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Optimising pandemic response through vaccination strategies using neural networks

Chang Zhai, Ping Chen, Zhuo Jin, David Pitt

TL;DR

This work develops an economic-epidemiological framework that integrates a stochastic SVEI3RD compartmental model with neural-network solvers to optimize vaccination strategies under uncertainty. It couples PINN-based parameter calibration with a deep neural network that directly learns time-varying vaccination policies, solving a high-dimensional stochastic control problem to minimize a multi-component cost function that includes vaccination, quarantine, healthcare, and economic losses. The approach is validated on Victoria, Australia’s COVID-19 data, showing that an initial high vaccination push followed by a gradual reduction can reduce infections and total expenditures, even when vaccination costs are high. Sensitivity analyses reveal how environmental noise, infection rates, hesitancy, and cost parameters shape optimal policies, highlighting the framework’s usefulness for adaptive pandemic preparedness and policy planning.

Abstract

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 whilst minimising economic losses. The proposed economic-epidemiological framework comprises three phases: modelling, optimising, and analysing. First, a stochastic compartmental model captures epidemic dynamics. Second, an optimal control problem is formulated to derive vaccination strategies that minimise pandemic-related expenditure. Given the analytical intractability of epidemiological models, neural networks are employed to calibrate parameters and solve the high-dimensional control problem. The framework is demonstrated using COVID-19 data from Victoria, Australia, empirically deriving optimal vaccination strategies that simultaneously minimise disease incidence and governmental expenditure. By employing this three-phase framework, policymakers can adjust input values to reflect evolving transmission dynamics and continuously update strategies, thereby minimising aggregate costs, aiding future pandemic preparedness.

Optimising pandemic response through vaccination strategies using neural networks

TL;DR

This work develops an economic-epidemiological framework that integrates a stochastic SVEI3RD compartmental model with neural-network solvers to optimize vaccination strategies under uncertainty. It couples PINN-based parameter calibration with a deep neural network that directly learns time-varying vaccination policies, solving a high-dimensional stochastic control problem to minimize a multi-component cost function that includes vaccination, quarantine, healthcare, and economic losses. The approach is validated on Victoria, Australia’s COVID-19 data, showing that an initial high vaccination push followed by a gradual reduction can reduce infections and total expenditures, even when vaccination costs are high. Sensitivity analyses reveal how environmental noise, infection rates, hesitancy, and cost parameters shape optimal policies, highlighting the framework’s usefulness for adaptive pandemic preparedness and policy planning.

Abstract

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 whilst minimising economic losses. The proposed economic-epidemiological framework comprises three phases: modelling, optimising, and analysing. First, a stochastic compartmental model captures epidemic dynamics. Second, an optimal control problem is formulated to derive vaccination strategies that minimise pandemic-related expenditure. Given the analytical intractability of epidemiological models, neural networks are employed to calibrate parameters and solve the high-dimensional control problem. The framework is demonstrated using COVID-19 data from Victoria, Australia, empirically deriving optimal vaccination strategies that simultaneously minimise disease incidence and governmental expenditure. By employing this three-phase framework, policymakers can adjust input values to reflect evolving transmission dynamics and continuously update strategies, thereby minimising aggregate costs, aiding future pandemic preparedness.

Paper Structure

This paper contains 37 sections, 2 theorems, 35 equations, 23 figures, 6 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Model formulation
  3. The epidemic model
  4. The SVEI3RD model
  5. The dependence structure between vaccination administration and hospitalization
  6. The expenditure function
  7. Model solving
  8. PINN for parameter calibration
  9. Deep neural network for high-dimensional stochastic control
  10. Numerical case study
  11. The Victoria dataset
  12. Modelling parameters
  13. Regression relationship
  14. Vital dynamic parameters
  15. Deterministic VS stochastic SVEI3RD model fitting
  16. ...and 22 more sections

Key Result

Theorem 1

For any initial values $(S_0,V_0,E_0,I_{1,0},I_{2 ,0},I_{3,0},R_0,D_0) \in \mathbb{R}^8_+$, there exists a unique positive solution $(S_t,V_t,E_t,I_{1,t},I_{2,t},I_{3,t},R_t,D_t)$ of Equation eqn: sto SVEI3RD without control on $t \geq 0$ and the solution will remain in $\mathbb{R}^8_+$ with probabi

Figures (23)

  • Figure 1: Overview of the economic epidemiological model framework.
  • Figure 2: Flow diagram of the SVEI3RD model.
  • Figure 3: Structural overview of the Physics Informed Neural Network (PINN).
  • Figure 4: Neural network architecture for solving the high-dimensional control problem.
  • Figure 5: Correlation between hospitalization rates and vaccination administration rates.
  • ...and 18 more figures

Theorems & Definitions (4)

  • Theorem 1
  • proof
  • Theorem 2
  • proof