Leaving To Rural Case Study

The leaving rate for rural susceptible individual to urban areas are due to ${\displaystyle l_{21}S_{11} \textrm{ as a result~~} S_{11} \rightarrow S_{11}-1 and S_{21} \rightarrow S_{21}+1}$, the urban susceptible individuals leaving to rural areas are due to ${\displaystyle l_{12}S_{22} \textrm{ thus} S_{22} \rightarrow S_{22}-1 and S_{12} \rightarrow S_{12}+1}$, the infectious individual leaving to urban areas is ${\displaystyle l_{21}I_{11} \textrm{ hence} I_{11} \rightarrow I_{11}-1 and I_{21} \rightarrow I_{21}+1}$, the urban infectious individual leaving to rural areas are due to ${\displaystyle l_{12}I_{22} \textrm{ so ~~that} I_{22} \rightarrow I_{22}-1 and I_{12} \rightarrow I_{12}+1}$, the rural removed individuals
The death due to natural deaths for, rural susceptible individual in rural areas is ${\displaystyle \mu_{11}S_{11} \textrm{ so ~~that} S_{11} \rightarrow S_{11}-1 }$, urban susceptible individual in rural areas is ${\displaystyle \mu_{12}S_{12} \textrm{ as~~a~~ result} S_{12} \rightarrow S_{12}-1 }$, rural susceptible individual in urban areas is ${\displaystyle \textrm{rate}= \mu_{21}S_{21} \textrm{ thus } S_{21} \rightarrow S_{21}-1 }$, the urban susceptible individual in urban areas is ${\displaystyle \mu_{22}S_{22} \textrm{ so ~~that} S_{22} \rightarrow S_{22}-1 }$, the rural infectious individual in rural areas is ${\displaystyle \textrm{rate}= \mu_{11}I_{11} \textrm{hence} I_{11} \rightarrow I_{11}-1 }$, the urban infectious individual in rural areas is ${\displaystyle \mu_{12}I_{12} \textrm{consequently} I_{12} \rightarrow I_{12}-1 }$, the rural infectious individual in urban areas is ${\displaystyle \mu_{21}I_{21} \textrm{ so ~~that} I_{21} \rightarrow I_{21}-1 }$, the urban infectious individual in urban areas is ${\displaystyle \mu_{22}I_{22} \textrm{ therefore} I_{22} \rightarrow I_{22}-1 }$, the Rural removed individual in rural areas is ${\displaystyle \mu_{11}R_{11} \textrm{ so ~~that} R_{11} \rightarrow R_{11}-1 }$, the urban removed individual in rural areas is ${\displaystyle \mu_{12}R_{12} \textrm{ then} R_{12} \rightarrow R_{12}-1 }$, the rural removed individual in rural areas is ${\displaystyle \mu_{21}R_{21} \textrm{ so
The HIV/AIDS induced death rate of rural susceptible individual in rural areas is ${\displaystyle \delta_{21}S_{11} \textrm{ as ~ a~result} S_{11} \rightarrow S_{11}-1 }$, the rural susceptible individual in urban is ${\displaystyle \delta_{21}S_{21} \textrm{ so ~~that} S_{21} \rightarrow S_{21}-1 }$, the urban susceptible individual in rural areas is ${\displaystyle \delta_{12}S_{12} \textrm{ thus} S_{12} \rightarrow S_{12}-1 }$, the urban susceptible individual in urban areas HIV/AIDS induced death ${\displaystyle \textrm{rate}= \delta_{22}S_{22} \textrm{consequently} S_{22} \rightarrow S_{22}-1 }$, the rural infectious individual in rural areas is ${\displaystyle \delta_{11}I_{11} \textrm{hence} I_{11} \rightarrow I_{11}-1 }$ and the rural total population in rural is ${\displaystyle N_{11} \rightarrow N_{11}-1 }$, the urban infectious individual in rural areas is ${\displaystyle \delta_{12}I_{12} \textrm{ as ~ a~ result} I_{12} \rightarrow I_{12}-1 }$ and the total urban total population in rural areas is ${\displaystyle N_{12} \rightarrow N_{12}-1 }$ , the rural infectious individual in urban areas is ${\displaystyle \delta_{21}I_{21} \textrm{ so ~~that} I_{21} \rightarrow I_{21}-1 }$ and the rural total population in urban areas is ${\displaystyle N_{21} \rightarrow N_{21}-1 }$, the urban infectious individual in urban areas is ${\displaystyle \delta_{22}I_{22} \textrm{consequently} I_{22} \rightarrow S_{22}-1 }$ and the urban total