Table 2 Possible transitions between model compartments that can occur in Δt units of time
From: Public health interventions for epidemics: implications for multiple infection waves
event | transition during Δt | transition rate |
|---|---|---|
infection of a susceptible | S(t) → S(t) – 1 | β(I + δ T I T + δ r (I r + I T,r ))S(Δt) + o(Δt) |
increase in exposure (sensitive infection) | E(t) → E(t) + 1 | β(I + δ T I T )S(Δt) + o(Δt) |
decrease in exposure (sensitive infection) | E(t) → E(t) – 1 | µ E E(Δt) + o(Δt) |
increase in exposure (resistant infection) | E r (t) → E r (t) + 1 | δ r β(I r + I T,r )S(Δt) + o(Δt) |
decrease in exposure (resistant infection) | E r (t) → E r (t) – 1 | µ E E r (Δt) + o(Δt) |
increase in untreated sensitive infection | I(t) → I(t) + 1 | (I – p)µ E E(Δt) + o(Δt) |
recovery from treated infection | I(t) → I(t) – 1 | γI(Δt) + o(Δt) |
increase in untreated resistant infection | I r (t) → I r (t) + 1 | (I – p)µ E E r (Δt) + o(Δt) |
recovery from untreated resistant infection | Ir(t) → I r (t) – 1 | γI r (Δt) + o(Δt) |
increase in treated sensitive infection | I T (t) → I T (t) + 1 | pqµ E E(Δt) + o(Δt) |
recovery from treated sensitive infection | I T (t) → I T (t) – 1 | (α + γ)I T (Δt) + o(Δt) |
increase in treated resistant infection | I T,r (t) → I T,r (t) + 1 | pqµ E E(Δt) + αIΔt + o(Δt) |
recovery from treated resistant infection | I T,r (t) → I T,r (t) – 1 | γI T,r (Δt) + o(Δt) |
increase in isolated infection | J(t) → J(t) + 1 | p(1 – q)µ E (E + E r )(Δt) + o(Δt) |
recovery from disease in isolation | J(t) → J(t) – 1 | γJ(Δt) + o(Δt) |