Investigating the effect of adaptive optimal control function in epidemic dynamics: predictions and strategy evolution based on SIR/V game theoretic framework

TL;DR

This work addresses early-stage epidemic control by coupling an SIR/V model with adaptive optimal control and evolutionary game dynamics for vaccination behavior. It develops an analytical and numerical framework where a control function $u(t)$ reduces transmission under a cost $\lambda c(u)$, solved via L-BFGS with a forward-backward sweep, while population behavior updates through IB-RA, SB-RA, or DC rules. Key contributions include a detailed Hessian structure for the quasi-Newton method, an explicit discretization of the objective, and a comparative analysis of six dynamics under two epidemic settings, demonstrating that adaptive control consistently lowers infections, costs, and peak loads compared to static policies. The findings underscore the practical value of jointly optimizing interventions and accounting for behavior and information flow in public health decision-making.

Abstract

In this paper, we consider an adaptive optimal control problem for an SIR/V epidemic model with human behavioral effects.We develop a model where effective management of infectious diseases are monitored by the means of non pharmaceutical interventions.This study develops an adaptive optimal control function within an SIR/V framework embedding a non cooperative game theoretic mechanism to capture the dynamic interplay between individual vaccination behavior and population level transmission. We derive analytical expression for the optimal control trajectory under resource constrain and heterogeneous susceptibility and we validate our model using numerical simulations,calibrated with the real world epidemic parameters. We find that for the adaptive optimal policy for a generally known SIR/V model depending on the game theoretic epidemic state leads to substantial reduction in expenses compared to non adaptive policies. Moreover, our results demonstrate that, adaptive strategies significantly outperform the static policies by achieving lower peak infections and faster epidemic extinctions while evolutionary game dynamics identify critical behavioral thresholds that drive strategy evolution and inform timely policy adaptation

Figures (12)

• Figure 1: Schematic diagram of SIR-V model with and without control
• Figure 2: (a) Adaptive control cost function (b)Infected Population with and without control (c) Vaccinated Population with and without control
• Figure 3: Infected population per vaccinated population ($I/V$) with variations of effectiveness with/ without control
• Figure 4: Maximum infected population with increasing effectiveness considering varying regularization parameter.
• Figure 5: Infected population trend with time considering varying regularization parameter.