Mathematical models are objects we use to predict or examine the behaviour of various physical, chemical, biological, or socio-economic systems. They’re everywhere in today’s world, from the stock exchange to traffic management. One area where they can be particularly helpful is in the study of diseases and how they spread throughout a population, but also how a disease, for example a viral infection, spreads and infects an individual host.
This is exactly what the TIV model, the focus of our study, does. It allows us to model some very important characteristics of an influenza infection. For example, we can get a sense of how severe a patient’s symptoms will be or how long they will remain ill given some ‘parameters’. These ‘parameters’ are determined by the circumstances the person is in, for example, how much of the virus they were exposed to, as well as their biology.
There was a 2018 study done by a team from East Carolina University and Texas Christian University. In their paper, they hoped to use this TIV model to examine the response of an influenza infection to different drug mechanisms, i.e. different ways that a drug could affect the aforementioned parameters. They studied not only the mechanisms associated with currently available drugs, but essentially all mechanisms that could be implemented straightforwardly in the TIV model. This was with the hope that they could motivate future drug development and treatment plans with their results. There is one potential problem here, however.
If we are given some data from a number of patients and are asked to find the parameters such that the TIV model fits this data best, that would not be an altogether difficult task. But what we are asking here is something else entirely. We are trying to use the model to make predictions about the behaviour of an infection under novel conditions. There are many sets of ‘reasonable’ parameters we could use here, and they would all give predictions that would be different from one another in some regard. If we want to use these predictions to motivate expensive experimental studies, it’s important to know that these predictions are at least in qualitative agreement, so that we don’t end up in a wild goose chase.
The work we did during the AMSI Vacation Research Scholarship is a small step towards answering this question. We looked at the behaviour of the TIV model under a different set of parameters to what was used in said study. After comparing results, we found patterns that some of the drugs would follow under both sets of parameters, but also stark differences that are often difficult to explain.
As is often the case in science, it would be foolish to draw a conclusion from what little we know, but we could see from our results that many of the drug actions we investigated had similar effects under our model and the one used in the original study. This is a promising first step!
Amir Farid Kaveh was a recipient of a 2018/19 AMSI Vacation Research Scholarship.