### Abstract

We consider two imperfect ways to protect against an infectious disease such as influenza, namely vaccination giving only partial immunity and a defense against contagion such as wearing a mask. We build up a new analytic framework considering those two cases instead of perfect vaccination, conventionally assumed as a premise, with the assumption of an infinite and well-mixed population. Our framework also considers three different strategy-updating rules based on evolutionary game theory: conventional pairwise comparison with one randomly selected agent, another concept of pairwise comparison referring to a social average, and direct alternative selection not depending on the usual copying concept. We successfully obtain a phase diagram in which vaccination coverage at equilibrium can be compared when assuming the model of either imperfect vaccination or a defense against contagion. The obtained phase diagram reveals that a defense against contagion is marginally inferior to an imperfect vaccination as long as the same coefficient value is used. Highlights - We build a new analytical framework for a vaccination game combined with the susceptible-infected-recovered (SIR) model. - Our model can evaluate imperfect provisions such as vaccination giving only partial immunity and a defense against contagion. - We obtain a phase diagram with which to compare the quantitative effects of partial vaccination and a defense against contagion.

Original language | English |
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Article number | 023407 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2018 |

Issue number | 2 |

DOIs | |

Publication status | Published - Feb 23 2018 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**Which is more effective for suppressing an infectious disease : Imperfect vaccination or defense against contagion?** / Kuga, Kazuki; Tanimoto, Jun.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Which is more effective for suppressing an infectious disease

T2 - Imperfect vaccination or defense against contagion?

AU - Kuga, Kazuki

AU - Tanimoto, Jun

PY - 2018/2/23

Y1 - 2018/2/23

N2 - We consider two imperfect ways to protect against an infectious disease such as influenza, namely vaccination giving only partial immunity and a defense against contagion such as wearing a mask. We build up a new analytic framework considering those two cases instead of perfect vaccination, conventionally assumed as a premise, with the assumption of an infinite and well-mixed population. Our framework also considers three different strategy-updating rules based on evolutionary game theory: conventional pairwise comparison with one randomly selected agent, another concept of pairwise comparison referring to a social average, and direct alternative selection not depending on the usual copying concept. We successfully obtain a phase diagram in which vaccination coverage at equilibrium can be compared when assuming the model of either imperfect vaccination or a defense against contagion. The obtained phase diagram reveals that a defense against contagion is marginally inferior to an imperfect vaccination as long as the same coefficient value is used. Highlights - We build a new analytical framework for a vaccination game combined with the susceptible-infected-recovered (SIR) model. - Our model can evaluate imperfect provisions such as vaccination giving only partial immunity and a defense against contagion. - We obtain a phase diagram with which to compare the quantitative effects of partial vaccination and a defense against contagion.

AB - We consider two imperfect ways to protect against an infectious disease such as influenza, namely vaccination giving only partial immunity and a defense against contagion such as wearing a mask. We build up a new analytic framework considering those two cases instead of perfect vaccination, conventionally assumed as a premise, with the assumption of an infinite and well-mixed population. Our framework also considers three different strategy-updating rules based on evolutionary game theory: conventional pairwise comparison with one randomly selected agent, another concept of pairwise comparison referring to a social average, and direct alternative selection not depending on the usual copying concept. We successfully obtain a phase diagram in which vaccination coverage at equilibrium can be compared when assuming the model of either imperfect vaccination or a defense against contagion. The obtained phase diagram reveals that a defense against contagion is marginally inferior to an imperfect vaccination as long as the same coefficient value is used. Highlights - We build a new analytical framework for a vaccination game combined with the susceptible-infected-recovered (SIR) model. - Our model can evaluate imperfect provisions such as vaccination giving only partial immunity and a defense against contagion. - We obtain a phase diagram with which to compare the quantitative effects of partial vaccination and a defense against contagion.

UR - http://www.scopus.com/inward/record.url?scp=85043585548&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85043585548&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/aaac3c

DO - 10.1088/1742-5468/aaac3c

M3 - Article

AN - SCOPUS:85043585548

VL - 2018

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

IS - 2

M1 - 023407

ER -