Inference in stochastic reaction-network models, such as the susceptible-exposed-infectious-recovered (SEIR) epidemic model, is crucial for understanding the dynamics of interacting systems in epidemiology, ecology, and systems biology. These models are typically represented as Markov jump processes (MJPs), with discrete, noisy observations and intractable likelihoods. Particle Markov chain Monte Carlo (PMCMC) offers a natural mechanism for inference on these hidden Markov models, but, even in moderate dimensional state spaces, particle degeneracy typically leads to poor mixing of the PMCMC algorithm. This paper focuses on improving the efficiency of particle Gibbs for inference on reaction networks by addressing the degeneracy problem. Building on recent work on the exchangeable particle Gibbs (xPG) sampler for diffusions, this paper develops a novel version of xPG tailored to discrete-state-space reaction networks, where randomness is driven by Poisson processes rather than Brownian motion. We focus on the $τ$-leap discretisation of the MJPs. The proposed method retains the exchangeability framework of xPG while adapting it to the structural and computational challenges specific to reaction networks. The new method is applied to several examples, including four coupled SEIR models, where it substantially improves mixing efficiency compared with standard particle Gibbs. In this example, xPG improves sample efficiency by more than an order of magnitude relative to standard particle Gibbs, making inference feasible in hours rather than weeks. As part of our tuning strategy, we provide a mechanism for tuning the number of particles that is applicable more generally, to any particle Gibbs algorithm.

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