Optimising pandemic response through vaccination strategies using neural networks.

Epidemic risk assessment poses inherent challenges, with traditional approaches often failing to balance health outcomes and economic constraints. This paper presents a data-driven decision support tool that models epidemiological dynamics and optimises vaccination strategies to control disease spread while minimising economic losses. The proposed economic-epidemiological framework comprises three phases: modelling, optimising, and analysing. First, a stochastic SVEI3RD compartmental model with eight state variables captures epidemic dynamics, stratifying infections by severity to enable detailed healthcare cost estimation. Second, an optimal control problem is formulated to derive vaccination strategies that minimise pandemic-related expenditures, encompassing vaccination costs, quarantine subsidies, healthcare expenditures, and economic productivity losses. The resulting high-dimensional stochastic control problem renders classical numerical methods computationally intractable due to the curse of dimensionality. To overcome this challenge, Physics-Informed Neural Networks are employed to calibrate model parameters by embedding the stochastic differential equations into the loss function. For the optimal control problem, a deep neural network architecture comprising feedforward subnetworks at each time step directly approximates the time-varying vaccination rate. The framework is demonstrated using COVID-19 data from Victoria, Australia. The numerical results show that, compared to the no-vaccination strategy, the optimal strategy reduces cumulative hospital-days by 85.3%, deaths by 84.4%, and total costs by 22.3%. These reductions exceed those achieved by the actual government rollout by approximately 4 to 6 percentage points. By employing this framework, policymakers can continuously update strategies to minimise aggregate costs and aid future pandemic preparedness.