Optimizing epidemic control: Nash game approach to stochastic modeling with Brownian motion

Abstract

This research expands upon stochastic modeling for COVID-19 management by incorporating Nash game theory to optimize control strategies for disease transmission. Building on our original model, which has integrated Brownian motion and nonlinear dynamics to enhance diagnosis and isolation procedures, we now apply Nash game theory to explore the interactions between multiple control variables. Using Pontryagin’s Maximum Principle for theoretical analysis and MATLAB and Python for numerical simulations, we demonstrate that Nash control offers a more practical approach than traditional game theory for balancing interventions. The model’s performance, validated with Worldometer data, achieves low Root Mean Square Error (RMSE) and Mean Absolute Percentage Error (MAPE), underscoring its high predictive accuracy. Our findings suggest that Nash control provides a superior framework for real-time epidemic management by optimizing disease control policies, particularly when coordinating antiviral treatments and isolation measures. This work highlights the advantages of Nash-based strategies in developing robust and adaptive epidemic management systems.