchers explain findings more clearly and identify what questions the public may have about the results.

Step 6: Is the customer happy with the cake?

When models are created to help policymakers make decisions about vaccination programmes there will be another step.

Once policymakers see the results from a model, they may have new questions or ask for changes. Sometimes they want to explore a slightly different question, or have different information to include, or they need to look at a different scenario.

This is a bit like making a cake for a customer. After seeing the finished cake, they might ask for a few tweaks, such as different decorations or a new message on top. Occasionally, they may decide they need a different type of cake altogether, meaning it has to be baked again. In the same way, policymakers may ask modellers to make small adjustments to a model or to rebuild parts of it to address new questions.

Why is PPIE in vaccine modelling important?

A model is not only built from maths. It is also built from choices: what question to ask, what evidence to include, what assumptions to make, and what outcomes matter. Public contributors can help researchers think more carefully about those choices. Using our cake analogy, PPIE is a bit like inviting the people the cake is for into the kitchen before the baking is finished. They may not write the recipe or help with the baking, but they can still help you make something more useful, more realistic, and more likely to be right for the occasion.

PPIE is important because vaccination policy affects people’s lives directly. Decisions about who should be offered a vaccine, when, and why can have consequences for families, communities, and public trust.

Public involvement can help make modelling more:

relevant, by focusing attention on the issues that matter most
credible, by testing assumptions against real-world experience
transparent, by opening up decisions that might otherwise stay hidden inside technical work
accountable, by recognising that vaccination policy is not only a scientific issue but also a public issue
practical, by helping researchers think about implementation in the real world

Good PPIE in modelling is not just about asking for an opinion once. It is about creating a process where public contributors can understand the work, question it, and influence it in meaningful ways. The MEMVIE framework for vaccination modelling shows that public contributors can make useful contributions across both epidemiological modelling (looking at the pattern of the disease and what happens when people are vaccinated) and health economics (how the costs and benefits of vaccination are calculated and accounted for).

Summary

Mathematical models are tools that help researchers and policy teams think through complex vaccination questions. Like baking a cake, modelling involves deciding what you are trying to make, choosing the right method, gathering the right ingredients, solving problems along the way, and checking whether the final result makes sense. PPIE (Patient and Public Involvement and Engagement) helps ensure that vaccine models are relevant, understandable, and focused on the questions that matter most to the people affected by them. By involving patients and the public throughout the process, modellers can make better decisions about what to include in a model, how to communicate results, and how to ensure the evidence generated is useful for real-world decision-making.