Mathematical Modelling and Modelling assumptions In our final

Modelling assumptions In our final model, we consider a third compartment. This allows individuals

An improved compartmental model Susceptibles, S Or we can form the equation: Infectives, I

Rates of change To understand the spread of this disease, we want to know

A level Maths does not equip us to solve these differential equations. A numerical

Explore the S-I-R curves Generate the curves for your derivatives. Look at how the

Modelling assumptions ay vary m s e t a r n io s is

b) Use your curves to make observations such as: the maximum proportion of the

Have a look at how academic institutes have responded to COVID-19 Other areas to

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Mathematical Modelling and

Modelling assumptions In our final model, we consider a third compartment. This allows individuals to move out of the infectives group. partm m o c r e h t r u f a e Us ent roup g e h t t s a f w o h Consider owing. r g is s e iv t c e f in of ious t c e f in is l a u id iv An ind ys. a d f o r e b m u n d for a fixe tious Model: the infec s period is T day

An improved compartmental model Susceptibles, S Or we can form the equation: Infectives, I Removed, R

COVID-19

Rates of change To understand the spread of this disease, we want to know how fast the group of Infectives is growing. Introduce derivatives.

Rates of change

A level Maths does not equip us to solve these differential equations. A numerical process is used beyond the scope of our course. We can input the gradient functions into a graph plotter.

Explore the S-I-R curves Generate the curves for your derivatives. Look at how the peak can be delayed and reduced. Learn how to input the derivative functions.

Modelling assumptions ay vary m s e t a r n io s is m Trans oups. r g b u s t n e r e f if d for With a third compartment, the curve of infectives resembles the characteristic curve for the spread of an infectious disease. or f s e v r u c e v a h l: Mode icity, … n th e , r e d n e g , e ag What further considerations could we take into account? Incubat ion peri o Also consider: ity, n u m im l a r u t a N Herd immunity accine v a f o t c a p im e Th d. Model: conside r indivi have be duals w en expo ho sed to a infectio n n but ar e not ye infectio t us.

Independent tasks

Discuss: transmission & recovery rates

b) Use your curves to make observations such as: the maximum proportion of the population who are infected at one time. how long it takes for the whole population to be infected. c) Compare the peak of the infective curve for different transmission rates. d) List intervention measures that could take place and give reasons why a community may want to flatten the curve by reducing and delaying the peak

Ideas to explore further

Have a look at how academic institutes have responded to COVID-19 Other areas to investigate How do tech giants use mobile phone data to monitor movement and R values? How does the study of mathematical sociology help to understand social interactions and the spread of diseases? How far can we get with computer simulation and artificial intelligence?