I managed to get a fit for the CA coronavirus data presented in the last blog. The first step was fit a cubic polynomial of the known cases, K, to dK/dt.
Which gave the following results.
This equation was then integrated numerically to construct an integral table for Δt as a function of K. The initial value of Δt was chosen to give the best fit for K.
This table was interpolated to determine the value of K for a given value of Δt. Then the value of Δt0 was chosen to minimize ΔK.
The values of N, r, a and ρ given with the coefficients of the polynomial for dK/dt are estimates of the parameters for the SIR pandemic model. The reduced value of N may be the result of imperfect mixing.
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