[Population Modeling] Introduction

[Robert Smith?]

Hi everyone,

My name is Robert Smith? Yes, with the question mark. I was cursed with the most boring name in the world but now, thanks to punctuation, I have the most interesting name in the world :-)

I'm a professor at the University of Ottawa, cross-appointed between the department of mathematics and the faculty of medicine. I used impulsive differential equations to model infectious diseases, such as HIV, Ebola, malaria... and zombies! In fact, my students and I even won a Guinness World Record for the latter, much to our surprise. Impulsive differential equations consist of continuous, deterministic models supplemented by a series of shocks or jumps. These can be predetermined or adaptive, depending on the system (or both). For example, your body metabolises a drug, which is a continuous process. But taking a pill is a shock to the system, which can be approximated by an insantaneous change. You might take a pill according to a schedule (eg every 24 hours) or you might only take a pill when you have a headache. In the latter case, the time between pills becomes a dependent variable and adapts to the system itself. I've applied these models to drug dynamics, insecticide control and vaccines, although they have many other uses, of course. 

I'm interested in using mathematics as a tool to understand intervention methods for disease control. But I'm also interested in the ways that mathematics can reach a much wider audience, which is why I use zombies and other elements of pop culture to reach people who wouldn't usually be interested. I've written or edited 11 books that are largely populist examinations of either pop culture, academia or both. I also won the Partners in Research Mahematics Ambassador award last year for efforts to communicate mathematics to the general public.

You can find details here:

http://mysite.science.uottawa.ca/rsmith43/publications.html

A summary of some of my recent work:

A few years ago, a group of researchers proposed a program for HIV called "Test and Treat". The idea was to test everyone in the world (or as many as they reasonably could) and, if someone was found to be HIV positive, then they would start treatment immediately. This sounds like a good idea in theory... but it doesn't account for the rise of drug resistance (which wasn't included in the model). The mathematical model that was used was flawed, but the World Health Organisation adopted it anyway and began this widescale program. Our modelling took the original model but added in both drug resistance and also education (manifested through behaviour changes). We showed that, in the absence of education but with drug resistance included, then the "test and treat" program was highly likely to make matters worse, leading to widespread treatment failure down the line. However, if good-quality education was provided, either at the time of treatment or subsequently, then the effects of drug resistance could be overcome. This is true even if education is only partially effective.

Polio is a disease that's almost been eradicated from the world... but not quite. In 2013, the number of cases doubled from the previous year, prompting the World Health Organisation to declare a polio emergency. We have a good vaccine (although in some cases, the vaccine itself can give you polio), but a key question is when to take it. Many countries undertake mass vaccinations, on National Immunisation Days (NIDs). A single NID can result in millions of children being vaccinated at once. However, different countries vaccinate at different times. We wondered if these should be synchronised? Using impulsive differential equations to model pulse vaccinations, we see the benefits of synchronisaton: they overcome the issue of migration, because migrants aren't lost between different NIDs. We can prove that, under some conditons, synchronising the pulses is a local minimum and hence the best strategy. However, seasonal effects can change the picture: it's important to vaccinate before the high-transmission season. If migration is low, then two countries with different seasonal patterns should de-link their NIDs. (Something that was not done recently when it should have been.) However, if migration is high, then this will swamp the effects of seasonality and neighbouring countries with high migration should re-synchronise their NIDs. It follows that understanding the effects of human behaviour is crucial if we are to eradicate this disease in the next few years.

 - Robert Smith?