Table 1 State transitions and rates of all possible events involving susceptible, infected and temporally immune (recovered) animals.
From: Permafrost dynamics and the risk of anthrax transmission: a modelling study
Event | State transition | Event rate |
|---|---|---|
Birth of a susceptible | \(\mathscr {(S,I,R)}\rightarrow \mathscr {(S}+1\mathscr {,I,R)}\) | \(e_1=\mu H\) |
Death of a susceptible | \(\mathscr {(S,I,R)}\rightarrow \mathscr {(S}-1\mathscr {,I,R)}\) | \(e_2=\mu {\mathscr {S}}\) |
Symptomatic infection | \(\mathscr {(S,I,R)}\rightarrow ({\mathscr {S}}-1,{\mathscr {I}}+1,{\mathscr {R}})\) | \(e_3=\sigma {\mathscr {F}}(t) {\mathscr {S}}\) |
Death of an infected | \(\mathscr {(S,I,R)}\rightarrow \mathscr {(S,I}-1, {\mathscr {R}})\) | \(e_4=\mu {\mathscr {I}}\) |
Anthrax-related death | \(\mathscr {(S,I,R)}\rightarrow \mathscr {(S,I}-1,{\mathscr {R}})\) | \(e_5=\alpha {\mathscr {I}}\) |
Asymptomatic infection | \(\mathscr {(S,I,R)}\rightarrow ({\mathscr {S}}-1,{\mathscr {I}},{\mathscr {R}}+1)\) | \(e_6=(1-\sigma ){\mathscr {F}}(t) {\mathscr {S}}\) |
Death of a recovered | \(\mathscr {(S,I,R)}\rightarrow \mathscr {(S,I,R}-1)\) | \(e_7=\mu {\mathscr {R}}\) |
Immunity loss | \(\mathscr {(S,I,R)}\rightarrow ({\mathscr {S}}+1,{\mathscr {I}},{\mathscr {R}}-1)\) | \(e_8=\rho {\mathscr {R}}\) |
