Consider the following paper:

https://reader.elsevier.com/reader/sd/pii/S0893965917301611?token=4D46CE0CD4DEC9D9B6A988B5C5EBD28E17BA830CC4004D7262A209F791CC7AC11BA4C3183E572636E3A9E8113FBB17EB&originRegion=eu-west-1&originCreation=20220214125151

The methodology is understood in this paper apart from some technical things; How did the author arrive at constants $m_i, i=1,...,5$? They achieved this by killing the variable terms($xu, xv, z, u, v, yu, yv$), however when I try solving the system, it outputs all $m_i$'s equalling zero. Can someone show a detailed answer how they arrived at these constants and how they got their final form of the Lyapunov function(page 168)?

Code:

sol = Solve[{-m1 \[Beta] is + m3 l \[Beta] ss is/ls + 
     m4 (1 - l) \[Beta] ss == 
    0, -m1 \[Rho]1 \[Beta] ts + m3 \[Rho]1 l \[Beta] ss ts/ls + 
     m4 (1 - l) \[Beta] \[Rho]1 ss ts/is == 
    0, -(\[Mu] + \[Delta]) m3 + m4 \[Delta] ls/is == 0, 
   m1 \[Beta] is + m2 \[Rho]2 \[Beta] is - 
     m4 (\[Mu] + \[Alpha] + \[Gamma]) + m5 (\[Mu] + \[Rho]) == 0, 
   m1 \[Rho]1 \[Beta] ts + m2 \[Rho]1 \[Rho]2 \[Beta] ts + 
     m3 \[Rho] ts/ls - m5 (\[Mu] + \[Rho]) == 
    0, -m2 \[Rho]2 \[Beta] is + m3 \[Rho]2 \[Beta] vs is/ls == 
    0, -m2 \[Rho]1 \[Rho]2 \[Beta] ts + 
     m3 \[Rho]1 \[Rho]2 \[Beta] vs ts/ls == 0 }, {m1, m2, m3, m4, m5}]