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prevalence_ode#
View page sourceThe Prevalence Only ODE#
Theorem#
If \(S\) and \(C\) satisfy the dismod_at Ordinary Differential Equation then prevalence \(P = C / (S + C)\) satisfies
Proof#
Suppose that \(S(a)\) and \(C(a)\) satisfy the dismod_at Ordinary Differential Equation
It follows that
Using \(C = (S + C) P\), we also have
Advantage#
One advantage of this approach, over the original ODE in \((S, C)\), is that the solution is stable as \(S + C \rightarrow 0\). The \((S, C)\) approach computes \(P = C / (S + C)\).
Integrands#
All of the current integrands, except for susceptible and withC can be computed from \(P\) (given that the rates are inputs to the ODE).
S and C#
If we know all cause mortality \(\alpha = \omega + \chi P\), once we have solved for \(P\), we can compute \(\omega = \alpha - \chi P\). Furthermore
We can also compute \(S + C\), and \(C = P (S + C)\), \(S = (1 - P)(S + C)\).