[Paper Review] Reduced mobility of infected agents suppresses but lengthens disease in biased random walk

Genki Ichinose, Yoshiki Satotani+2 more|arXiv (Cornell University)|Jul 3, 2018

thermodynamics and calorimetric analysesChemistry4 citations

TL;DR

This study develops an agent-based SIR model in 2D continuous space with biased random walk and reduced mobility for infected agents. It finds that while reduced mobility suppresses final epidemic size by limiting transmission, it prolongs disease duration due to slower spread, highlighting a trade-off in isolation policies for controlling outbreaks.

ABSTRACT

Various theoretical models have been proposed to understand the basic nature of epidemics. Recent studies focus on the effects of mobility to epidemic process. However, uncorrelated random walk is typically assumed as the type of movement. In our daily life, the movement of people sometimes tends to be limited to a certain direction, which can be described by biased random walk. Here, we developed an agent-based model of susceptible-infected-recovered (SIR) epidemic process in a 2D continuous space where agents tend to move in a certain direction in addition to random movement. Moreover, we mainly focus on the effect of the reduced mobility of infected agents. Our model assumes that, when people are infected, their movement activity is greatly reduced because they are physically weakened by the disease. By conducting extensive simulations, we found that when the movement of infected people is limited, the final epidemic size becomes small. However, that crucially depended on the movement type of agents. Furthermore, the reduced mobility of infected agents lengthened the duration of the epidemic because the infection progressed slowly.

Motivation & Objective

• To investigate how biased random walk and reduced mobility of infected individuals affect epidemic dynamics in a 2D spatial setting.
• To examine the interplay between movement bias, infection radius, and recovery rate on final epidemic size and extinction time.
• To assess whether reduced mobility of infected agents suppresses or prolongs disease spread in realistic spatial movement scenarios.
• To provide insights into isolation strategies by analyzing trade-offs between epidemic suppression and duration.

Proposed method

• Agents perform biased random walks in a 2D continuous space with periodic boundaries, favoring rightward movement.
• Infected agents have reduced mobility (lower diffusion coefficient σI) and reduced directional persistence (lower εI), modeling physical weakening.
• The SIR model is implemented via agent-based simulation with state transitions: S → I upon contact within radius r, I → R after exponential recovery time.
• Contact occurs when susceptible and infected agents are within distance r, and infection is probabilistic based on proximity and duration.
• Extensive simulations vary parameters: infection radius r, population size N, mobility parameters σI and εI, and initial infected count I0.
• Key metrics include final epidemic size (number of recovered agents) and extinction time (when no infected agents remain).

Experimental results

Research questions

• RQ1 How does reduced mobility of infected agents affect the final size of an epidemic in a 2D space with biased movement?
• RQ2 Does the presence of directional bias in agent movement alter the impact of reduced mobility on disease spread?
• RQ3 How does the duration of the epidemic (extinction time) change under different mobility conditions for infected individuals?
• RQ4 What is the relationship between population density and the effectiveness of isolation in suppressing outbreaks?
• RQ5 How does infection radius influence the balance between epidemic suppression and prolonged duration under reduced mobility?

Key findings

• Reduced mobility of infected agents significantly suppresses the final epidemic size, with the minimum size occurring when infected agents move only in one direction at the same speed as others (σI = 0, εI = 1).
• Despite suppressing transmission, reduced mobility of infected agents lengthens the extinction time due to slower spatial spread of infection.
• When population size is small (N ≤ 300), the minimum contact case (σI = 0, εI = 1) leads to the shortest extinction time due to sparse contact opportunities.
• For larger populations (N > 600), the extinction time increases when the final epidemic size is small, confirming the trade-off between suppression and duration.
• The extinction time peaks at medium infection radii (r), corresponding to intermediate epidemic sizes, as full-population spread leads to faster recovery.
• High movement (σI = 1, εI = 1) increases final epidemic size even at low r, while the minimum contact case (σI = 0, εI = 1) shows the slowest increase in epidemic size with increasing r.