Abstract
The unprecedented global spread of COVID-19 has prompted dramatic public-health measures like strict stay-at-home orders and economic shutdowns. Some governments have resisted such measures in the hope that naturally acquired shield immunity could slow the spread of the virus. In the absence of empirical data about the effectiveness of these measures, policymakers must turn to epidemiological modelling to evaluate options for responding to the pandemic. This paper combines compartmental epidemiological models with the concept of behavioural dynamics from evolutionary game theory (EGT). This innovation allows us to model how compliance with an economic lockdown might wane over time, as individuals weigh the risk of infection against the certainty of the economic cost of staying at home. Governments can, however, increase spending on social programmes to mitigate the cost of a shutdown. Numerical analysis of our model suggests that emergency-relief funds spent at the individual level are effective in reducing the duration and overall economic cost of a pandemic. We also find that shield immunity takes hold in a population most easily when a lockdown is enacted with relatively low costs to the individual. Our qualitative analysis of a complex model provides evidence that the effects of shield immunity and economic shutdowns are complementary, such that governments should pursue them in tandem.
Highlights
The COVID-19 pandemic presents urgent policy questions that must be addressed with modelling, as no vaccine is available and data about the pandemic is scarce [1,2,3,4]
In hopes of modelling the social-learning aspect [11,12] of decision-making within the epidemic more realistically, we have followed Bauch in modelling decisions to vaccinate or self-isolate according to the imitation dynamic [13], a concept drawn from evolutionary game theory (EGT) [14,15]
Our qualitative analyses of increasingly complex models suggest that complex social-learning dynamics can be captured in compartmental epidemic models that include game-theoretic concepts of imitation in an evolutionary game
Summary
The COVID-19 pandemic presents urgent policy questions that must be addressed with modelling, as no vaccine is available and data about the pandemic is scarce [1,2,3,4]. Mobility restrictions, self-isolation and social distancing have been attempted across the globe, and empirical evaluations of their effectiveness are difficult with such an unprecedented virus [5,6,7,8,9] The effectiveness of such measures will be affected by the socio-economic cost of those measures, which can be modelled in game-theoretic terms. Japan [20], the United States and the United Kingdom [21], for example, have implemented several emergency-relief packages that benefit people and businesses affected by the COVID-19 pandemic These measures highlight economic disparities among countries, and those with fewer resources are less able to provide social support. The risk of infection is modelled with a term for shield immunity [29], which reduces the spread of infection as more recovered or vaccinated individuals are no longer at risk of spreading the disease
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