Simple agent based exchange models are a commonplace in the study of wealth distribution in an artificial economy. Generally, in a system that is composed of many agents characterized by their wealth and risk-aversion factor, two agents are selected sequentially and randomly to exchange wealth, allowing for its redistribution. Here we analyze how the effect of a social protection policy, which favors agents of lower wealth during the exchange, influences stability and some relevant economic indicators of the system. On the other hand, we study how periods of interruption of these policies produce, in the short and long term, changes in the system. In most cases, a steady state is reached, but with varying relaxation times. We conclude that regulations may improve economic mobility and reduce inequality. Moreover, our results indicate that the removal of social protection entails a high cost associated with the hysteresis of the distribution of wealth. Economic inequalities increase during a period without social protection, but also they remain high for an even longer time and, in some extreme cases, inequality may be irreversible, indicating that the withdrawal of social protection yields a high cost associated with the hysteresis of the distribution of wealth.

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Due to the COVID-19 pandemic, Susceptible-Infective-Recovered (SIR) models and their variants are in high demand for predicting the number of cases in urban areas. Aiming to correctly use the experience of the epidemic evolution from one local to another, we present an analysis of the transmission rate of COVID-19 as a function of population size at the metropolitan area level for the United States. Contrary to the usual hypothesis in epidemics modeling, we observe that the disease transmissibility scales with the logarithm of the local's population size. The analysis, made possible by a large amount of data available on simultaneous epidemics of the same type, is universal for any human-to-human transmission disease. We present a contact rate scaling theory that explains the results.

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