; From Hannah Slater, 2016-02-09
METHOD RK4

STARTTIME = 0
STOPTIME=365
DT = 0.01

init S = N - 1
init E = 0
init I =1
init R = 0

Births = b*N
b = 1/10
N = 1e7
beta = 10
sigma = 1/3
delta = 1/21
lat_hum = 14

new_inf = beta*S*I/N   ; people developing latent infection
surv = exp(-b*lat_hum)  ; i.e. proportion of humans surviving the latent period
lag_inf = delay(new_inf * surv, lat_hum)  ; people that become latent 'lath_um' days ago, less those that died during that time

d/dt( S ) = Births - b*S - beta*S*I/N+delta*R
d/dt( E ) = new_inf - lag_inf - b*E
d/dt( I ) = lag_inf  - (b+sigma)*I
d/dt( R ) = sigma*I - b*R-delta*R

Ntot =S+E+I+R
prev = I/Ntot*100
