Skip to main content

Theory and Modern Applications

Table 1 Transition of the FMD model

From: Numerical techniques for stochastic foot and mouth disease epidemic model with the impact of vaccination

\((\Delta {A})_{i}=\mathrm{Transitions}\)

\({P}_{i} =\mathrm{Probabilities}\)

(ΔA)1=[1000]T

\({P}_{1} =\mu {N}\Delta {t}\)

\(( \Delta {A} )_{2} = \begin{bmatrix} -1 & 0 & 1 & 0 \end{bmatrix}^{{T}}\)

\({P}_{2} =\beta {IS}\Delta {t}\)

\(( \Delta {A} )_{3} = \begin{bmatrix} -1 & -1 & 0 & 0 \end{bmatrix}^{{T}}\)

\({P}_{3} = ( \omega {S}+ \emptyset {V} ) \Delta {t}\)

(ΔA)4=[−1000]T

\({P}_{4} =\mu {S}\Delta {t}\)

(ΔA)5=[0−100]T

\({P}_{5} =\mu {V}\Delta {t}\)

\(( \Delta {A} )_{6} = \begin{bmatrix} 0 & 0 & -1 & 1 \end{bmatrix}^{{T}}\)

\({P}_{6} =\gamma {L}\Delta {t}\)

\(( \Delta {A} )_{7} = \begin{bmatrix} 0 & 0 & -1 & 0\end{bmatrix}^{{T}}\)

\({P}_{7} = ( \mu +\delta ) {L}\Delta {t}\)

(ΔA)8=[000−1]T

\({P}_{8} = ( \mu +\alpha +d ) {I}\Delta {t}\)