A Combined Simulation Framework for Disease Spread Simulation

During the pandemic, prior to the availability of pharmaceutical interventions such as vaccines and treatments, non-pharmaceutical interventions (NPIs) were the primary methods employed to mitigate the spread of infectious diseases. We observed that the efficacy of NPIs is crucial in controlling the magnitude of spread and preventing the collapse of medical systems. Among the various estimation tools for pandemic spread, compartmental modeling and agent-based simulation are identified as the two most efficient and accurate methodologies. However, both methods have limitations to be fully employed in controlling the spread of pandemic.

To address these gaps, we propose a simulation framework that integrates the advantages of compartmental modeling and agent-based simulation methods. This framework comprises three primary modules: (1) generation of pseudo-populations, (2) population movement, and (3) infection spread. Firstly, it is essential to develop a model for generating pseudo-populations and algorithms for simulating population movement. An agent-based modeling approach is utilized to capture the individual characteristics of the population and the impact of population movement, while an extended SEIRD (susceptible, exposed, infected, recovered, death) compartmental model is employed to stochastically simulate infection spread based on the state changes of individuals.

The proposed framework was implemented to analyze outbreaks in Seoul, Republic of Korea, thus validating its effectiveness. Also comparative study on efficacy of NPIs between Australia and Korea is provided.

Table 1 NPI comparison South Korea and Australia

The main difference among NPIs is the partial lockdown in Australia. The scenarios we developed to compare the efficacy of NPIs is listed below. Mainly, we tried the partial lockdown in Korea.

Figure 1 Relationship between government policy and population movement

In Republic of Korea, mask wearing and isolation were consistently used to control the spread of COVID-19. The social distancing measures applied changed depending on the spread situation. Therefore, social distancing measures can be a control measure to reduce the contact rate. Depending on the level of social distancing measures, changes in population activities within a region and movement between regions occurred, resulting in a decrease in R and suppression of spread. Figure 1 shows the changes in population movements within each region of Seoul and the level of social distancing measures from March 2020 to February 2021. As shown in Figure 1, population movement partially reflects the effectiveness of social distancing policies. The y-axis is the movement rate and the x-axis is representing the date. If population movement is used in infection spreading models, it can partly reflect the impact of social distancing. Thus, population movement shows a strong correlation with disease spread. To conduct an effective analysis of disease spread, changes in contact rates due to population movement should be reflected in the model. This study proposes a framework that includes population movement models that reflect these factors. We propose a simulation framework that combines the advantages of compartmental and agent-based models while compensating for their respective limitations.

Figure 2 Proposed simulation framework for disease spread analysis

Figure 2 shows the simulation framework of the proposed infectious disease spread model consisting of population generation, mobility, and infection. The population generation and mobility components define each individual population as an agent with individual attributes and implements their movement process using a probability distribution. This model reflects the movement of the population, which has a significant impact on the spread of infectious diseases and utilises agent-based modelling concepts to reflect regional infection probability changes. The population mobility model is essential to capture the changing infection environment of each individual population and considers population movement using probability distributions according to age and sex. The infection model is based on representative SEIR compartmental models that can reflect various characteristics of infectious diseases. A new model that subdivides compartments based on infection status, symptom manifestation, and isolation status is defined and implemented through a Monte Carlo simulation. The infection model reflects changes in the infection environment of each individual owing to population movement and uses an algorithm to determine the infection and status changes of each population in the corresponding region based on the individual infection rate at that time. To validate the simulation framework proposed in this study, the number of confirmed cases during the second and third waves ofCOVID-19 in Seoul, Republic of Korea, in 2020 was utilised. The number of infections shifted alongside changes in government policy, though these effects appeared only after a noticeable lag as shown in Figure 3.

Figure 3 Cases confirmed during waves

Figure 4 Shows the comparison on confirmed case between Korea and Australia during the waves.

Figure 4 Comparison of infection spread in big waves based on the level of NPIs changing

NPIs (Non Pharmaceutical Interventions) can increase public fatigue depending on their type and intensity. However, prior to the development of pharmaceuticals (vaccines or   treatments), they are the only countermeasures available to determine the extent of infection spread; therefore, applying them appropriately is crucial.

• South Korea: In the early stages ofthe influx, the country managed to control the number of infected individuals through intensive epidemiological investigations. However, by implementing "soft" NPIs based on social distancing, they were unable to effectively suppress mass infection clusters. This resulted in a pattern where cases rose rapidly toward a peak, and waves failed to end completely, leading directly into new subsequent waves.

• Australia: As the spread intensified, Australia implemented "strict" NPIs based on powerful lockdown policies. This approach slowed the rate of spread leading up to the peak and ultimately succeeded in completely terminating the wave of infection.

The disease transmission module we adopted in this study is shown in Figure 5. At each simulation time step, every individual determines whether to transition to the next state based on the transition probabilities between states and the probability distribution of state duration. The contact probability with an infected person, is determined by the population movement and population size in each region, while other parameters are determined by the characteristics of the infectious disease and various environmental factors.

Figure 5 Disease Transmission Module

The scenario we compared is explained is in Figure 6. The scenario, where some of Australia’s strict NPIs were modified into a form applicable to the proposed model, is applied to South Korea's 'big wave' situation. At the point when infections begin to rise after the simulation starts, all the following NPIs are applied simultaneously.

Figure 6 Scenario adopted in simulation study

Discussion on Simulation Results