According to this article in Scientific American, stockpiling and hoarding supplies is not a solution.

The reality is that there is little point “preparing“ for the most catastrophic scenarios some of these people envision. As a species, we live and die by our social world and our extensive infrastructure—and there is no predicting what anybody needs in the face of total catastrophe. In contrast, the real crisis scenarios we’re likely to encounter require cooperation and, crucially, “flattening the curve” of the crisis exactly so the more vulnerable can fare better, so that our infrastructure will be less stressed at any one time.

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The infectiousness of a virus, for example, depends on how much we encounter one another; how well we quarantine individuals who are ill; how often we wash our hands; whether those treating the ill have proper protective equipment; how healthy we are to begin with—and such factors are all under our control. After active measures were implemented, the R0 for the 2003 SARS epidemic, for example, went from around three, meaning each person infected three others, to 0.04. It was our response to SARS in 2003 that made sure the disease died out from earth, with less than a thousand victims globally.