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The aerodynamic effects of various configurations of an urban array were investigated in a wind-tunnel experiment. Three aerodynamic parameters characterising arraysthe drag coefficient (C d ), roughness length (z o ) and displacement height (d)-are used for analysis. C d is based on the direct measurement of the total surface shear using a floating element, and the other two parameters are estimated by logarithmic fitting of the measured wind profile and predetermined total drag force. The configurations of 63 arrays used for measurement were designed to estimate the effects of layout, wind direction and the height variability of the blocks on these parameters for various roughness packing densities. The results are summarised as follows: (1) The estimated C d and z o of the staggered arrays peak against the plan area index (λ p ) and frontal area index (λ f ), in contrast with values for the square arrays, which are less sensitive to λ p and λ f . In addition, the square arrays with a wind direction of 45 • have a considerably larger C d , and the wind direction increases z o /H by up to a factor of 2. (2) The effect of the non-uniformity of roughness height on z o is more remarkable when λ f exceeds 20%, and the discrepancy in z o is particularly remarkable and exceeds 200%. (3) The effect of the layout of tall blocks on C d is stronger than that of short blocks. These results indicate that the effects of both wind direction and the non-uniformity of the heights of buildings on urban aerodynamic parameters vary greatly with λ p and λ f ; hence, these effects should be taken into account by considering the roughness packing density.

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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.