{"id":1241,"date":"2020-04-09T12:01:00","date_gmt":"2020-04-09T02:01:00","guid":{"rendered":"http:\/\/blogs.unsw.edu.au\/mathssciencechampions\/?p=1241"},"modified":"2024-05-23T11:47:44","modified_gmt":"2024-05-23T01:47:44","slug":"reading-between-the-lines-some-simple-maths-in-the-time-of-covid-19","status":"publish","type":"post","link":"https:\/\/blogs.unsw.edu.au\/stemmchampions\/blog\/2020\/04\/reading-between-the-lines-some-simple-maths-in-the-time-of-covid-19\/","title":{"rendered":"Reading between the lines: some simple maths in the time of COVID-19"},"content":{"rendered":"\n

By Sara Loo<\/strong><\/p>\n\n\n\n

You don\u2019t need me to tell you that things are not as they used to be. Unless you have recently emerged from a 3-month long hike, you should be well aware of the current global atmosphere. Working from home, social distancing, lockdown. Words that have entered our everyday vernacular. There is a never-ending stream of news and updated case numbers, late night press conferences and a continually changing list of do\u2019s and don\u2019ts. <\/p>\n\n\n\n

Staying informed is important. But in these anxious times,\nkeeping up to date can be exhausting. I have seen more scientific terms in the\nnews than ever, and have been sent articles from family and friends with words\nI thought were confined to the depths of my research, never to see the light of\nday. <\/p>\n\n\n\n

To non-mathematicians, there is a long list of scientific and mathematical terms to be understood, and just So. Much. News. COVID-19 has taken over the news cycle. And, with it come phrases like enveloped viruses, antivirals, doubling time, mortality and morbidity, exponential growth. <\/p>\n\n\n\n

Though I do not by any means claim to be an expert in viral epidemiology, I currently work in understanding the evolution of infectious diseases and can claim to knowing something or other about mathematics. And there may be no better time than now to spread the good news of mathematics and its usefulness to our everyday lives. <\/p>\n\n\n\n

Exponential growth<\/strong><\/h2>\n\n\n
\n
\"\"<\/a><\/figure>\n<\/div>\n\n\n

An exponential graph can be scary to look at. When we\u2019re\ntracking cases of a disease and seeing it get larger, and then get larger even\nquicker, it\u2019s easy to see how the changing numbers may fan our fear. <\/p>\n\n\n\n

However, it\u2019s important to note that exponential growth has\nits limits, and can be slowed by employing certain preventative measures, as\nwe\u2019ve seen in countries such as Singapore, Japan and South Korea \u2013 countries that\nseem to have successfully \u2018flattened the curve\u2019. <\/p>\n\n\n\n

Even in the most dire case, the curve will flatten when\neveryone has become infected; when there\u2019s no one else left to infect. <\/p>\n\n\n\n

As an example of exponential growth slowing down, let\u2019s take\nfor example your productivity during a day of working from home. You might\nstart the day with the goal of writing a scientific manuscript, or a blog piece.\nIt might be slow to get going. Other than the inevitable writer\u2019s block,\nthere\u2019s that second coffee you need to go to the kitchen to make, and a child\u2019s\nIT issues to fix so they can join their online class. <\/p>\n\n\n\n

Once you have that hot cuppa and you\u2019ve told your child to\n\u201ctry turning it off and on again\u201d, you get to sit down and focus. Then, the\nwriting just starts. Words flow quickly. <\/p>\n\n\n\n

But then you have lunch, and you accidentally eat too much\nof last night\u2019s leftover pasta. Your kids get more and more irritable as they\nget bored of being cooped up in front of their computer screen, starting to\nthrow said leftover pasta at each other. Things get crazy at home. <\/p>\n\n\n\n

Your manuscript sits forgotten for a time. Nothing new is\nwritten. After returning to your desk, you start typing, but slowly. The excess\ncarbs slow your thinking. The length of your article still grows, but slowly. <\/p>\n\n\n\n

Like the speed of your writing in a day of working from home, we want to slow down the spread of infection. We want to impose a post-lunch carbo crash onto the outbreak. We want to reduce new cases quickly. <\/p>\n\n\n\n

SIR modelling<\/strong><\/h2>\n\n\n\n

You may have seen this simulation of little dots getting infected with COVID-19,<\/a> and the effects of social distancing on the overall spread of the outbreak (if you haven’t, please do. It’s a great visualisation). This is based on a simple mathematical model commonly used in epidemiology known as an SIR model. <\/p>\n\n\n\n

The letters stand for Susceptible, Infectious, and\nRecovered.  Individuals can be\nsusceptible to a disease, be infected by a disease, or have recovered from that\ndisease. <\/p>\n\n\n\n

Mathematical modelling is based around tracking changes to different categories of things (in this case, categories of people and their state based on whether they have a certain disease or not), assuming these changes follow a set of average behaviours. An SIR model follows this basic structure. <\/p>\n\n\n\n

Based on what we know about these average behaviours, how will the outbreak progress?<\/p>\n\n\n

\n
\"\"
An example SIR model, with mathematical detail for those so inclined<\/figcaption><\/figure>\n<\/div>\n\n\n

If 1 infected individual, say, hops off a plane into Sydney Airport, will an outbreak in Sydney? If there are 100 people in the arrival hall of the airport at the time they arrive, and we know the disease is transmissible at a certain rate, will there be an outbreak in Sydney?  <\/p>\n\n\n\n

Will all the susceptible individuals become infectious, provided they move from susceptible to infectious at a certain rate (\u03b2<\/em>)? <\/p>\n\n\n\n

R0<\/sub><\/strong><\/h2>\n\n\n\n

Understanding how quickly the outbreak progresses in infectious disease modelling revolves around a value called R0<\/sub> (pron. arr-naught). The basic description of R0<\/sub> is that it is a measure of the average number of new infections every infected individual is likely to cause.<\/p>\n\n\n\n

Without going into the mathematical details, this is often dependent on the population size, the rate of transmission (how easy it is to transmit \u2013 i.e. can I get it by just touching the same elevator button as someone who is sick, or do they need to sneeze directly into my mouth), and how many other people are around that are likely to get sick too. <\/p>\n\n\n\n

Numerically, an R0<\/sub> greater than 1 indicates that a disease will spread throughout a population. Public health initiatives aim to reduce this value to less than 1, in order to minimise the effect of a disease outbreak and eliminate it from a population. <\/p>\n\n\n\n

#stayhome aims to reduce this R0<\/sub> by effectively removing people from the population. If they\u2019re infected they can\u2019t infect any more people. If they\u2019re susceptible, they can\u2019t get infected and subsequently infect more people. <\/p>\n\n\n\n

You may have seen this represented in the form of match\nsticks, dominoes, or a family-tree-like transmission chain. Whatever the medium\nyou\u2019ve seen the information conveyed, the message is the same. If possible,\nstay home. It may not be possible for everyone, but for those who can: stay\nhome. <\/p>\n\n\n\n

While we are living in uncertain times, and though\nmathematics has the reputation of being stressful and equally anxiety-inducing,\nthe numbers and predictions you see in the news are based on well-studied\nmodels. I, for one, take comfort in that. <\/p>\n\n\n\n

Follow Sara on Twitter<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

By Sara Loo You don\u2019t need me to tell you that things are not as they used to be. Unless you have recently emerged from a 3-month long hike, you should be well aware of the current global atmosphere. Working from home, social distancing, lockdown. Words that have entered our everyday vernacular. There is a … Continue reading “Reading between the lines: some simple maths in the time of COVID-19”<\/span><\/a><\/p>\n","protected":false},"author":101473,"featured_media":1258,"comment_status":"open","ping_status":"open","sticky":true,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"ngg_post_thumbnail":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false,"_members_access_role":[],"_members_access_error":""},"categories":[57407],"tags":[],"class_list":["post-1241","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-archives"],"yoast_head":"\nReading between the lines: some simple maths in the time of COVID-19 - UNSW STEMM Champions Program Blog<\/title>\n<meta name=\"description\" content=\"An exponential graph can be scary to look at. 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