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Epidemic evolution: Source, lock-down and removal modifications to the SIR model

Abstract The original purpose of this article was to modify the original SIR equations to allow for a direct source of infection (without which the original equations would have no solutions unless one starts with an already infected population) and also to see to what extent one could obtain multiple outbreaks of an infectious disease. In the course of developing the basic ideas several other factors arose to take prominent roles. Perhaps one of the more salient factors is the point that choosing an arbitrary time to change conditions from say a lock-down for the population to a less stringent social behavior, such as allowing partial or complete opening of businesses and schools, etc. should be based on knowledge of the disease and its evolution. Such decisions are usually made by politicians who have less than full information concerning the consequences of their actions. Several examples are given to illustrate these points.