This is a bit ugly, but should give you the general idea
Manipulate[
p = {(1 + Subscript[\[Epsilon], 1 ])/Subscript[\[Epsilon],
0 ], (Subscript[\[Epsilon], 0 ] - Subscript[\[Epsilon], 1 ] -
1)/(Subscript[\[Epsilon],
0 ] (1 + Subscript[\[Epsilon], 1 ]))};
Show[
{
Graphics[
{AbsolutePointSize[5], Point[p, VertexColors -> Red], Black,
Text[ToString@Round[p, 0.01], {First@p, Last@p + .02}]},
PlotRange -> {{dimmin, dimmax}, {dimmin, dimmax}}],
StreamPlot[
{1 - s - Subscript[\[Epsilon], 0 ] i s,
Subscript[\[Epsilon], 0 ]
i s - (1 + Subscript[\[Epsilon], 1 ]) i}, {s, dimmin,
dimmax},
{i, dimmin, dimmax}, StreamStyle -> {Automatic},
StreamColorFunction -> Automatic, FrameLabel -> {s, i},
StreamScale -> Automatic, ImageSize -> Full, Axes -> True,
AxesStyle -> Black, LabelStyle -> {13, GrayLevel[0], Bold}]
}
],
{{Subscript[\[Epsilon], 0 ], 3}, -30,
30, .1}, {{Subscript[\[Epsilon], 1 ], 1}, -30, 30, .1}
]
dimmin = 0 ; dimmax = 1.1 ;
The second question is very different and should be a separate post.