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Theory and Modern Applications

Table 2 State transitions and rates describing the CTMC Zika dynamics.

From: On the effect of postponing pregnancy in a Zika transmission model

Description

State Transition

Rate

Pregnancy

\((S_{h},S_{p})\to (S_{h}-1,S_{p}+1)\)

W

Death of \(S_{p}\)

\(S_{p}\to S_{p}-1\)

\(\mu _{h} S_{p}\)

Infection of \(S_{p}\)

\((S_{p},I_{p})\to (S_{p}-1,I_{p}+1)\)

\(\beta _{h}S_{p}I_{v}/N_{h}\)

Death of \(I_{p}\)

\(I_{p}\to I_{p}-1\)

\(\mu _{h}I_{p}\)

Recovery of \(I_{p}\)

\((I_{p},R_{p})\to (I_{p}-1,R_{p}+1)\)

\(\gamma _{h}I_{p}\)

Loss of \(S_{p}\)

\((S_{p},S_{h})\to (S_{p}-1,S_{h}+1)\)

\(\alpha S_{p}\)

Loss of \(I_{p}\)

\((I_{p},I_{h})\to (I_{p}-1,I_{h}+1)\)

\(\alpha I_{p}\)

Loss of \(R_{p}\)

\((R_{p},R_{h})\to (R_{p}-1,R_{h}+1)\)

\(\alpha R_{p}\)

Birth of \(S_{h}\)

\(S_{h}\to S_{h}+1\)

\(\alpha S_{p}+\alpha (1-\rho )(I_{p}+R_{p})\)

Death of \(S_{h}\)

\(S_{h}\to S_{h}-1\)

\(\mu _{h}S_{h}\)

Infection of \(S_{h}\)

\((S_{h},I_{h})\to (S_{h}-1,I_{h}+1)\)

\(\beta _{h}S_{h}I_{v}/N_{h}\)

Death of \(I_{h}\)

\(I_{h}\to I_{h}-1\)

\(\mu _{h}I_{h}\)

Recovery of \(I_{h}\)

\((I_{h},R_{h})\to (I_{h}-1,R_{h}+1)\)

\(\gamma _{h}I_{h}\)

Death of \(R_{h}\)

\(R_{h}\to R_{h}-1\)

\(\mu _{h}R_{h}\)

Birth of B

B→B + 1

\(\rho \alpha (I_{p}+R_{p})\)

Death of B

B→B − 1

\(\mu _{h}B\)

Vector recruitment

\(S_{v}\to S_{v}+1\)

\(A_{v}\)

Death of \(S_{v}\)

\(S_{v}\to S_{v}-1\)

\(\mu _{v}S_{v}\)

Vector infection

\((S_{v},I_{v})\to (S_{v}-1,I_{v}+1)\)

\(\beta _{v}S_{v}(I_{h}+I_{p})/N_{h}\)

Death of \(I_{v}\)

\(I_{v}\to I_{v}-1\)

\(\mu _{v}I_{v}\)