Name five mathematical tools which have proved useful to analys this spread and forecast preventive measures against it.
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In the wake of the recent global health threat from the novel coronavirus, the World Health Organization (WHO) issued immediate counter-measures to control the spread of the disease. Have you wondered how experts gain insights that lead to timely decisions? Or how they arrive at estimates of the number of people who might get infected? How do experts visualise the progress of the infection and its capacity to cross borders? Based on what conclusions, are lockdown directives issued? And finally, how can experts predict how long an epidemic will last?
The answer lies in maths. Mathematical functions can be applied as tools to describe the dynamics of how infectious diseases propagate among people. Mathematical Modelling generates a picture or a ‘model’ of the dynamics of the disease, which can be visually represented by graphs, charts and comparative tables.
Models provide valuable inputs to visualise how diseases affect people. Hence, epidemiologists — public health experts – use them extensively to assess risk or to analyse intervention strategies to control or prevent diseases. Insights available from models facilitate disease management protocols like mass vaccination drives, treatment patterns, and precautionary procedures.
When the infectious disease is an unknown one, such as the present coronavirus pandemic, models become all the more vital for policymaking. “Models can help answer several questions that impact policy. In most cases, they are the only rational way of formulating such questions and evaluating how different interventions might shape the spread of the disease,” says Gautam I Menon, Professor, Departments of Physics and Biology, Ashoka University (Sonipat) and Institute of Mathematical Sciences (Chennai).
The hidden patterns
Mathematical models have century-old roots. In the 1920s, William O Kermack and AG McKendrick observed that a population that is exposed to an infection can be divided into three categories– Susceptible, Infected, and Recovered. They found a way of representing the numbers in each of these groups mathematically.
They translated their idea into differential equations, which draw a relationship between a physical quantity and its rate of change. The Kermack-McKendrick equation estimates what fraction of the population, over time, enters into one or the other of these categories, starting from an initial state in which one infectious person ‘seeds’ the infection among the rest.
From this, Kermack and McKendrick devised their classic SIR (Susceptible-Infected-Recovered) model that could predict disease spread. Since then, mathematical models have played a prominent role in transforming public health care. Governments, health organisations, scientists and hospitals depend heavily on models to deal with the onslaught of issues that arise out of medical problems.
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