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Table 3 Further constraints on model parameters

From: A model of gene-gene and gene-environment interactions and its implications for targeting environmental interventions by genotype

Condition Limits on pDZg Limits on cSD
V e ≥ 0 p g D Z ≤ p g t o p D Z MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCdaqhaaWcbaGaem4zaCgabaGaemiraqKaemOwaOfaaOGaeyizImQaemiCaa3aa0baaSqaaiabdEgaNjabdsha0jabd+gaVjabdchaWbqaaiabdseaejabdQfaAbaaaaa@3D22@  
V ge ≥ 0 p g D Z ≥ p g min D Z MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGWbaCdaqhaaWcbaGaem4zaCgabaGaemiraqKaemOwaOfaaOGaeyyzImRaemiCaa3aa0baaSqaaiabdEgaNjGbc2gaTjabcMgaPjabc6gaUbqaaiabdseaejabdQfaAbaaaaa@3D14@  
V g ≥ 0   C SD ≤ R SD
γmax ≥ γmin   If λ MD > y e + 1 require:
c SD ≥ c SDm where
c S D m = 1 − ( λ D Z − 1 ) ( 1 − R S D ) [ c M D + f g e 2 ( λ D Z − 1 ) R M D + y e f g e 2 ( c M D − 1 ) ] [ 1 + f g e 2 ( λ D Z − 1 ) ] [ ( λ D Z − 1 ) R M D − y e ] MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=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T7aSnaaBaaaleaacqWGebarcqWGAbGwaeqaaOGaeyOeI0IaeGymaedacaGLOaGaayzkaaaacaGLBbGaayzxaaWaamWaaeaadaqadaqaaiab=T7aSnaaBaaaleaacqWGebarcqWGAbGwaeqaaOGaeyOeI0IaeGymaedacaGLOaGaayzkaaGaemOuai1aaSbaaSqaaiabd2eanjabdseaebqabaGccqGHsislcqWG5bqEdaWgaaWcbaGaemyzaugabeaaaOGaay5waiaaw2faaaaaaaa@8C1F@
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Theoretical Biology and Medical Modelling

ISSN: 1742-4682