Table 4 Probabilities associated with changes in SEIRS model

1

\([1, 0, 0, 0, 0, 0, 0]^T\)

\((\Lambda _h + \psi _h N_{h,\zeta }) \Delta t\)

A new host enters the human susceptible class

2

\([1, 0, 0, -1, 0, 0, 0]^T\)

\(\rho _h R_{h,\zeta } \Delta t\)

A recovered host becomes susceptible again

3

\([-1, 1, 0, 0, 0, 0, 0]^T\)

\(\frac{\sigma _v \sigma _h \beta _{hv}I_{v,\zeta }S_{h,\zeta }}{\sigma _v N_{v,\zeta } + \sigma _h N_{h,\zeta }}\Delta t\)

A susceptible host enters exposed state

4

\([-1, 0, 0, 0, 0, 0, 0]^T\)

\((\mu _{1h} + \mu _{2h} N_{h,\zeta })S_{h,\zeta } \Delta t\)

A susceptible host dies

5

\([0, -1, 1, 0, 0, 0, 0]^T\)

\(\nu _h E_{h,\zeta } \Delta t\)

An exposed host enters infectious state

6

\([0, -1, 0, 0, 0, 0, 0]^T\)

\((\mu _{1h} + \mu _{2h} N_{h,\zeta })E_{h,\zeta } \Delta t\)

An exposed host dies

7

\([0, 0, -1, 1, 0, 0, 0]^T\)

\(\gamma _h I_{h,\zeta } \Delta t\)

An infectious host enters recovered state

8

\([0, 0, -1, 0, 0, 0, 0]^T\)

\((\mu _{1h} + \mu _{2h} N_{h,\zeta } + \delta _h) I_{h,\zeta } \Delta t\)

An infectious host dies

9

\([0, 0, 0, -1, 0, 0, 0]^T\)

\((\mu _{1h} + \mu _{2h} N_{h,\zeta }) R_{h,\zeta } \Delta t\)

A recovered host dies

10

\([0, 0, 0, 0, 1, 0, 0]^T\)

\(\psi _v N_{v,\zeta } \Delta t\)

A new mosquito enters the vector susceptible class

11

\([0, 0, 0, 0, -1, 1, 0]^T\)

\(\frac{\sigma _v \sigma _h \beta _{hv}I_{v,\zeta } S_{h,\zeta }}{\beta _{vh} I_{h,\zeta } + \tilde{\beta }_{vh} R_{h,\zeta }} \Delta t\)

A susceptible vector enters exposed state

12

\([0, 0, 0, 0, -1, 0, 0]^T\)

\((\mu _{1v} + \mu _{2v} N_{v,\zeta }) S_{v,\zeta } \Delta t\)

A susceptible vector dies

13

\([0, 0, 0, 0, 0, -1, 1]^T\)

\(\nu _v E_{v,\zeta } \Delta t\)

An exposed vector enters infectious state

14

\([0, 0, 0, 0, 0, -1, 0]^T\)

\((\mu _{1v} + \mu _{2v} N_{v,\zeta }) E_{v,\zeta } \Delta t\)

An exposed vector dies

15

\([0, 0, 0, 0, 0, 0, -1]^T\)

\((\mu _{1v} + \mu _{2v} N_{v,\zeta }) I_{v,\zeta } \Delta t\)

An infectious vector dies