Stochastic disease spreading and containment policies under state-dependent probabilities.

We analyze the role of disease containment policy in the form of treatment in a stochastic economic-epidemiological framework in which the probability of the occurrence of random shocks is state-dependent, namely it is related to the level of disease prevalence. Random shocks are associated with the diffusion of a new strain of the disease which affects both the number of infectives and the growth rate of infection, and the probability of such shocks realization may be either increasing or decreasing in the number of infectives. We determine the optimal policy and the steady state of such a stochastic framework, which is characterized by an invariant measure supported on strictly positive prevalence levels, suggesting that complete eradication is never a possible long run outcome where instead endemicity will prevail. Our results show that: (i) independently of the features of the state-dependent probabilities, treatment allows to shift leftward the support of the invariant measure; and (ii) the features of the state-dependent probabilities affect the shape and spread of the distribution of disease prevalence over its support, allowing for a steady state outcome characterized by a distribution alternatively highly concentrated over low prevalence levels or more spread out over a larger range of prevalence (possibly higher) levels.

Infectious diseases and social distancing under state-dependent probabilities.

We analyze the implications of infectious diseases and social distancing in an extended SIS framework to allow for the presence of stochastic shocks with state dependent probabilities. Random shocks give rise to the diffusion of a new strain of the disease which affects both the number of infectives and the average biological characteristics of the pathogen causing the disease. The probability of such shock realizations changes with the level of disease prevalence and we analyze how the properties of the state-dependent probability function affect the long run epidemiological outcome which is characterized by an invariant probability distribution supported on a range of positive prevalence levels. We show that social distancing reduces the size of the support of the steady state distribution decreasing thus the variability of disease prevalence, but in so doing it also shifts the support rightward allowing eventually for more infectives than in an uncontrolled framework. Nevertheless, social distancing is an effective control measure since it concentrates most of the mass of the distribution toward the lower extreme of its support.

Mobility Choices and Strategic Interactions in a Two-Group Macroeconomic-Epidemiological Model.

We analyze the implications of strategic interactions between two heterogeneous groups (i.e., young and old, men and women) in a macroeconomic-epidemiological framework. The interactions between groups determine the overall prevalence of a communicable disease, which in turn affects the level of economic activity. Individuals may lower their disease exposure by reducing their mobility, but since changing mobility patterns is costly, each group has an incentive to free ride negatively affecting the chances of disease containment at the aggregate level. By focusing on an early epidemic setting, we explicitly characterize the cooperative and noncooperative equilibria, determining how the inefficiency induced by noncooperation (i.e., failure to internalize epidemic externalities) depends both on economic and epidemiological parameters. We show that long-run eradication may be possible even in the absence of coordination, but coordination leads to a faster reduction in the number of infectives in finite time. Moreover, the inefficiency induced by noncooperation increases (decreases) with the factors increasing (decreasing) the pace of the disease spread.

COVID-19 epidemic and mitigation policies: Positive and normative analyses in a neoclassical growth model.

The COVID-19 pandemic is still ravaging the planet, but its (short-, medium-, and long-term) diverse effects on health, economy, and society are far from being understood. This article investigates the potential impact of a deadly epidemic and its main nonpharmaceutical control interventions (social distancing vs. testing-tracing-isolation, TTI) on capital accumulation and economic development at different time scales. This is done by integrating an epidemiological susceptible-infectious-recovered model with a Solow-type growth model including public expenditure, as a parsimonious setting to offer insights on the trade-off between protecting human lives and the economy and society. The work clarifies (i) the long-term interactions amongst a deadly infection, demography, and capital accumulation, (ii) the lack of viability of persistent social distancing measures also using an analytical characterization, and the threat of policy-enhanced COVID-19 endemicity, (iii) the potentially high return on investments in TTI activities to avoid future lockdowns and related capital disruption. It also quantifies the welfare effects of a range of policies, confirming a counterintuitive role for tax-funded preventive investments aimed at strengthening TTI as more desirable interventions than generalized lockdowns.

Epidemics and macroeconomic outcomes: Social distancing intensity and duration.

We analyze the determination of the optimal intensity and duration of social distancing policy aiming to control the spread of an infectious disease in a simple macroeconomic-epidemiological model. In our setting the social planner wishes to minimize the social costs associated with the levels of disease prevalence and output lost due to social distancing, both during and at the end of epidemic management program. Indeed, by limiting individuals' ability to freely move or interact with others (since requiring to wear face mask or to maintain physical distance from others, or even forcing some businesses to remain closed), social distancing has on the one hand the effect to reduce the disease incidence and on the other hand to reduce the economy's productive capacity. We analyze both the early and the advanced epidemic stage intervention strategies highlighting their implications for short and long run health and macroeconomic outcomes. We show that both the intensity and the duration of the optimal social distancing policy may largely vary according to the epidemiological characteristics of specific diseases, and that the balancing of the health benefits and economic costs associated with social distancing may require to accept the disease to reach an endemic state. Focusing in particular on COVID-19 we present a calibration based on Italian data showing how the optimal social distancing policy may vary if implemented at national or at regional level.

Fractal attractors in economic growth models with random pollution externalities.

We analyze a discrete time two-sector economic growth model where the production technologies in the final and human capital sectors are affected by random shocks both directly (via productivity and factor shares) and indirectly (via a pollution externality). We determine the optimal dynamics in the decentralized economy and show how these dynamics can be described in terms of a two-dimensional affine iterated function system with probability. This allows us to identify a suitable parameter configuration capable of generating exactly the classical Barnsley's fern as the attractor of the log-linearized optimal dynamical system.