I want to plot the (SI)-phase plane for the following epidemiological system:
m, b, a, g are parameters > 0
S'= m - b*S*I - m*S
E'=b*S*I - g*E-m*E
I'=g*E-a*I-m*I
R'=a*I-m*R
(S=susceptible individuals, E=Infected but not infectious, I=infectious, R=recovered)
Data:
m=1/(365*81)
a=1/10
b=1/3
g=1/3
all in 1/[days].
It can be shown that with those parameters the System should converge to the so-called endemic equilibrium which is circa (0.3001, 0.000071, 0.00024, 0.6996) for t to infinity.
I want to plot the (SI)-phase plane with Matlab to visualize the convergence, but it shows: KLICK ME, You can't see any "oszillation" around the equilibrium point, nor any "convergence". Zooming in won't help, maybe the numbers for I, E are too low?
My ODE-code and plot-code:
seir := {diff(e(t), t) = b*s(t)*i(t) - (m + g)*e(t), diff(i(t), t) = g*e(t) - (m + a)*i(t), diff(r(t), t) = a*i(t) - m*r(t), diff(s(t), t) = m - b*s(t)*i(t) - m*s(t)};
DEplot(seir, [s(t), e(t), i(t), r(t)], t = 0 .. 11000, [[s(0) = 0.999, e(0) = 0.001, i(0) = 0, r(0) = 0]], scene = [s(t), i(t)], stepsize = 0.1);
Changing "m" to "1/81" results in: KLICK ME This looks better. But then, of course, the equilibrium point is wrong (this way, in my equation for S' I will add 1/[years]+1/[days] which is wrong).
Any help would be appreciated. Thanks in advance.