Plot with Epilog doesn't show up in Show [duplicate]

This question already has an answer here:

With[{r = 0.3, q = 10},
ans = NSolve[r u (1 - u/q) - u^2/(1 + u^2) == 0, u]
]

Then:

With[{r = 0.3, q = 10},
vp = VectorPlot[{1, r u (1 - u/q) - u^2/(1 + u^2)},
{t, 0, 12}, {u, 0, 0.8},
PlotRange -> {{0, 12}, {0, 0.8}},
VectorScale -> {0.03, 0.03, None},
VectorPoints -> 16,
VectorStyle -> {GrayLevel[0.8]},
Axes -> True, AxesLabel -> {t, u}]
]

Which produces this plot. Then:

pfun = ParametricNDSolveValue[
{u'[t] == r u [t] (1 - u[t]/q) - u[t]^2/(1 + u[t]^2), u == a},
u, {t, 0, 12}, {r, q, a}];
With[{r = .3, q = 10},
plt3 = Plot[
Evaluate@Table[pfun[r, q, a][t], {a, 0.1, 0.7, 0.1}], {t, 0, 12},
PlotStyle -> Blue,
PlotRange -> {{0, 12}, {0, 0.8}},
Epilog -> {{Red, Thick, Dashed, Line[{{0, 0}, {12, 0}}]},
{Red, Line[{{0, u}, {12, u}} /. ans[]]}}]
]

Which produces this plot. But here is what happens with the Show command.

Show[vp, plt3]

Plot result. See, my red equilibrium solutions don't show up in the Show command. Reason? I know I can fix this with Graphics added to Show command, but I am wondering why this doesn't work.

Proving Guess who it is's Comment

pfun = ParametricNDSolveValue[
{u'[t] == r u [t] (1 - u[t]/q) - u[t]^2/(1 + u[t]^2), u == a},
u, {t, 0, 12}, {r, q, a}];

With[{r = 0.3, q = 10},
ans = NSolve[r u (1 - u/q) - u^2/(1 + u^2) == 0, u];
vp = VectorPlot[{1, r u (1 - u/q) - u^2/(1 + u^2)},
{t, 0, 12}, {u, 0, 0.8},
PlotRange -> {{0, 12}, {0, 0.8}},
VectorScale -> {0.03, 0.03, None},
VectorPoints -> 16,
VectorStyle -> {GrayLevel[0.8]},
Axes -> True, AxesLabel -> {t, u},
Epilog -> {{Red, Thick, Dashed, Line[{{0, 0}, {12, 0}}]},
{Red, Line[{{0, u}, {12, u}} /. ans[]]}}];
plt3 = Plot[
Evaluate@Table[pfun[r, q, a][t], {a, 0.1, 0.7, 0.1}], {t, 0, 12},
PlotStyle -> Blue,
PlotRange -> {{0, 12}, {0, 0.8}}]
];
Show[vp, plt3] 