Finding the Best Route During the Pandemic Disease

TL;DR

A mathematical model for identifying the safest travel routes during a pandemic by minimizing disease contraction risks, such as COVID-19 is presented and demonstrates that combined pedestrian-subway-BRT routes exhibit significantly lower infection risks compared to car or bus routes.

Abstract

This article presents a mathematical model for identifying the safest travel routes during a pandemic by minimizing disease contraction risks, such as COVID-19. We formulate this as the LEAST INFECTION PROBABILITY PATH (LIPP) problem, which optimizes routes between two nodes in a transportation network based on minimal disease transmission probability. Our model evaluates risk factors including environmental density, likelihood of encountering carriers, and exposure duration across multiple transportation modes (walking, subway, BRT, buses, and cars). The probabilistic framework incorporates additional variables such as ventilation quality, activity levels, and interpersonal distances to estimate transmission risks. Applied to Tehran's transportation network using routing applications (Neshan and Balad), our model demonstrates that combined pedestrian-subway-BRT routes exhibit significantly lower infection risks compared to car or bus routes, as illustrated in our case study of peak-hour travel between Sadeghiyeh Square and Amirkabir University. We develop a practical routing algorithm suitable for integration with existing navigation software to provide pandemic-aware path recommendations. Potential future extensions include incorporating additional variables like waiting times and line changes, as well as adapting the model for other infectious diseases. This research offers a valuable tool for urban travelers seeking to minimize infection risks during pandemic conditions.

Figures (6)

• Figure 1: Diagram of a combined route showing different microenvironment segments
• Figure 2: Infection risk ($\phi(r_{ij})$) for an uninfected individual (blue path) exposed to *n* infected individuals (red). The gold star highlights a sample cell’s risk variables ($r_(ij), T_j, \phi$).
• Figure 3: Probability of COVID-19 infection after 5 hours of exposure in low-activity environments as a function of room area.
• Figure 4: Disease transmission probability versus sidewalk length for pedestrian exposure (1-hour duration, 4m width). Curves represent different population densities (0.25--2.5 individuals/m2), showing risk plateau at the knee point (30.3m length in average) for low-density scenarios. The inflection point indicates optimal pedestrian segment length where marginal transmission risk becomes negligible below 1 individual/m2 density.
• Figure 5: Comparison of COVID-19 infection risks across different transportation routes.

Theorems & Definitions (6)

• Theorem 1
• Definition 1: Infection Probability Function
• Theorem 2
• Theorem 3
• Theorem 4
• Theorem 5