$+R_h-{}_1{I}_m{S}_h-b_h{S}_h=0$cdots$(1)$

${}_1{I}_m{S}_h-(+b_h+d)I_h=0$cdots$(2)$

$I_h-(+b_h)R_h=0$cdots$(3)$

$c{S}_m-\frac{c{E}_g}{k}{S}_m+c{I}_m-\frac{c{E}_h}{k}{I}_m-(+d_L)E_g=0$cdots$(4)$

$E_g-(+d_L)L_a=0$cdots$(5)$

$L_a-{}_2{I}_h{S}_m-{}_3{R}_h{S}_m-b_m{S}_m=0$cdots$(6)$

${}_2{I}_h{S}_m+{}_3{R}_h{S}_m-b_m{I}_m=0$cdots$(7)$

Solve this simultaneously for

$S_h,I_h,R_h,S_m,I_m,E_g,L_a$

Note: Might be difficult to solve by hand so will recommend the use of maple or python. clearly show the approach $($codes$)$ used. Do not change anything in the question and present the final solution as well as the codes if you used any programming language.