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Table 2 Permissibility conditions for the κ X models of Eq. (4)

From: Spatiotemporal modelling and mapping of the bubonic plague epidemic in India

(ν, μ) c a ζ b ρ a ρζ
(0,0) c ≥ 0 a0 ≥ 0 b0 ≥ 0 a00 ≥ 0
(0,1) c ≥ 0 a0,a1 ≥ 0 b0 ≥ 0 a00,a01 ≥ 0
(0,2) c ≥ 0 a0,a2 ≥ 0 a1 ≥ - b0 ≥ 0 a00,a01 ≥ 0 a01 ≥ 0-
(1,0) c ≥ 0 a0 ≥ 0 b0,b1 ≥ 0 a00,a10 ≥ 0
(1,1) c ≥ 0 a0,a1 ≥ 0 b0,b1 ≥ 0 a00,a01,a10,a11 ≥ 0
(1,2) c ≥ 0 a0,a2 ≥ 0 a1 ≥ - b0,b1 ≥ 0 a00,a10,a02,a12 ≥ 0 a01 ≥ - a11 ≥ -
(2,0) c ≥ 0 a0 ≥ 0 b0,b2 ≥ 0 b1 ≥ - a00,a20 ≥ 0 a10 ≥ -
(2,1) c ≥ 0 a0,a1 ≥ 0 b0,b2 ≥ 0 b1 ≥ - a00,a01,a20,a21 ≥ 0 a10 ≥ - a11 ≥ -
(2,2) c ≥ 0 a0,a2 ≥ 0 a1 ≥ - b0,b2 ≥ 0, b1 ≥ - a00,a02,a20,a22 ≥ 0 a10 ≥ - a01 ≥ - a11 ≥ - a21 ≥ - a12 ≥ -