Skip to main content

Table 2 Probabilities associated with changes in ELPA\(_{s}\) model

From: Stochastic lattice-based modelling of malaria dynamics

l

Change, \(\Delta X^{l}_{k,\zeta }(t)\)

Probability, \(p^{l}_{k,\zeta }(t)\)

Description

1

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

\(b \psi ^{\mathsf {W}}_{\zeta } \rho _{A_o} \mathcal {A}_{o,\zeta } \Delta t\)

A new egg E is deposited by \(A_o\)

2

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

\(\mu _E \mathcal {E}_{\zeta } \Delta t\)

An egg E dies

3

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

\(\rho _E \mathcal {E}_{\zeta } \Delta t\)

An egg E hatches into a larva L

4

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

\((\mu _{L_1} + \mu _{L_2} \mathcal {L}_{\zeta } ) \mathcal {L}_{\zeta } \Delta t\)

A larva L dies

5

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

\(\rho _L \mathcal {L}_{\zeta } \Delta t\)

A larva L develops into a pupa P

6

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

\(\mu _P \mathcal {P}_{\zeta } \Delta t\)

A pupa P dies

7

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

\(\rho _P \mathcal {P}_{\zeta } \Delta t\)

A pupa P develops into a host-seeking adult \(A_h\)

8

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

\(\psi ^\mathsf {W}_{\zeta } \rho _{A_o} \mathcal {A}_{o,\zeta } \Delta t\)

An oviposition adult \(A_o\) enters host-seeking state

9

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

\(\mu _{A_h} \mathcal {A}_{h,\zeta } \Delta t\)

A host-seeking adult \(A_h\) dies

10

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

\(\psi ^\mathsf {H}_{\zeta } \rho _{A_h} \mathcal {A}_{h,\zeta } \Delta t\)

A host-seeking adult \(A_h\) enters resting state

11

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

\(\mu _{A_r} \mathcal {A}_{r,\zeta } \Delta t\)

A resting adult \(A_r\) dies

12

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

\(\rho _{A_r} \mathcal {A}_{r,\zeta } \Delta t\)

A resting adult \(A_r\) enters oviposition searching state

13

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

\(\mu _{A_o} \mathcal {A}_{o,\zeta } \Delta t\)

An oviposition searching adult \(A_o\) dies