  Agent-based model (ABM) has been widely used to study infectious disease
transmission by simulating behaviors and interactions of autonomous individuals
called agents. In the ABM, agent states, for example infected or susceptible,
are assigned according to a set of simple rules, and a complex dynamics of
disease transmission is described by the collective states of agents over time.
Despite the flexibility in real-world modeling, ABMs have received less
attention by statisticians because of the intractable likelihood functions
which lead to difficulty in estimating parameters and quantifying uncertainty
around model outputs. To overcome this limitation, we propose to treat the
entire system as a Hidden Markov Model and develop the ABM for infectious
disease transmission within the Bayesian framework. The hidden states in the
model are represented by individual agent's states over time. We estimate the
hidden states and the parameters associated with the model by applying particle
Markov Chain Monte Carlo algorithm. Performance of the approach for parameter
recovery and prediction along with sensitivity to prior assumptions are
evaluated under various simulation conditions. Finally, we apply the proposed
approach to the study of COVID-19 outbreak on Diamond Princess cruise ship and
examine the differences in transmission by key demographic characteristics,
while considering different network structures and the limitations of COVID-19
testing in the cruise.
