Author: Chandrika Prakash Vyasarayani; Anindya Chatterjee
Title: New approximations, and policy implications, from a delayed dynamic model of a fast pandemic Document date: 2020_4_14
ID: ca92pbvi_119
Snippet: In the above approximation S(t) = η 1 (t) + η 2 (t) + η 3 (t) and I(t) = η 4 (t) + η 5 (t) + η 6 (t). Here, β(t) has delays but the state variables do not. Note that we approximate the dynamical system here, and not a specific solution as we did with the long wave approximation. The accuracy of the reduced order model is shown in figure 7 . For each of several sets of parameters, we find an excellent match between numerical solutions of th.....
Document: In the above approximation S(t) = η 1 (t) + η 2 (t) + η 3 (t) and I(t) = η 4 (t) + η 5 (t) + η 6 (t). Here, β(t) has delays but the state variables do not. Note that we approximate the dynamical system here, and not a specific solution as we did with the long wave approximation. The accuracy of the reduced order model is shown in figure 7 . For each of several sets of parameters, we find an excellent match between numerical solutions of the DDEs and the Galerkin based ODEs. Both continuous and discontinuous β's are considered. The reduced order model shows that our DDEs (equations (67) and (68)), though formally infinite-dimensional systems, are effectively finite-dimensional. The remaining dynamics consists of rapidly decaying components that are soon inconsequential.
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