ODE equations for PWID on OAT

ode.list.OAT Calculate the change of population in cells of PWID on OAT population by the ODE model.

ode.list.OAT(
  x,
  x.offoat,
  beta_o,
  beta_s,
  gamma,
  rho,
  ws,
  wp,
  mu_mat,
  mo,
  eta,
  psi,
  psi.p,
  theta.ai,
  theta.ad,
  phi,
  v2,
  v3,
  alpha,
  alpha.re,
  theta.1,
  theta.2,
  theta.t12,
  theta.t13,
  theta.t21,
  theta.t23,
  theta.t31,
  theta.t32,
  theta.t1O,
  theta.t2O,
  theta.t3O,
  oat.e,
  oat.q,
  rho.m
)

Arguments

x	a vector containing the number of individuals on OAT x = c(S1,S2,Sp,Ia,I1,I2,I3,Iap,Ip,Da,D1,D2,D3,T1,T2,T3,O1,O2,O3)
x.offoat	a vector containing # of individuals off OAT
rho	the entry rate (assume the same for all groups)
mu_mat	maturation rates (age>65)
mo	mortality rates for 19 states
eta	PrEP entry rate
psi	screening rates for susceptible or infected
psi.p	screening rates for Iap (acute HIV on PrEP)
theta.ai	transition rate from acute states (Ia) to chronic state (CD4>=500; I1)
theta.ad	transition rate from acute states (Da) to chronic state (CD4>=500; D1)
phi	% infected of people receiving ART once diagnosed
v2, v3	symptom-based case finding rate for I2 and I3, respectively
alpha	ART initiation rate for D1,D2, and D3
alpha.re	ART re-initiation rate for o1,O2, and O3
theta.1	HIV disease progression rate for those not on ART, from I1/D1 to I2/D2
theta.2	HIV disease progression rate for those not on ART, from I2/D2 to I3/D3
oat.e	OAT entry rate
oat.q	OAT dropout rate
lambda	the sufficient contact rate
lambda.p	the sufficient contact rate for those on PrEP.
1/ws	average duration uninfected individuals in compartment S remain identified after screening
1/wp	average duration uninfected individuals in compartment Sp remain on PrEP
psi.pr	entry rate for PrEP
theta.t	transition probabilities for those on ART
theta.o	ART dropout probability from states T1,T2,T3

Value

HIV diagnoses, incidence and deaths for PWID on OAT