Why reducing relative deprivation but not reducing income inequality might bring down COVID-19 infections

We examine an assumed link between reducing inequality in income distribution, namely reducing the Gini coefficient on one hand, and improving public health in general and lowering the incidence and severity of COVID-19 in particular on the other hand. The Gini coefficient can be shown to consist of two components, one of which is (a measure of) relative deprivation, which was found to cause social stress that harms public health. Because a component is not the whole, the lowering of inequality in the income distribution by means of reducing the Gini coefficient does not necessarily result in lowering relative deprivation. Specifically, we show that a policy of reducing income inequality aimed at improving public health might not be effective - even when, in the process, no-one's income is reduced, or all incomes increase.