Numerical investigation of the effect of macro control measures on epidemics transport via a coupled PDE crowd flow - epidemics spreading dynamics model

Abstract

This work aims to provide an approach to the macroscopic modeling and simulation of pedestrian flow, coupled with contagion spreading, towards numerical investigation of the effect of certain, macro-control measures on epidemics transport dynamics. To model the dynamics of the pedestrians, a second-order macroscopic model, coupled with an Eikonal equation, is used. This model is coupled with a macroscopic Susceptible-Exposed-Infected-Susceptible-Vaccinated (SEISV) contagion model, where the force-of-infection $β$ coefficient is modeled via a drift-diffusion equation, which is affected by the air-flow dynamics due to the ventilation. The air-flow dynamics are obtained assuming a potential flow that can imitate the existence of ventilation in the computational domain. Numerical approximations are considered for the coupled model along with numerical tests and results. In particular, we investigate the effect of employment of different, epidemics transport control measures, which may be implemented through real-time manipulation of i) ventilation rate and direction, ii) maximum speed of pedestrians, and iii) average distances between pedestrians, and through iv) incorporation in the crowd of masked or vaccinated individuals. Such simulations of disease spreading in a moving crowd can potentially provide valuable information about the risks of infection in relevant situations and support the design of systematic intervention/control measures.

Figures (24)

• Figure 1: Equilibrium speed-density relations for flow (left) and velocity (right) for two different values of $u_{\max}$.
• Figure 2: Time evolution of the total number of pedestrians $R(t)$ (left) and percentage of exposed pedestrians (right) with $u_{\max}=2$$m/s$ (top) and $u_{\max}=1.4$$m/s$ (bottom), for three different values of $C_0$ with $\rho_0^V = 0$.
• Figure 3: Total density profiles (top), infection coefficient profile (middle) and exposed pedestrians' profile at different time instances with $u_{\max}=1.4$$m/s$, $C_0=0.5$, with no ventilation and $\rho_0^V = 0$.
• Figure 4: Total density profiles (top), infection coefficient profile (middle) and exposed pedestrians' profile at different time instances with $u_{\max}=1.4$$m/s$, $C_0=1.2$, with no ventilation and $\rho_0^V = 0$.
• Figure 5: Time evolution of the percentage of exposed pedestrians with $u_{\max}=2m/s$ (left) and $u_{\max}=1.4m/s$ (right), for three different values of $C_0$ for $\rho_0^V=0.15\rho_0$.