# Modeling infections

## 781 days ago by calkin

How can we model viral infections?

One way is with a logistic function.  This is a function $f(t)$ which is a solution to

a differential equation of the form something like

$f'(t) = cf(t)(L-f(t))$

Typically, equations like this have the form

$f(t) = \frac{L}{1+de^{-ct}}$

L=100 c=1 f(t)= L/(1+exp(-c*t)) A=plot(f(t),t,-10,10,color='blue') plot(f(t),t,-10,10,color='blue') Another potential model for these sorts of phenomena is the question of how big the largest component of a random graph is.

What happens with random graphs?

We get functions appearing like

$g(t)=e^{-e^{-ct}}$

M=100 d=1 g(t)=M* exp(-exp(-d*t))
B=plot(g(t),t,-10,10,color='red') plot(g(t),t,-10,10,color='red') How do these functions compare?  Let's plot them on the same axes: $f(t)$ in blue, $g(t)$ in red.

show(A+B) We see that we have a later start, with a steeper trajectory for $g(t)$ than we do with $f(t)$.

How about modeling a population consisting of two separate groups who don't (basically) infect each other.

For example, Hubei + rest of china.

h(t)= 3*f(t) + f(t-7) plot(h(t),t,-10,20) 