  We study the collective dynamics of a multi-particle system with three
epidemic states as an internal state. For the collective modeling of active
particle system, we adopt modeling spirits from the swarmalator model and the
SIR epidemic model for the temporal evolution of particles' position and
internal states. Under suitable assumptions on system parameters and
non-collision property of initial spatial configuration, we show that the
proposed model does not admit finite-time collisions so that the standard
Cauchy-Lipschitz theory can be applied for the global well-posedness. For the
relaxation dynamics, we provide several sufficient frameworks leading to the
relaxation dynamics of the proposed model. The proposed sufficient frameworks
are formulated in terms of system parameters and initial configuration. Under
such sufficient frameworks, we show that the state configuration relaxes to the
fixed constant configuration via the exponentially perturbed gradient system
and explicit dynamics of the SIR model. We present explicit lower and upper
bounds for the minimal and maximal relative distances.
