Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses.

Nonpharmaceutical interventions (NPI) are an important tool for countering pandemics such as COVID-19. Some are cheap; others disrupt economic, educational, and social activity. The latter force governments to balance the health benefits of reduced infection and death against broader lockdown-induced societal costs. A literature has developed modeling how to optimally adjust lockdown intensity as an epidemic evolves. This paper extends that literature by augmenting the classic SIR model with additional states and flows capturing decay over time in vaccine-conferred immunity, the possibility that mutations create variants that erode immunity, and that protection against infection erodes faster than protecting against severe illness. As in past models, we find that small changes in parameter values can tip the optimal response between very different solutions, but the extensions considered here create new types of solutions. In some instances, it can be optimal to incur perpetual epidemic waves even if the uncontrolled infection prevalence would settle down to a stable intermediate level.

The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes?

The COVID-19 pandemic has devastated lives and economies around the world. Initially a primary response was locking down parts of the economy to reduce social interactions and, hence, the virus' spread. After vaccines have been developed and produced in sufficient quantity, they can largely replace broad lock downs. This paper explores how lockdown policies should be varied during the year or so gap between when a vaccine is approved and when all who wish have been vaccinated. Are vaccines and lockdowns substitutes during that crucial time, in the sense that lockdowns should be reduced as vaccination rates rise? Or might they be complementary with the prospect of imminent vaccination increasing the value of stricter lockdowns, since hospitalization and death averted then may be permanently prevented, not just delayed? We investigate this question with a simple dynamic optimization model that captures both epidemiological and economic considerations. In this model, increasing the rate of vaccine deployment may increase or reduce the optimal total lockdown intensity and duration, depending on the values of other model parameters. That vaccines and lockdowns can act as either substitutes or complements even in a relatively simple model casts doubt on whether in more complicated models or the real world one should expect them to always be just one or the other. Within our model, for parameter values reflecting conditions in developed countries, the typical finding is to ease lockdown intensity gradually after substantial shares of the population have been vaccinated, but other strategies can be optimal for other parameter values. Reserving vaccines for those who have not yet been infected barely outperforms simpler strategies that ignore prior infection status. For certain parameter combinations, there are instances in which two quite different policies can perform equally well, and sometimes very small increases in vaccine capacity can tip the optimal solution to one that involves much longer and more intense lockdowns.

Fertility in second unions in Austria: findings from the Austrian FFS.

The simultaneity of decreasing fertility and changing family structures in many European countries has led to a growing interest in fertility behavior in its relation to different family structures. The growing prevalence of higher-order unions (and the consequences for parity progression arising therefrom) is one example of an ongoing change in fertility behavior. Childbearing is not restricted to a single union but may extend over several partnerships. Fertility behavior in higher-order unions is becoming more and more important for determining completed fertility. Motivated by the work of Vikat et al. 1999, the authors investigate fertility behavior in second unions in Austria, focusing on whether and how it is influenced by the number of pre-union children of either partner.

Endogenous growth of population and income depending on resource and knowledge.

PIP: This study focuses on the dynamic, endogenous, nonlinear interactions between the economy, population growth and the environment. Literature on endogenous growth theory was reviewed and the 3-sector demoeconomic model was provided as the analytical framework for the study of sustainable development through the integration of population growth, resource use and economic growth. The model is described in such a way that the labor force is considered as a free migrating variable among three different kinds of employment: the primary sector, which harvests a renewable resource, the secondary or industrial sector, and the tertiary sector, which is responsible for the accumulation of the stock that represents a public good for all three sectors. Presented in this paper is a nontechnical outline of the model that describes the economic, demographic, and environmental interactions considered. Also given are dynamics, market equilibrium and dynamic feedback rules. Furthermore, numerical analysis of the model quantifying the resulting time paths of the variables involved is included. The dynamics are simply the outcome of the nonlinear interactions of the demographic, economic and environmental modules. Numerical studies have also shown that the system variables move with different velocity. Technology and population can generally be regarded as slow moving variables by comparison with resources.^ieng

A model on the escape from the Malthusian trap.

"We propose a model to capture the escape from the Malthusian trap in the longrun. Our aim is to emphasize the key role of endogenous technological progress--as initiated by population growth and education--for longrun economic development. In addition we stress the importance to consider the level of fertility and mortality as the determinants of economic development and not only the rate of population growth. In particular, we may observe different economic growth rates in countries with the same rate of population growth, but differing levels of birth and death rates."

A brain gain with a brain drain.

"We study human capital depletion and formation in an economy open to out-migration, as opposed to an economy which is closed. Under the assumption of asymmetric information, the enlarged opportunities and the associated different structure of incentives can give rise to a brain gain in conjunction with a brain drain. Migration by high-skill members of its workforce notwithstanding, the home country can end up with a higher average level of human capital per worker."

Slow-fast dynamics in a model of population and resource growth.

"Models of the interaction of population, the economy, and the environment often contain nonlinear functional relationships and variables that move at different speeds. These properties foster apparent unpredictabilities in system behaviour. Using a simple deterministic model of demographic, economic and environmental interactions we illustrate the usefulness of geometric singular perturbation theory in environmental population economics. In contrast to local stability analysis, the theory of slow-fast dynamics helps to gain new insights into the global behaviour of the system. In particular, the knowledge of the basins of attraction of the stationary states enables one to determine the regions of sustainable future paths of resources and population." (SUMMARY IN FRE)

Life expectancy at age 60--epidemiologic scenarios assuming delayed mortality for selected causes of death.

"The present analysis offers a projection of life expectancy at advanced ages in Austria for the year 2010. To estimate the gains in life expectancy the Simultaneous Multiple Cause-Delay (SIMCAD) method is used. This model takes into account the epidemiological concept of an additional delay in the onset of particular chronic-degenerative diseases. While the results of the SIMCAD method vary only slightly on the whole from the official projection of life expectancy at age 60, the similarity between the two projections decreases steadily with increasing age. The SIMCAD model predicts higher gains in life expectancy for the oldest age-groups of the population than do the official statistics." (SUMMARY IN FRE)

[Economic aspects of migration: remittances by migrant workers]. / Okonomische Aspekte von Migration: der Kapitaltransfer auslandischer Arbeitskrafte.

PIP: "Worldwide annual remittances...by migrant workers to their home countries amount to some 70 billion U.S. dollars, exceeded by oil export earnings only.... The amount of remittances depends on the income of both the migrants and their family members.... Remittances meant for investment at home are determined by interest rates, foreign exchange regulations, exchange rates, monetary stability etc. in the immigration and emigration countries. Home remittances and saving habits of emigrants also depend on whether or not they expect to return to their home countries and the prospects of family reunification, all of which is directly linked to the (immigration) policy and economic conditions of both the countries of origin and residence." The factors influencing remittances flowing into and out of Austria are analyzed using data from the Austrian National Bank. (EXCERPT)^ieng

Endogenous population growth may imply chaos.

The authors consider a discrete-time neoclassical growth model with an endogenous rate of population growth. The resulting one-dimensional map for the capital intensity has a tilted z-shape. Using the theory of nonlinear dynamical systems, they obtain numerical results on the qualitative behavior of time paths for changing parameter values. Besides stable and periodic solutions, erratic time paths may result. In particular, myopic and far-sighted economies--assumed to be characterized by low and high savings rate respectively--are characterized by stable per capita capital stocks, while solutions with chaotic windows exist between these two extremes.

Endogenous population growth and the exploitation of renewable resources.

The authors consider a demo-economic model where the economy consists of two sectors ("hunting and farming" and "industry"), and both sectors depend directly or indirectly on the explanation of a renewable resource. The primary sector harvests a renewable resource (fish, corn, or wood) which is used as the input into industrial production, the secondary sector of our economy. Labor is divided up between these two sectors under the assumption of competitive labor markets. A system of two nonlinear differential equations for the resources and the population is studied by phase space analysis. Using the Hopf bifurcation theorem, the authors obtain two different routes to limit cycles and prove numerically the existence of a stable Malthusian limit cycle.