begin{minipage}{0.5textwidth}   %left column
begin{align*}
    frac{mathrm{d} R1(t)}{mathrm{d} I(t)} & = frac{gamma bar{k} I(t) S(t)  +  alpha bar{k} S(t) R2(t)  + delta S(t)}{- bar{k} I(t)S(t)} \
     & =  - gamma - alpha frac{R2(t)}{I(t)}  -  frac{delta}{bar{k} I(t)}
end{align*}
end{minipage}
hfillvlinehfill
begin{minipage}{0.5textwidth} %right column
begin{align*}
    frac{mathrm{d} R1(t)}{mathrm{d} I(t)} & = frac{5.3 I(t) S(t) + 4.5 S(t) R2(t) + 0.5 S(t)}{-10 I(t) S(t)}  \
     & =  - 0.53 - 0.45 frac{R2(t)}{I(t)}  -  frac{0.05}{I(t)}
end{align*}
end{minipage}