Answer Happy

Should be in Matlab code.
**This is the RK4 function.
function [yR4, ts] = MyRK4Method(f, y0, t0, te, h)
ts = t0:h:te;
yR4 = zeros(1, length(ts));
yR4(1) = y0;
% Iterate through time
for i=1:length(ts)-1
t = ts(i);
v1 = f(t, yR4(i));
v2 = f(t + (h/2), yR4(i) + (h/2)*v1);
v3 = f(t + (h/2), yR4(i) + (h/2)*v2);
v4 = f(t + h, yR4(i) + h*v3);
yR4(i+1) = yR4(i) + (h/6)*(v1 + 2*v2 + 2*v3 + v4);
end
end
1. A common model for the spread of transmissible diseases is called the SIR model (which stands for the susceptible, infected, recovered model). It is based on the idea that if there are a large number of susceptible and infected people, they will come into contact more often and increase the rate at which people are being infected. After some time of infection, infected people no longer have symptoms and move to the recovered population. A simple model with this behavior can be written as a system of coupled differential equations: = d S(t) = -as(t)/(t) dt d t) (6) I(t) = aS(t)/(t) – BI(t) dt d t) + R(t) = BI(t). dt Where S is susceptible, I is infected, and R is recovered. In this model: • a represents the level of exposure between susceptible and infected people (which could be decreased by doing something like a quarantine)

B is the rate of recovery for infected people The variables S, I, R are usually treated as proportions of the population, so 0 < S,I,R <1. Use the model above with time t in days, parameters B = { and a = 2 (which roughly describe an infection of 3 days and a transmission of infection once every 2 days) and initial conditions: S(0) = 1 – 1.27 x 10-6 I(0) = 1.27 x 10-6 (almost nobody is infected!) R(0) = 0. - - Adapt the Runge-Kutta 4 method included in the lab template to work for vectors (see Equation 1 and the Lab Examples file) and find an approximate solution for this system using an initial time to = 0, a final time te = 150 (days), and a step size of h = 1 (one day). Plot the curves of the susceptible, infected, and recovered populations with a legend identifying each curve and answer the question: Even though we started with a very very small portion of the population infected, what proportion of the population is ultimately infected at some point? Note: This model is very simple. In practice, agencies like the CDC and WHO use much more complicated and realistic models that account for transmission more accurately.