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Table 4 Probabilities associated with changes in SEIRS model

From: Stochastic lattice-based modelling of malaria dynamics

l Change, \(\Delta Y^{l}_{k,\zeta }(t)\) Probability, \(p^{l}_{k,\zeta }(t)\) Description
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