Abstract
Delay differential equations are set up for zeroth-order pandemic models in analogy with traditional SIR and SEIR models by specifying individual times of incubation and infectiousness prior to recovery. Independent linear delay relations in addition to a nonlinear delay differential equation are found for characterizing time-dependent compartmental populations. Asymptotic behavior allows a link between parameters of the delay and traditional models for their comparison. In analogy with transformation of the traditional equations into linear form giving populations and time in parametric form, approximation of the delay equations results in a simple accurate finite recursive solution. Otherwise, straightforward numerical solution is effected in terms of linearized boundary conditions specifying the distribution of instigators as to their initial infection progress—in contrast to traditional models specifying only initial average infectious and exposed populations. Examples contrasting asymptotically-linked traditional and delay models are given.
Competing Interest Statement
The authors have declared no competing interest.
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No funding was involved in this research.
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The Chan Zuckerberg Initiative, Cold Spring Harbor Laboratory, the Sergey Brin Family Foundation, California Institute of Technology, Centre National de la Recherche Scientifique, Fred Hutchinson Cancer Center, Imperial College London, Massachusetts Institute of Technology, Stanford University, University of Washington, and Vrije Universiteit Amsterdam.
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