Model Analysis

Theoretical Basis

Our Agent-Based Model (ABM) is a simulation based on a research titled "Analyzing the dynamics of COVID-19 transmission in select regions of the Philippines: A modeling approach to assess the impact of various tiers of community quarantines" by Mata et. al. Their study introduced a modified Susceptible-Exposed-Infectious-Recovered (SEIR) compartmental model. This model was specifically made to analyze the unique transmission patterns in the Philippines while accounting for regional differences in population density and government interventions.

A key feature of this theoretical framework is the division of the "Infectious" state into two distinct sub-compartments: Reported (Ir) and Unreported (Iu). This modification is crucial because many cases remained undetected due to asymptomatic carriers or limited testing capabilities in the local area during the pandemic.

The movement between these states is governed by the following system of differential equations: 

Each differential equation represents the rate of change for a specific population group over time:

• The 1st equation in Figure 1, Susceptible differential equation, calculates how quickly healthy individuals move to "Exposed" state when on contact with both Reported and Unreported infected agents 

• The 2nd equation, Exposed differential equation, represents those who have contracted the virus but are not yet infectious, in where they eventually transition out based on the latency rate

• The 3rd and 4th equation, Reported and Unreported infected differential equation,  describe the "infectious" population. They are split based on the reporting ratio, determining which agents are detected by the system or are hidden carriers

• Lastly, the 5th and 6th equation, Recovered and Deceased differential equation, represents the final stages. Agents move here from the infectious part based on the recovery rate or death rate, basically "removing" them from the simulation.

Model Assumptions

To ensure these differential equations will accurately reflect the intended dynamics, the following assumptions are used:

• It is assumed that every individual within a region has an equal probability of coming into contact with others. (Homogeneous Mixing)

• Individuals who transition to the Recovered state are assumed to be permanently immune and cannot return to the Susceptible pool. (No Reinfection)

• The model assumes a fixed population at the start of a quarantine period. While the total number can decrease due to disease-related fatalities, there are no births, natural deaths, or outside migrations. (Closed Population)

• Transmission and death rates are assumed to be piecewise constant, meaning the rules of the virus remain static during a specific quarantine tier and only shift when a new policy period (ex. moving from ECQ to GCQ) is implemented.

• The model assumes a uniform demographic profile. Factors such as age, pre-existing health conditions, or occupation are not factored into an individual agent's susceptibility, recovery, or mortality rates.

• The simulation space does not account for specific geographic clustering such as households, hospitals, or workplaces, relying instead on random walks to simulate community interaction.

Explanation of Constants used in the Model

The following constants define the "rules" of the virus and the effectiveness of health interventions derived from real-world data in the National Capital Region (NCR), Davao City, and Baguio City:

• Transmission Rate (βi), represents the number of people an infected individual can transmit the virus to per day.

• Latency Rate (αi), the rate at which exposed individuals become infectious, with its reciprocal (1/α) being the incubation period.

• Reporting Ratio (ρi), the proportion of infectious cases officially reported and determines if an agent is identified as reported or a hidden carrier.

• Recovery Rate (γi), the daily probability that an infected agent moves to the recovered state.

• Death Rate (μi), the rate at which infected individuals pass away.

• Multiplicative Factor (σi), accounts for the increased transmissibility of unreported cases because these individuals are not isolated and remain active in the community.

• Interacting Population (g01), the maximum percentage of the population allowed to interact under specific quarantine protocols like ECQ/GCQ.