Mathematica Not Graphing Diff Eqs Properly

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I have a system of differential equations that I'm trying to graph, which have logistic growth and should be leveling out around their respective carrying capacities. However, they're going off to infinity for some indiscernible reason.

My code is:

eqn1 = (-(S[t]/K2)T[t] + r2(1 - S[t]/K2)*S[t])

eqn2 = ((S[t]/K2)T[t] + r1(1 - T[t]/K1)*T[t])

K2 = 2.5*10^10

K1 = 10^11

r1 = .001

r2 = .001

solns = NDSolve[{S'[t] == eqn1, T'[t] == eqn2, S[0] == 10000 , T[0] == 10000}, {S, T}, {t, 0, 5000}]

Plot[Evaluate[{S[t], T[t]} /. solns], {t, 0, 100000}, PlotStyle -> {Red, Blue}]

Any insights would be much appreciated.

asked 1 min ago

user161310

1