A Spatial Agent-Based Model for Studying the Effect of Human Mobility Patterns on Epidemic Outbreaks in Urban Areas
Abstract
:1. Introduction
- How does population (density) in an urban environment affect outbreak dynamics?
- How does the number of population accumulation points (POIs) scale with the impact of an outbreak?
- How do mobility restrictions (reducing the maximum travel distance and the number of visited POIs) reduce the outbreak intensity?
- How does the quarantine policy for new cases reduce the impact of the outbreak?
2. The Urban Spatial Agent-Based Model
Algorithm 1 Agent mobility update for agent during each iteration t. |
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Algorithm 2 ABM setup phase. |
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Theoretical and Practical Performance Analysis
- Reset agent lists in all urban POIs −.
- Check the proximity of all agents in all POIs − (approximated as worst case).
- Interaction between all pairs of agents in each POI −) (worst case).
Algorithm 3 Agent interactions inside POIs during each iteration t. |
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3. Materials and Methods
3.1. The SICARQD Epidemic Model
- : The rate of susceptible agents becoming infected in the vicinity of an infectious agent (which is in either of the two infectious states CTG or AWR). An agent in the state will not infect other agents.
- : The rate of incubating agents becoming contagious after a specific period (depending on the modeled virus). In this state, an agent does not know that it is infected (has no symptoms yet), but it infects others.
- : The rate of contagious agents becoming aware after a specific period. In this state, an agent knows that it is infected (has symptoms) and infects other agents in its vicinity.
- : The rate of aware (or quarantined) agents recovering after an infectious period. The transition determines whether an agent has fully recovered, becoming temporarily immune (), or if the agent has died () based on the death ratio . Recovered agents may not be infected.
- : The recurrence rate of recovered agents to become susceptible again after a specific period of recovery from infection.
- Proactive quarantine (proact-Q)—agents may be quarantined immediately as they become contagious and require real-time contact tracing and detection before symptoms appear).
- Reactive quarantine (react-Q)—agents may be quarantined as they become aware , and require home isolation as symptoms appear.
- No quarantine (no-Q)—all infected agents remain active in the population.
- Quick recurrence (quick-R)—short immunity duration of 3 months on average.
- Slow recurrence (slow-R)—longer immunity duration of 12 months on average.
- No recurrence (no-R)—meaning the rate and all recovered agents remain permanently immune.
3.2. Real-World Epidemic Parameters for SICARQD
Model Parameter | Symbol | Literature Values | Assumed Value | References |
---|---|---|---|---|
Incubation rate | 0–5% | 5% ** | [26,35] | |
Incubation period | 3–7 days | 5 days | [36,37,38] | |
Contagion to symptoms onset | 4–7 days | 5.5 days | [35,36] | |
Symptoms onset to recovery | 10–14 days–6 w | 14 days | [39,40,41] | |
Death ratio | 2–3.6% | 3.6% ** | [39,42] | |
Quarantine policy | various | react/proact-Q | [22,28] | |
Quarantine ratio | unknown | 0–1 | [22] | |
Recurrence scenario/rate | 3–12 months | 12 months | [31,34] |
3.3. Experimental Setup
4. Simulation Results
5. Discussion and Conclusions
- Agent population (A)/density ()—linear increase.
- Maximum permitted travel distance for agents ()—linear increase but only above .
- Number of agent POIs ()—logarithmic increase for = 1–5, then negligible increase after .
- Number of urban POIs (P)—logarithmic decrease for P = 1–100, then negligible decrease after .
- Ratio of quarantined infected individuals ()—logarithmic decrease, pronounced after .
- The epidemic recurrence phenomenon is induced by the emergent agent mobility modeled in our system. More specifically, recovered agents lose their immunity in time (based on either slow-R or quick-R) and may travel to infected POIs again, and thus, infectious hotspots will be maintained for a very long duration, replicating the residual waves seen after the COVID-19 pandemic started.
- The proactive quarantine (proact-Q) in correlation to a higher quarantine ratio () triggers a phase transition, reducing the total infected population by over 90% (Figure 10b) compared to the reactive quarantine (Figure 10a). Therefore, a proactive quarantine associated with a strict quarantine ratio can almost completely inhibit infectious spread.
Funding
Data Availability Statement
Conflicts of Interest
References
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Model Parameter | Symbol | Default | Range |
---|---|---|---|
Agent population | A | 1000 | 100–10,000 agents |
Urban (total) POIs | P | 100 | 1–1000 POIs |
Agent POIs | 10 | 1–50 POIs | |
Max. travel distance | 500 | 100–1000 | |
Quarantine ratio | 0.5 | 0–1 | |
Peak infection ratio | output | 0–1 | |
Total cases ratio | output | 0...>1 |
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Topîrceanu, A. A Spatial Agent-Based Model for Studying the Effect of Human Mobility Patterns on Epidemic Outbreaks in Urban Areas. Mathematics 2024, 12, 2765. https://doi.org/10.3390/math12172765
Topîrceanu A. A Spatial Agent-Based Model for Studying the Effect of Human Mobility Patterns on Epidemic Outbreaks in Urban Areas. Mathematics. 2024; 12(17):2765. https://doi.org/10.3390/math12172765
Chicago/Turabian StyleTopîrceanu, Alexandru. 2024. "A Spatial Agent-Based Model for Studying the Effect of Human Mobility Patterns on Epidemic Outbreaks in Urban Areas" Mathematics 12, no. 17: 2765. https://doi.org/10.3390/math12172765