Optimal control model for the spatial spread of COVID-19: An interacting fluid flow approach

Abstract

This study develops an optimal control model to analyze the spatial and temporal spread of COVID-19 using an interacting fluid flow approach. Susceptible and infected populations are treated as interacting inviscid fluids governed by Euler’s equations, allowing for the spatial dynamics of disease transmission to be captured effectively. Control interventions, specifically vaccination (targeting susceptibility) and medical treatment (enhancing recovery rates), are incorporated as key strategies to mitigate the spread of infection. The model’s spatio-temporal dynamics are explored using high-order computational methods, namely the weighted essentially non-oscillatory (WENO) scheme for spatial discretization and the fourth-order Runge-Kutta method for time integration. Numerical simulations demonstrate the effectiveness of the proposed controls, emphasizing that a strategic combination of vaccination and treatment significantly reduces disease prevalence, especially in densely populated regions. This modeling framework offers valuable insights for policymakers, emphasizing efficient resource allocation and strategic intervention planning to manage COVID-19 or similar infectious diseases effectively.