Table 1 Transition probabilities

\((\Delta Y)_{1} = [1,0,0,0,0]^{T} \)

\(P_{1} = \mu _{h} \Delta t \)

\((\Delta Y)_{2} = [-1,1,0,0,0]^{T}\)

\(P_{2} = \beta _{h} S I_{v} ( \frac{c}{\mu _{v}} ) \Delta t\)

\((\Delta Y)_{3} = [-1,0,0,0,0]^{T}\)

\(P_{3} = \mu _{h} S\Delta t \)

\((\Delta Y)_{4} = [0,-1,1,0,0]^{T}\)

\(P_{4} = \alpha _{h} X\Delta t \)

\((\Delta Y)_{5} = [0,-1,0,0,0]^{T}\)

\(P_{5} = \mu _{h} X\Delta t \)

\((\Delta Y)_{6} = [0,0,-1,0,0]^{T}\)

\(P_{6} = (r+\mu _{h} )\Delta t \)

\((\Delta Y)_{7} = [0,0,0,1,0]^{T} \)

\(P_{7} = \beta _{v} I N_{T} \Delta t \)

\((\Delta Y)_{8} = [0,0,0,-1,0]^{T}\)

\(P_{8} = \beta _{v} I N_{T} X_{v} \Delta t \)

\((\Delta Y)_{9} = [0,0,0,-1,0]^{T} \)

\(P_{9} = \beta _{v} I N_{T} I_{v} \Delta t \)

\((\Delta Y)_{10} = [0,0,0,-1,1]^{T}\)

\(P_{10} = \alpha _{v} X_{v} \Delta t \)

\((\Delta Y)_{11} = [0,0,0,-1,0]^{T}\)

\(P_{11} = \mu _{v} X_{v} \Delta t \)

\((\Delta y)_{12} = [0,0,0,0,-1]^{T} \)

\(P_{12} = \mu _{v} I_{v} \Delta t \)