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Grass D, Wrzaczek S, Caulkins JP, Feichtinger G, Hartl RF, Kort PM, Kuhn M, Prskawetz A, Sanchez-Romero M, Seidl A. Riding the waves from epidemic to endemic: Viral mutations, immunological change and policy responses. Theor Popul Biol 2024; 156:46-65. [PMID: 38310975 DOI: 10.1016/j.tpb.2024.02.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2022] [Revised: 01/30/2024] [Accepted: 02/01/2024] [Indexed: 02/06/2024]
Abstract
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.
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Affiliation(s)
- D Grass
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Research Group Economics, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria
| | - S Wrzaczek
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria.
| | - J P Caulkins
- Heinz College, Carnegie Mellon University, Pittsburgh, USA
| | - G Feichtinger
- Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria; Research Group Variational Analysis, Dynamics & Operations Research, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria
| | - R F Hartl
- Department of Business Decisions and Analytics, University of Vienna, Vienna, Austria
| | - P M Kort
- Tilburg School of Economics and Management, Tilburg University, Tilburg, Netherlands
| | - M Kuhn
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria
| | - A Prskawetz
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria; Research Group Economics, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria
| | - M Sanchez-Romero
- International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria; Research Group Economics, Institute of Statistics and Mathematical Methods in Economics, TU Wien, Vienna, Austria; Vienna Institute of Demography (VID), Austrian Academy of Sciences (OeAW), Vienna, Austria
| | - A Seidl
- Department of Business Decisions and Analytics, University of Vienna, Vienna, Austria; Faculty of Management, Seeburg Castle University, Seekirchen am Wallersee, Austria
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Caulkins JP, Grass D, Feichtinger G, Hartl RF, Kort PM, Kuhn M, Prskawetz A, Sanchez-Romero M, Seidl A, Wrzaczek S. The hammer and the jab: Are COVID-19 lockdowns and vaccinations complements or substitutes? Eur J Oper Res 2023; 311:233-250. [PMID: 37342758 PMCID: PMC10131897 DOI: 10.1016/j.ejor.2023.04.033] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 04/14/2022] [Accepted: 04/19/2023] [Indexed: 06/23/2023]
Abstract
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.
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Affiliation(s)
- J P Caulkins
- Heinz College, Carnegie Mellon University, Pittsburgh, USA
| | - D Grass
- International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, Laxenburg 2361, Austria
| | - G Feichtinger
- Department for Operations Research and Control Systems, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria
| | - R F Hartl
- Department of Business Decisions and Analytics, University of Vienna, Vienna, Austria
| | - P M Kort
- Tilburg School of Economics and Management, Tilburg University, Tilburg, Netherlands
| | - M Kuhn
- International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, Laxenburg 2361, Austria
- Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria
| | - A Prskawetz
- International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, Laxenburg 2361, Austria
- Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria
- Research Group Economics, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria
| | - M Sanchez-Romero
- International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, Laxenburg 2361, Austria
- Research Group Economics, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Vienna, Austria
| | - A Seidl
- Department of Business Decisions and Analytics, University of Vienna, Vienna, Austria
| | - S Wrzaczek
- International Institute for Applied Systems Analysis (IIASA), Schlossplatz 1, Laxenburg 2361, Austria
- Wittgenstein Centre for Demography and Global Human Capital (IIASA, VID/OeAW, University of Vienna), Austria
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Prskawetz A, Feichtinger G, Luptacik M, Milik A, Wirl F, Hof F, Lutz W. Endogenous growth of population and income depending on resource and knowledge. Eur J Popul 2002; 14:305-31. [PMID: 12158986 DOI: 10.1007/bf02863319] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Abstract
We set up a time-continuous version of the first-order difference equation model of cocaine use introduced by Everingham and Rydell [S.S. Everingham, C.P. Rydell, Modeling the Demand for Cocaine, MR-332-ONDCP/A/DPRC, RAND, Santa Monica, CA, 1994] and extend it by making initiation an endogenous function of prevalence. This function reflects both the epidemic spread of drug use as users 'infect' non-users and Musto's [D.F. Musto, The American Disease: Origins of Narcotic Control, Oxford University, New York, 1987] hypothesis that drug epidemics die out when a new generation is deterred from initiating drug use by observing the ill effects manifest among heavy users. Analyzing the model's dynamics suggests that drug prevention can temper drug prevalence and consumption, but that drug treatment's effectiveness depends critically on the stage in the epidemic in which it is employed. Reducing the number of heavy users in the early stages of an epidemic can be counter-productive if it masks the risks of drug use and, thereby, removes a disincentive to initiation. This strong dependence of an intervention's effectiveness on the state of the dynamic system illustrates the pitfalls of applying a static control policy in a dynamic context.
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Affiliation(s)
- D A Behrens
- Department of Operations Research and Systems Theory, Vienna University of Technology, Austria.
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Abstract
"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."
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Prskawetz A, Feichtinger G. Endogenous population growth may imply chaos. J Popul Econ 1995; 8:59-80. [PMID: 12289750 DOI: 10.1007/bf00172038] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
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.
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Abstract
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.
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Feichtinger G, Novak AJ. How stock dependent flow rates may imply chaos in educational planning. Math Popul Stud 1994; 5:75-121. [PMID: 12288880 DOI: 10.1080/08898489409525388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
"The aim of the present paper is to illustrate how extremely complex patterns may be generated in a simple model of educational planning. In particular, we will show that certain dependencies of the flow rates on the teacher/student ratio imply nonlinearities which are substantial enough to generate erratic behaviour of the time paths. The main message is that chaos in educational planning may result from assumptions which are indeed qualitatively realistic but which are quantitatively exaggerated." (SUMMARY IN FRE)
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Stockenhuber K, Seggl W, Feichtinger G, Szyszkowitz R. [Conservative and semiconservative treatment of calcaneus fractures]. Orthopade 1991; 20:43-54. [PMID: 2034444] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 12/29/2022]
Abstract
The functional closed and percutaneous techniques for the treatment of fractures of the os calcis are described. We compare the different classifications, reduction techniques, advantages and disadvantages, as well as the results, after open reduction and internal fixation in an attempt to determine the special indications.
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Affiliation(s)
- K Stockenhuber
- Universitätsklinik für Chirurgie, Department für Unfallchirurgie, Graz
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Feichtinger G, Sorger G. Capital accumulation, aspiration adjustment, and population growth: limit cycles in an Easterlin-type model. Math Popul Stud 1990; 2:93-161. [PMID: 12282602 DOI: 10.1080/08898489009525296] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
"One of the recent interesting hypotheses of population growth is due to Easterlin who suggests the possibility of self-generating fluctuations in birth numbers. The present paper tries to answer the question whether feedback mechanisms produce persistent oscillations in population growth. A system of two nonlinear differential equations for the per capita capital stock and the aspiration level is studied by a phase portrait analysis. Using the Poincare-Bendixson theorem we derive sufficient conditions for the existence of a stable limit cycle." (SUMMARY IN FRE)
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Feichtinger G, Dockner EJ. Capital accumulation, endogenous population growth, and Easterlin cycles. J Popul Econ 1990; 3:73-87. [PMID: 12283297 DOI: 10.1007/bf00187285] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
"In this paper we attempt to explain the occurrence of population cycles in industrialised economies where the birth rate depends on the difference between the actual and the expected consumption rate. This model of an endogenously growing population brings together Easterlin's idea of an adapting aspiration level with the neoclassical optimal growth paradigm. It is shown that in this highly aggregated demo-economic system (i.e., without inclusion of the age structure of a population) swings both in the economic and demographic variables may exist. The reason behind this 'strange' optimal behaviour is identified to be an intertemporal substitution effect between current and future levels of consumption."
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Feichtinger G, Sorger G. Self-generated fertility waves in a non-linear continuous overlapping generations model. J Popul Econ 1989; 2:267-280. [PMID: 12282647 DOI: 10.1007/bf00171004] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
In this paper, Samuelson's simplified version of the Easterlin theory is extended to a continuous-time model with 3 age groups. This approach enables one to apply the qualitative theory of nonlinear differential equations to show the existence of Easterlin-type cycles. In contrast to the discrete time model we obtain information about the period length of the cycle.
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Feichtinger G, Hannan EJ, Schmidt KD, Mandl P, Moses LE. Book reviews. METRIKA 1982. [DOI: 10.1007/bf01893381] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Feichtinger G, Strelec H, Pflug G, Keil KH, Fleissner P. Buchbesprechungen. METRIKA 1979. [DOI: 10.1007/bf01893472] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Feichtinger G. [Formal demography--where to? Development tendencies of population mathematics]. Mittbl Osterr Ges Stat Inform 1979; 9:1-14. [PMID: 12279071] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Key Words] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 04/19/2023]
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Feichtinger G. [Population models]. All Stat Arch 1977; 61:325-48. [PMID: 12263573] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Key Words] [MESH Headings] [Subscribe] [Scholar Register] [Indexed: 04/19/2023]
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Lamla E, Hund F, Boschke F, Feichtinger G, Jacobs J, Preu� H, D�rckheimer W, Angermeier WF, Renger G, Autrum H. Buchbesprechungen. Naturwissenschaften 1975. [DOI: 10.1007/bf00608968] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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Kangro H, Boschke FL, Feichtinger G, Primas H, Kundt W, Reeh H, Lehner G, v. Minnigerode G, Steeb S, Habermehl G, Hoppe R, Kessler H, Horner L, Kuhnert-Brandstätter M, Jaenicke L, Neubert D, Mothes K, Rembold H, Dietz R, Karlson P, Ziswiler V, Martin EP, Ruthmann A, Neuhoff V, Bauer RD, Sioli H. Buchbesprechungen. Naturwissenschaften 1972. [DOI: 10.1007/bf00591798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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22
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Feichtinger G. Ueber einen neuen Zahnkitt. European J Org Chem 1859. [DOI: 10.1002/jlac.18591100114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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