Mob-Cov is a stochastic, spatially explicit Agent-Based Model (ABM) developed to analyze COVID-19 transmission under hierarchical geographical mobility patterns. The model represents human movement through nested spatial containers—ranging from rooms and buildings to cities and countries—capturing how multiscale mobility structures shape epidemic diffusion. By embedding stochastic infection processes within realistic mobility hierarchies, Mob-Cov provides a powerful framework for assessing regional containment, border effects, and the feasibility of achieving a stable “zero-COVID” state.
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🧱 Compartmental Structure and Flow
Mob-Cov adopts a bottom-up modeling philosophy, where epidemic dynamics emerge from individual-level interactions constrained by geography and mobility rules.
Individual Disease States (Agent Level)
Each agent occupies a disease state consistent with a reduced SIR-type structure.
• Healthy (Susceptible): Individuals not currently infected but at risk upon contact with infectious agents in shared locations.
• Infected: Individuals capable of transmitting infection to nearby agents within the same local container.
• Recovered/Removed: After an infection duration, agents transition back to a non-infectious state, effectively removed from transmission.
Hierarchical Geographical Structure
Physical space is represented as a hierarchy of nested containers with L levels.
• Lower levels correspond to fine-scale spaces (rooms, workplaces).
• Higher levels represent broader regions (districts, cities, countries).
Agents are always located within exactly one container at each level.
Mobility Flow
At each time step, agents probabilistically decide whether to move. If movement occurs, the destination is selected through a hierarchical process: first choosing a spatial level, then selecting a container within that level. This structure reproduces realistic short-range frequent travel and rare long-distance movements.
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📐 Mathematical Formulation (Stochastic Mobility–Infection System)
Mob-Cov does not rely on a single global ODE system. Instead, epidemic dynamics arise from stochastic transition rules. However, the expected behavior of agents can be summarized mathematically.
Hierarchical Movement Probability
The probability that an agent moves from location j to k is defined as:
P(j → k) = P_lv(l) × ∏(i ≤ l) P_i(k_i)
where l is the selected hierarchical level.
The probability of selecting level l follows an exponential decay:
P_lv(l) = exp(−d · l), for l = 1, … , L
This reflects that movements across higher-level regions are less frequent.
Container selection within each level follows a long-tailed distribution:
P_i(k) = k^(−(c₀ + c₁ · i)), for i = 1, … , l
This allows occasional long-distance movements while preserving local clustering.
Infection Probability within Local Containers
If a healthy agent j is colocated with k infected agents within a level-2 container, the probability of infection is:
P_j = 1 − ∏(i = 1 to k) (1 − P_ij)
where P_ij is the per-contact infection probability.
This formulation links epidemic risk directly to local crowding and mobility-induced contact heterogeneity.
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🔢 Table 1. Parameter Definitions
| Parameter | Definition |
|---|---|
| P_m | Probability that an agent initiates a movement event |
| r_lm | Fraction of low-mobility population |
| P_ij | Probability of infection upon contact with an infected agent |
| T_inf | Duration of infectiousness before recovery |
| c₁ | Exponent controlling decay of long-range movement |
| d | Exponential decay parameter for inter-level travel |
| L | Number of hierarchical spatial levels |
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📊 Table 2. Typical Parameter Ranges (General Viral Disease Context)
| Parameter | Typical Range | Interpretation |
|---|---|---|
| P_m | 0.2 – 0.4 | Daily probability of movement for general population |
| P_m (low mobility) | ≈ 0.03 | Restricted movement subgroup |
| P_ij | 0.02 – 0.30 | Low- to high-risk contact transmission |
| T_inf | 7 – 14 days | Typical viral infectious period |
| c₁ | 0.25 – 0.40 | Controls local crowding vs. long trips |
| d | 0.5 – 1.5 | Inverse mean travel distance across hierarchy |
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🌍 Applicability and Limitations
Applicability
Mob-Cov is particularly well suited for respiratory viral diseases such as COVID-19, where transmission is dominated by close contact and mobility patterns. The model excels in multiscale forecasting, linking individual movements to regional and national epidemic outcomes. It is especially useful for evaluating mobility restrictions, border controls, and hierarchical containment strategies.
Policy and Intervention Analysis
The hierarchical container structure enables systematic testing of travel limitations at different spatial scales. The model can identify conditions under which epidemic extinction or sustained low prevalence (“zero-COVID”) becomes stable.
Strengths
Mob-Cov generates realistic mobility patterns without assuming random mixing or static networks. The coupling of stochastic movement with local infection processes captures emergent clustering, superspreading conditions, and regional heterogeneity.
Limitations
As an ABM, Mob-Cov is computationally intensive for large populations. The disease representation is intentionally simplified, relying on a reduced Healthy–Infected–Recovered structure rather than full SEIR detail. Mobility parameters governing hierarchical travel (such as c₁ and d) require high-resolution mobility or GPS data for reliable calibration, which may limit generalizability.
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📚 Selected References
Chen, K., Jiang, X., Li, Y., and Zhou, R. A stochastic agent-based model to evaluate COVID-19 transmission influenced by human mobility.
Alessandretti, L., Aslak, U., and Lehmann, S. The scales of human mobility.
Oshinubi, K., Chen, Y., Doerry, E., et al. A systematic review of spatial epidemiological modeling approaches applied during the COVID-19 pandemic.
Kerr, C. C., Stuart, R. M., Mistry, D., et al. Covasim: An agent-based model of COVID-19 dynamics and interventions.