A multi-scale agent-based model of infectious disease transmission to assess the impact of vaccination and non-pharmaceutical interventions: The COVID-19 case

Abstract

Mathematical and computational models are useful tools for virtual policy experiments on infectious disease control. Most models fail to provide flexible and rapid simulation of various epidemic scenarios for policy assessment. This paper establishes a multi-scale agent-based model to investigate the infectious disease propagation between cities and within a city using the knowledge from person-to-person transmission. In the model, the contact and infection of individuals at the micro scale where an agent represents a person provide insights for the interactions of agents at the meso scale where an agent refers to hundreds of individuals. Four cities with frequent population movements in China are taken as an example and actual data on traffic patterns and demographic parameters are adopted. The scenarios for dynamic propagation of infectious disease with no external measures are compared versus the scenarios with vaccination and non-pharmaceutical interventions. The model predicts that the peak of infections will decline by 67.37% with 80% vaccination rate, compared to a drop of 89.56% when isolation and quarantine measures are also in place. The results highlight the importance of controlling the source of infection by isolation and quarantine throughout the epidemic. We also study the effect when cities implement inconsistent public health interventions, which is common in practical situations. Based on our results, the model can be applied to COVID-19 and other infectious diseases according to the various needs of government agencies.

Keywords: Agent-based model; Epidemic simulation; Policy assessment; Public health; Transmission risk.

Fig. 1

Schematic diagram of MSABM.

Fig. 2

Framework of multi-scale agent-based infectious disease transmission.

Fig. 3

Mobility behavior. For agent ${\mathit{a}}_{ij}^g\left(t\right)$, $t$ denotes time step; $i$ indicates the type of population including floating population ($i=1$), permanent working residents ($i=2$), and non-working population ($i=3$); $g$ represents the city to which the agent belongs($g=\{1,2\}$ in the case shown in this figure).

Algorithm 1

The micro-scale simulation.

Algorithm 2

The meso-scale simulation.

Fig. 4

Snapshots of meso-scale simulation using the MSABM model. $\epsilon$ denotes the infection proportion of an agent.

Fig. 5

The coefficient of linear regression equation under different cases. $v^r$: vaccination rate. $\sigma$: contact rate.

Fig. 6

Variability in the proportion of infected people in four cities with no external intervention on disease propagation.

Fig. 7

Chi-square-like distributions with different values of $\gamma$ that represents the efficiency of isolation and strength of quarantine. The smaller value of $\gamma$ refers to the stricter isolation and quarantine measure.

Fig. 8

Disease propagation with different efficiency of isolation and strength of quarantine measures. A smaller value of $\gamma$ denotes a more timely isolation of infectious individuals and a more extensive quarantine of close contacts.

Fig. 9

The effects of duration of immunity on disease transmission dynamics ($\gamma =0.7$ is assumed in all the cases).

Fig. 10

Infectious disease propagation with different vaccination rate ($\gamma =1$ and $v^e=0.8$ are assumed in all the cases).

Fig. 11

Infectious disease propagation with different values of $\gamma$ when 80% of population has been vaccinated with vaccine efficacy 80%. $\gamma$ represents the strength of isolation and quarantine.

Fig. 12

Effect of the duration of NPIs adoption on infectious disease propagation. NPIs are assumed to be adopted during the first three months (A), the first three months as well as months 5.5 to 6.5 (B), the first four months (C), or all the time (D).

Fig. 13

Infectious disease transmission with coordinated and inconsistent measures. In Case I, the four cities implement coordinated public health interventions. While in Case II, the measures in Hangzhou are not as strict as that in the other three cities.