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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.

What do corruption, resource overexploitation, climate inaction, vaccine hesitancy, traffic congestion, and even cancer metastasis have in common? All these socioeconomic and sociobiological phenomena are known as social dilemmas because they embody in one form or another a fundamental conflict between immediate self-interest and long-term collective interest. A shortcut to the resolution of social dilemmas has thus far been reserved solely for highly stylised cases reducible to dyadic games (e.g., the Prisoner’s Dilemma), whose nature and outcome coalesce in the concept of dilemma strength. We show that a social efficiency deficit, measuring an actor’s potential gain in utility or fitness by switching from an evolutionary equilibrium to a social optimum, generalises dilemma strength irrespective of the underlying social dilemma’s complexity. We progressively build from the simplicity of dyadic games for which the social efficiency deficit and dilemma strength are mathematical duals, to the complexity of carcinogenesis and a vaccination dilemma for which only the social efficiency deficit is numerically calculable. The results send a clear message to policymakers to enact measures that increase the social efficiency deficit until the strain between what is and what could be incentivises society to switch to a more desirable state.

Outbreaks of repeated pandemics and heavy epidemics are daunting threats to human life. This study aims at investigating the dynamics of disease conferring temporary or waning immunity with several forced-control policies aided by vaccination game theory. Considering an infinite and well-mixed homogenous population, our proposed model further illustrates the significance of introducing two well-known forced control techniques, namely, quarantine and isolation, in order to model the dynamics of an infectious disease that spreads within a human population where pre-emptive vaccination has partially been taken before the epidemic season begins. Moreover, we carefully examine the combined effects of these two types (pre-emptive and forced) of protecting measures using the SEIR-type epidemic model. An in-depth investigation based on evolutionary game theory numerically quantifies the weighing impact of individuals’ vaccinating decisions to improve the efficacy of forced control policies leading up to the relaxation of the epidemic spreading severity. A deterministic SVEIR model, including vaccinated (V) and exposed (E) states, is proposed having no spatial structure while implementing these intervention techniques. This study uses a mixed control strategy relying on quarantine and isolation policies to quantify the optimum requirement of vaccines for eradicating disease prevalence completely from human societies. Furthermore, our theoretical study justifies the fact that adopting forced control policies significantly reduces the required level of vaccination to suppress emerging disease prevalence, and it also confirms that the joint policy works even better when the epidemic outbreak takes place at a higher transmission rate. Research reveals that the isolation policy is a better disease attenuation tool than the quarantine policy, especially in endemic regions where the disease progression rate is relatively higher. However, a meager progression rate gradually weakens the speed of an epidemic outbreak and, therefore, applying a moderate level of control policies is sufficient to restore the disease-free state. Essentially, positive measures (pre-emptive vaccination) regulate the position of the critical line between two phases, whereas exposed provisions (quarantine or isolation) are rather dedicated to mitigating the disease spreading in endemic regions. Thus, an optimal interplay between these two types of intervention techniques works remarkably well in attenuating the epidemic size. Despite having advanced on the development of new vaccines and control strategies to mitigate epidemics, many diseases like measles, tuberculosis, Ebola, and flu are still persistent. Here, we present a dynamic analysis of the SVEIR model using mean-field theory to develop a simple but efficient strategy for epidemic control based on the simultaneous application of the quarantine and isolation policies. Highlights • This model incorporates the elements of mathematical epidemiology and a vaccination game into a single framewor...

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