Tipping Point I

"For any given population of susceptibles, there is some critical combination of contact frequency, infectivity, and disease duration just great enough for the positive loop to dominate the negative loops. That threshold is known as the tipping point. Below the tipping point, the system is stable: if the disease is introduced into the community, there may be a few new cases, but on average, people will recover faster than new cases are generated. Negative feedback dominates and the population is resistant to an epidemic. Past the tipping point, the positive loop dominates .The system is unstable and once a disease arrives, it can spread like wildfire that is, by positive feedback-limited only by the depletion of the susceptible population." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"If the contact rate, infectivity, and duration of infection are small enough, the system is below the tipping point and stable. Such a situation is known as herd immunity because the arrival of an infected individual does not produce an epidemic (though a few unlucky individuals may come in contact with any infectious arrivals and contract the disease, the group as a community is protected). However, changes in the contact rate, infectivity, or duration of illness can push a system past the tipping point." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"The existence of the tipping point means it is theoretically possible to completely eradicate a disease. Eradication does not require a perfect vaccine and universal immunization but only the weaker condition that the reproduction rate of the disease fall and remain below one so that new cases arise at a lower rate than old cases are resolved." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world. ", 2000)

"The sharp boundary between an epidemic and stability defined by the tipping point in the deterministic models becomes a probability distribution characterizing the chance an epidemic will occur for any given average rates of interaction, infectivity, and recovery. Likewise, the SI and SIR models assume a homogeneous and well-mixed population, while in reality it is often important to represent subpopulations and the spatial diffusion of an epidemic." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"In the real world, advertising is expensive and does not persist indefinitely. The marketing plan for most new products includes a certain amount for a kickoff ad campaign and other initial marketing efforts. If the product is successful, further advertising can be supported out of the revenues the product generates. If, however, the product does not take off, the marketing budget is soon exhausted and external sources of adoption fall. Advertising is not exogenous, as in the Bass model, but is part of the feedback structure of the system. There is a tipping point for ideas and new products no less than for diseases." (John D Sterman, "Business Dynamics: Systems thinking and modeling for a complex world", 2000)

"The tipping point is that magic moment when an idea, trend, or social behavior crosses a threshold, tips, and spreads like wildfire." (Malcolm T Gladwell, "The Tipping Point: How Little Things Can Make a Big Difference", 2000)

"This possibility of sudden change is at the center of the idea of the Tipping Point and might well be the hardest of all to accept. [...] The Tipping Point is the moment of critical mass, the threshold, the boiling point." (Malcolm T Gladwell, "The Tipping Point: How Little Things Can Make a Big Difference", 2000)

"But in mathematics there is a kind of threshold effect, an intellectual tipping point. If a student can just get over the first few humps, negotiate the notational peculiarities of the subject, and grasp that the best way to make progress is to understand the ideas, not just learn them by rote, he or she can sail off merrily down the highway, heading for ever more abstruse and challenging ideas, while an only slightly duller student gets stuck at the geometry of isosceles triangles." (Ian Stewart, "Why Beauty is Truth: A history of symmetry", 2007)

"The product that first gets over its own tipping point attracts many consumers and this may make the competing product less attractive. Being the first to reach this tipping point is very important - more important than being the 'best' in an abstract sense." (David Easley & Jon Kleinberg, "Networks, Crowds, and Markets: Reasoning about a Highly Connected World", 2010)

"Stochastic variability and tipping points in the catch are two different dynamical phenomena. Yet they are both compatible with real-world data [...]" (John D W Morecroft, "Strategic Modelling and Business Dynamics: A Feedback Systems Approach", 2015)