I'm a biologist and recently started mathematical modelling. I'm trying to find the equilibrium solutions to a set of six differential equations that represent a six-compartment model of infectious disease transmission. Although I can set this model up and run it, I'm interested in how I can solve for the unknown equilibirum prevalences in the model in terms of the known parameters (as this would be a useful way to describe aspects of the system). These are the equations:
dA/dt = m + o * C - A * (p + q + n)
dB/dt = p * A - B * (s + q * r + n)
dC/dt = s * B - C * (q + o + n)
dD/dt = q * A + o * F - D * (p * t + u + n)
dE/dt = p * t * D + q * r * B - E * (s * v + u + n)
dF/dt = s * v * E + q * C - F * (o + u + n)
And I'd like to solve for equilibrium when:
dA/dt = dB/dt = dC/dt = dD/dt = dE/dt = dF/dt = 0
i.e. solve for (A*, B*, C*, D*, E*, F*) in terms of m, o, p, q, n, s, r, t, v and u.
Any help or advice on this would be very much appreciated.