. 2017 Jun 5;11(6):e0005613. doi: 10.1371/journal.pntd.0005613

Table 1. Events and reactions of the tick-capybara-disease stochastic process.

Event	Reaction
Birth of capybara	$S_{C} \overset{μ_{C} N}{\to} S_{C} + 1$
Birth of susceptible detached larvae	$S_{L D} \overset{ρ_{S S} S_{A A} + ρ_{S I} I_{A A}}{\to} S_{L D} + 1$
Birth of infected detached larvae	$I_{L D} \overset{ρ_{I I} I_{A A}}{\to} I_{L D} + 1$
Engorgement of a susceptible larva	$S_{L D} \overset{α_{L} S_{L D}}{\to} (S_{L D} - 1) + (S_{L A} + 1)$
Engorgement of an infected larva	$I_{L D} \overset{α_{L} I_{L D}}{\to} (I_{L D} - 1) + (I_{L A} + 1)$
Transmission from an infected capybara to a susceptible larvae	$S_{L A} \overset{β_{L} \frac{I_{C}}{N} θ_{S L} E_{L} S_{L A}}{\to} (S_{L A} - 1) + (I_{N D} + 1)$
Transmission from an infected larvae to a susceptible capybara	$S_{C} \overset{λ_{L} \frac{S_{C}}{N} I_{L A}}{\to} (S_{C} - 1) + (I_{C} + 1)$
Stage change from susceptible larvae to detached nymph	$S_{L A} \overset{θ_{S_{L}} E_{L} S_{L A}}{\to} (S_{L A} - 1) + (S_{N D} + 1)$
Stage change from infected larvae to detached nymph	$S_{L A} \overset{θ_{I_{L}} E_{L} I_{L A}}{\to} (S_{L A} - 1) + (S_{N D} + 1)$
Recovery rate of capybara	$I_{C} \overset{γ_{C} I_{C}}{\to} (I_{C} - 1) + (R_{C} + 1)$
Death of a susceptible capybara	$S_{C} \overset{δ_{C} S_{C}}{\to} S_{C} - 1$
Emigration of a susceptible capybara	$S_{C} \overset{ϵ_{C} S_{C}}{\to} S_{C} - 1$
Death of an infected capybara	$I_{C} \overset{δ_{C} I_{C}}{\to} I_{C} - 1$
Emigration of an infected capybara	$I_{C} \overset{ϵ_{C} I_{C}}{\to} I_{C} - 1$
Death of a recovered capybara	$R_{C} \overset{δ_{C} R_{C}}{\to} R_{C} - 1$
Emigration of a recovered capybara	$R_{C} \overset{ϵ_{C} R_{C}}{\to} R_{C} - 1$
Engorgement rate of a susceptible nymph	$S_{N D} \overset{α_{N} S_{N D}}{\to} (S_{N D} - 1) + (S_{N A} + 1)$
Engorgement rate of an infected nymph	$I_{N D} \overset{α_{N} I_{N D}}{\to} (I_{N D} - 1) + (I_{N A} + 1)$
Transmission from an infected nymph to a susceptible capybara	$S_{C} \overset{λ_{N} \frac{S_{C}}{N} I_{N A}}{\to} (S_{C} - 1) + (I_{C} + 1)$
Transmission from an infected capybara to a susceptible nymph	$S_{N A} \overset{β_{N} \frac{I_{C}}{N} θ_{S N} E_{N} S_{N A}}{\to} (S_{N A} - 1) + (I_{A D} + 1)$
Stage change from susceptible nymph to detached adult	$S_{N A} \overset{θ_{S_{N}} E_{N} S_{N A}}{\to} (S_{N A} - 1) + (S_{A D} + 1)$
Stage change from infected nymph to detached adult	$I_{N A} \overset{θ_{I_{N}} E_{N} I_{N A}}{\to} (I_{N A} - 1) + (I_{A D} + 1)$
Engorgement of a susceptible adult	$S_{A D} \overset{α_{A} S_{A D}}{\to} (S_{A D} - 1) + (S_{A A} + 1)$
Engorgement of an infected adult	$I_{A D} \overset{α_{A} I_{A D}}{\to} (I_{A D} - 1) + (I_{A A} + 1)$
Transmission from an infected adult tick to a susceptible capybara	$S_{C} \overset{λ_{A} \frac{S_{C}}{N} I_{A A}}{\to} (S_{C} - 1) + (I_{C} + 1)$