. 2009 Apr 1;259(2):253–263. doi: 10.1016/j.jtbi.2009.03.029

Table 1.

Possible transitions between compartments of the stochastic model that can occur in $Δ t$ unit of time.

Event	Transition during $Δ t$	Transition rate
Infection of a susceptible	$S (t) \to S (t) - 1$	$β (I_{U} + δ_{T} I_{T} + δ_{r} I_{r}) S Δ t + o (Δ t)$
Increase of untreated infection	$I_{U} (t) \to I_{U} (t) + 1$	$(1 - p) β (I_{U} + δ_{T} I_{T}) S Δ t + o (Δ t)$
Increase of treated infection	$I_{T} (t) \to I_{T} (t) + 1$	$p β (I_{U} + δ_{T} I_{T}) S Δ t + o (Δ t)$
Development of drug resistance	$I_{T} (t) \to I_{T} (t) - 1$	$α_{T} I_{T} Δ t + o (Δ t)$
Increase of resistant infection	$I_{r} (t) \to I_{r} (t) + 1$	$(β δ_{r} I_{r} S + α_{T} I_{T}) Δ t + o (Δ t)$
Recovery from untreated infection	$I_{U} (t) \to I_{U} (t) - 1$	$γ_{U} I_{U} Δ t + o (Δ t)$
Recovery from treated infection	$I_{T} (t) \to I_{T} (t) - 1$	$γ_{T} I_{T} Δ t + o (Δ t)$
Recovery from resistant infection	$I_{r} (t) \to I_{r} (t) - 1$	$γ_{U} I_{r} Δ t + o (Δ t)$
Increase in immune population	$R (t) \to R (t) + 1$	$(γ_{U} I_{U} + γ_{T} I_{T} + γ_{U} I_{r}) Δ t + o (Δ t)$
Death from untreated infection	$I_{U} (t) \to I_{U} (t) - 1$	$d_{U} I_{U} Δ t + o (Δ t)$
Death from treated infection	$I_{T} (t) \to I_{T} (t) - 1$	$d_{T} I_{T} Δ t + o (Δ t)$
Death from resistant infection	$I_{r} (t) \to I_{r} (t) - 1$	$d_{_{U, r}} I_{r} Δ t + o (Δ t)$
Increase in death	$D (t) \to D (t) + 1$	$(d_{U} I_{U} + d_{T} I_{T} + d_{U, r} I_{r}) Δ t + o (Δ t)$