Top

International Journal of Health Economics and Management

Open Access 22-03-2024 | Vaccination | Research article

Simple economics of vaccination: public policies and incentives

Authors: Jesús Villota-Miranda, R. Rodríguez-Ibeas

Published in: International Journal of Health Economics and Management

Abstract

This paper focuses on the economics of vaccination and, more specifically, analyzes the vaccination decision of individuals using a game-theoretic model combined with an epidemiological SIR model that reproduces the infection dynamics of a generic disease. We characterize the equilibrium individual vaccination rate, and we show that it is below the rate compatible with herd immunity due to the existence of externalities that individuals do not internalize when they decide on vaccination. In addition, we analyze three public policies consisting of informational campaigns to reduce the disutility of vaccination, monetary payments to vaccinated individuals and measures to increase the disutility of non-vaccination. If the public authority uses only one type of policy, herd immunity is not necessarily achieved unless monetary incentives are used. When the public authority is not limited to use only one policy, we find that the optimal public policy should consist only of informational campaigns if they are sufficiently effective, or a combination of informational campaigns and monetary incentives otherwise. Surprisingly, the requirement of vaccine passports or other restrictions on the non-vaccinated are not desirable.

Available only for authorised users

Vaccination costs include, among others, the value of the time required to go to the vaccination center, the pain of the syringe, and the adverse effects of the vaccine. Non-vaccination costs include the cost related to the symptoms of the disease and to possible hospitalizations and the cost individual bears from the restrictions that public authorities may impose on unvaccinated individual.

See also Francis (1997) who derives the same result in a continuous-time dynamic model.

$\frac{dS}{dz}=\frac{dS}{dt}\frac{dt}{dz}$ and $\frac{dI}{dz}=\frac{dI}{dt}\frac{dt}{dz}$, where $\frac{dt}{dz}=1/\gamma$.

$$\frac{d\phi (p)}{dp}=-\frac{1}{{R}_{0}{\left(1-p\right)}^{2}}<0$$ and $$\frac{{d}^{2}\phi (p)}{d{p}^{2}}=-\frac{2}{{R}_{0}{\left(1-p\right)}^{3}}<0$$.

$\frac{\partial {p}^{*}}{\partial {D}_{V}}=\frac{-r{D}_{I}}{{R}_{0}{\left(r{D}_{I}-{D}_{V}+{D}_{S}\right)}^{2}}<0; \frac{\partial {p}^{*}}{\partial {D}_{S}}=\frac{{R}_{0}r{D}_{I}}{{R}_{0}{\left(r{D}_{I}-{D}_{V}+{D}_{S}\right)}^{2}}>0; \frac{\partial {p}^{*}}{\partial {D}_{I}}=\frac{r\left({D}_{V}-{D}_{S}\right)}{{R}_{0}{\left(r{D}_{I}-{D}_{V}+{D}_{S}\right)}^{2}}>0; \frac{\partial {p}^{*}}{\partial r}=\frac{{D}_{I}\left({D}_{V}-{D}_{S}\right)}{{R}_{0}{\left(r{D}_{I}-{D}_{V}+{D}_{S}\right)}^{2}}>0; \frac{\partial {p}^{*}}{\partial {R}_{0}}=\frac{r{D}_{I}}{{R}_{0}^{2}\left(r{D}_{I}-{D}_{V}+{D}_{S}\right)}>0$.

Note that, since the equilibrium social cost does not depend on ${D}_{I}$, it would not make sense to adopt any measure affecting risk perception or the costs from infection.

Fining non-vaccinated has been considered in some countries (see, for example, Vogel and Duong (2022) for a discussion of this intervention applied to COVID-19 in Canada). In Europe, Austria and Greece have used fines to incentive COVID-19 vaccination. As stated by Vogel and Duong, this issue raises ethical considerations, and fines may excessively penalize poorer individuals. It is thought that financial penalties should be last resort to promote vaccination. We have not included fines in our analysis due to their low utilization in real world. Nevertheless, we think that modelling the use of fines for the non-vaccinated would be similar to the analysis of the monetary payments to the vaccinated. In the context of our model, the public authority would use the highest available fine compatible with achieving herd immunity. The analysis is available upon request.

Notice that $\frac{d{p}^{*}\left(m\right)}{dm}=\frac{r{D}_{I}}{{R}_{o}{\left[r{D}_{I}-{D}_{V}+{D}_{S}+m\right]}^{2}}$.

$\frac{\partial CT}{\partial y}={D}_{S}{\prime}\left(y\right)\left(1-{p}_{crit}\right)+H{\prime}(y)>0$.

Basu, S., Chapman, G. B., & Galvani, A. P. (2008). Integrating epidemiology, psychology, and economics to achieve HPV vaccination targets. Proceedings of the National Academy of Sciences, 105(48), 19018–19023.CrossRef

Bauch, C. T. (2005). Imitation dynamics predict vaccination behavior. Proceedings of the Royal Society b: Biological Sciences, 272(1573), 1669–1675.CrossRefPubMedCentral

Bauch, C. T., & Earn, D. J. (2004). Vaccination and the theory of games. Proceedings of the National Academy of Sciences, 101(36), 13391–13394.CrossRef

Bauch, C. T., Galvani, A. P., & Earn, D. J. (2003). Group interest versus self-interest in smallpox vaccination policy. Proceedings of the National Academy of Sciences, 101(18), 10564–10567.CrossRef

Campos-Mercade, P., Meier, A. N., Schneider, F. H., Meier, S., Pope, D., & Wengström, E. (2021). Monetary Incentives increase covid-19 vaccinations. Science, 374(6569), 879–882.CrossRefPubMedPubMedCentral

Brauer, F. (2008). Compartimental models in epidemiology. In Mathematical epidemiology, pages 19–79. Springer.

Chang, S. L., Piraveenan, M., Pattison, P., & Prokopenko, M. (2020). Game theoretic modelling of infectious disease dynamics and intervention methods: A review. Journal of Biological Dynamics, 14(1), 57–89.CrossRefPubMed

Craft, M. E., & Caillaud, D. (2011). Network models: an underutilized tool in wildlife epidemiology? Interdisciplinary perspectives on infectious diseases, 2011.

De Donder, P., Llavador, H., Penczynski, S., Roemer, J.E., Velez, R., et al. (2021). A game theoretic analysis of childhood vaccination behavior: Nash versus Kant. In Economics Working Papers 1808, Department of Economics and Business, Universitat Pompeu Fabra.

European Centre for disease Prevention and Control. (2021). Facilitating COVID-19 vaccination acceptance and uptake in the EU/EEA. ECDC (2021). Technical Report.

Francis, P. J. (1997). Dynamics epidemiology and the market for vaccinations. Journal of Public Economics, 63(3), 383–406.CrossRef

Galvani, A. P., Reluga, T. C., & Chapman, G. B. (2007). Long-standing influenza vaccination policy is in Accord with individual self-interest but not with the utilitarian optimum. Proceedings of the National Academy of Sciences, 104(13), 5692–5697.CrossRef

Gans, J. S. (2023). Vaccine hesitancy, Passports, And The demand for vaccination. International Economic Review, 64(2), 641–652.CrossRef

Iyer, G., Nandur, V., & Soberman, D. (2022). Vaccine hesitancy and monetary incentives. Humanities and Social Sciences Communications, 9 (1)

Lim, W., & Zhang, F. P. (2017). Herd immunity and a vaccination game. Working paper.

Lim, W., & Zhang, F. P. (2017b). Herd immunity and a vaccination game: An experimental study. PLoS ONE, 15(5), e02332652.

Liu, X.-T., Wu, Z. X., & Zhang, L. (2012). Impact of committed individual son vaccination behavior. Physical Review E, 86(5), 051132.CrossRef

Lloyd, A. L., & Valeika, S. (2007). Network models in epidemiology: An overview. Complex population dynamics: nonlinear modelling in ecology, epidemiology and genetics, pp. 189–214.

Neilson, W., & Xiao, Y. (2018). Equilibrium vaccination patterns in incomplete and heterogenous networks. European Economic Review, 105, 174–192.CrossRef

Perisic, A., & Bauch, C. T. (2009a). A simulation analysis to characterize the dynamics of vaccination behavior on contact networks. BMC Infectious Diseases, 9(1), 1–15.CrossRef

Perisic, A., & Bauch, C. T. (2009b). Social contact networks and disease eradicability under voluntary vaccination. PloS Computational Biology, 5(2), e1000280.CrossRefPubMedPubMedCentral

Rusu, E. (2015). Network models in epidemiology: Considering discrete and continuous dynamics. arXiv prepint arXiv:1511.01062.

Savalescu, J., Pugh, J., & Wilkinson, D. (2021). Balancing incentives and disincentives for vaccination in a pandemic. Nature Medicine, 27(9), 1500–1503.CrossRef

Sorensen, A. (2023). The role of vaccine effectiveness on individual vaccination decisions and welfare. Journal of Public Economic Theory. https://doi.org/10.1111/jpet.12644CrossRef

Vogel, L., & Duong, D. (2022). What’s is the evidence for fining the unvaccinated? Canadian Medical Association Journal, 194(4), E132–E133. https://doi.org/10.1503/cmaj.1095985CrossRefPubMedPubMedCentral

Yamin, D., & Gavious, A. (2013). Incentives effects in influenza vaccination policy. Management Science, 59(12), 2667–2686.CrossRef

Yamin, D., Gavious, A., Davidovitch, N., & Pliskin, J. S. (2014). Role of intervention programs to increase influenza vaccination in Israel. Israel Journal of Health Policy Research, 3(1), 1–7.CrossRef

Title: Simple economics of vaccination: public policies and incentives
Authors: Jesús Villota-Miranda
R. Rodríguez-Ibeas
Publication date: 22-03-2024
Publisher: Springer US
Keyword: Vaccination
Published in: International Journal of Health Economics and Management
Print ISSN: 2199-9023
Electronic ISSN: 2199-9031
DOI: https://doi.org/10.1007/s10754-024-09367-2

Keynote webinar | Spotlight on medication adherence

Springer Medicine

Simple economics of vaccination: public policies and incentives

Abstract

Keynote webinar | Spotlight on medication adherence

Springer Medicine

Abstract

Please log in to get access to this content