Despite overwhelming scientific evidence that vaccines are safe and effective in preventing childhood diseases, a significant minority remains skeptical, such as the anti-vax movement. Mathematicians show this may be due to “hysteresis”, where an effect persists despite changed initial conditions. : Health

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Despite overwhelming scientific evidence that vaccines are a safe and effective tool for the prevention of childhood diseases, a significant minority of the U.S. population remains skeptical of the practice, as evidenced by the persistence of the anti-vax movement.

In a study published in the journal Proceedings of the Royal Society B, Feng Fu, an assistant professor of mathematics, and colleagues showed that a phenomenon known as “hysteresis” may act as a roadblock for efforts to increase vaccination rates.

Hysteresis can be seen in many physical systems, however, it can also be applied to human society. Put simply, it refers to the persistence of a given effect even after the conditions of the initial system have been changed.

Journal Reference:

Xingru Chen, Feng Fu.

Imperfect vaccine and hysteresis.

Proceedings of the Royal Society B: Biological Sciences, 2019; 286 (1894): 20182406

DOI: 10.1098/rspb.2018.2406



Addressing vaccine compliance problems is of particular relevance and significance to public health. Despite resurgence of vaccine-preventable diseases and public awareness of vaccine importance, why is it so challenging to boost population vaccination coverage to desired levels especially in the wake of declining vaccine uptake? To understand this puzzling phenomenon, here we study how social imitation dynamics of vaccination can be impacted by the presence of imperfect vaccine, which only confers partial protection against the disease. Besides weighing the perceived cost of vaccination with the risk of infection, the effectiveness of vaccination is also an important factor driving vaccination decisions. We discover that there can exist multiple stable vaccination equilibria if vaccine efficacy is below a certain threshold. Furthermore, our bifurcation analysis reveals the occurrence of hysteresis loops of vaccination rate with respect to changes in the perceived vaccination cost as well as in the vaccination effectiveness. Moreover, we find that hysteresis is more likely to arise in spatial populations than in well-mixed populations, even for parameter choices that do not allow for bifurcation in the latter. Our work shows that hysteresis can appear as an unprecedented roadblock for the recovery of vaccination uptake, thereby helping explain the persistence of vaccine compliance problem.

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