Mean field based investigations for inducing socially optimal epidemic behavior in rational individuals - Roy, Amal.; Advised by Narahari, Y and Singh, Chandramani (Bangalore : Indian Institute of Science, 2024)
In the recent years, the world has been devastated by multiple pandemics arising out of different variants of the Corona virus. When an epidemic or pandemic strikes, it is important to move quickly to contain and suppress the spread of the disease to minimize the losses to life and suffering, as well as, to lower the burden on the healthcare system. Several interventions, pharmaceutical and non-pharmaceutical, have been devised for mitigating the damage. Deriving the benefits of these interventions calls for full participation of all individuals in the population. It is observed, however, that in spite of the threat posed by a pandemic, individuals tend to go by their freewill rather than adhering to best intervention practices. This could dangerously push the population towards alarming consequences. This thesis work investigates novel scientific methods for designing appropriate incentives to rational individuals, to enhance compliance to best practices to promote sustainable, socially optimal behavior. This dissertation work investigates three different problems along the above broad theme: contact factor control; testing control; and vaccination control. Guided by practical feasibility and computational tractability considerations, the thesis uses a mean field approach to compute a socially optimal policy as well as a Nash equilibrium policy in each investigation. Contact Factor Control: The thesis advances the state-of-the-art on this topic by conducting a holistic analysis of contact factor control in epidemic dynamics in the presence of vaccinations for both the socially optimal and the individually optimal cases. The study proceeds in two parts. The first part assumes that the individuals faithfully follow a socially optimal control policy prescribed by a regulatory authority. Here, the mean field approach is used to model the dynamics of the epidemic in the presence of vaccinations. The second part deals with the scenario where individuals exhibit strategic behavior and the dynamics are modeled as a mean field game. We characterize the symmetric Nash equilibrium for the underlying game and develop a numerical algorithm for computing the equilibrium. We carry out several carefully designed thought experiments to study the variation of the total cost incurred by the individuals in the population as a function of vaccination cost, vaccination rate, lockdown cost, and infection cost. The experiments suggest strategies for inducing and sustaining socially optimal contact behavior from rational individuals. Inducing Socially Optimal Testing Behavior: In this contribution, we explore how offering incentives for testing during epidemics can encourage people to test themselves responsibly, without having to undergo severe penalties for non-compliance. We compare two scenarios: one where testing decisions are centrally managed for maximum social benefit, and the second, where individuals make their own testing choices. By combining ideas from optimal control theory and mean field game theory, we investigate how policymakers can use subsidies to motivate people to test more responsibly during epidemics. This research offers valuable insights for policymakers on the quantum of subsidies needed to encourage desirable testing behavior of rational individuals in a population. Inducing Socially Optimal Vaccination Behavior: In this study, we investigate the following research question: In a population consisting of rational and intelligent individuals who make their own individual decisions regarding vaccination (to vaccinate or not), how can a policy maker incentivize individuals to achieve socially optimal vaccination behaviour? For this, we work with an extended SIR (Susceptible-Infected-Recovered) model of epidemics in the presence of vaccinations and with possibility of reinfections captured explicitly. We investigate two models: one where vaccination decisions are centrally managed for maximum social benefit, and the second, where individuals make their own vaccination decisions. Using mean field analysis, we compute a vaccination subsidy to achieve an outcome that is close to the socially optimal one. In a nutshell, this thesis work leads to new findings on how, in an epidemic situation, socially optimal outcomes could be achieved, through incentive measures, in a population of rational individuals who act on their freewill and may or may not comply with centrally prescribed policies.
Includes references.
PhD;2024;Computer Science and Automation.
Keywords: Mean field games; Epidemic modelling; Optimization